{"id":42534,"date":"2023-05-15T17:32:01","date_gmt":"2023-05-15T09:32:01","guid":{"rendered":"https:\/\/swarma.org\/?p=42534"},"modified":"2023-05-15T17:32:01","modified_gmt":"2023-05-15T09:32:01","slug":"nature-reviews-physics-%e7%bb%bc%e8%bf%b0%ef%bc%9a%e6%8e%a7%e5%88%b6%e5%85%b7%e6%9c%89%e5%a4%8d%e6%9d%82%e8%8a%82%e7%82%b9%e7%9a%84%e5%a4%8d%e6%9d%82%e7%bd%91%e7%bb%9c","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=42534","title":{"rendered":"Nature Reviews Physics \u7efc\u8ff0\uff1a\u63a7\u5236\u5177\u6709\u590d\u6742\u8282\u70b9\u7684\u590d\u6742\u7f51\u7edc"},"content":{"rendered":"
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Raissa M. D\u2019Souza, Mario di Bernardo & Yang-Yu Liu<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/p>\n

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\u771f\u5b9e\u4e16\u754c\u7684\u7f51\u7edc\u5e38\u542b\u6709\u6570\u767e\u4e07\u4e2a\u5f02\u8d28\u8282\u70b9\uff0c\u8fd9\u4e9b\u8282\u70b9\u6709\u8de8\u65f6\u95f4\u5c3a\u5ea6\u548c\u7a7a\u95f4\u5c3a\u5ea6\u76f8\u4e92\u4f5c\u7528\u3002\u4e3a\u7406\u89e3\u3001\u5efa\u6a21\u548c\u63a7\u5236\u8fd9\u4e9b\u7cfb\u7edf\uff0c\u7edf\u8ba1\u7269\u7406<\/span>\uff08statistical physics\uff09<\/span>\u548c\u63a7\u5236\u7406\u8bba<\/span>\uff08control theory\uff09<\/span>\u7b49\u9886\u57df\u90fd\u63d0\u4f9b\u4e86\u4e0d\u540c\u7684\u89c6\u89d2\u3002\u8fd9\u4e9b\u9886\u57df\u4e4b\u95f4\u66f4\u591a\u7684\u4ea4\u4e92\u548c\u65b0\u8303\u5f0f<\/span>\uff08\u5982\u5f02\u8d28\u6027\u548c\u591a\u5c42\u6b21\u8868\u793a\uff09<\/span>\u7684\u96c6\u6210\uff0c\u5bf9\u89e3\u51b3\u73b0\u5b9e\u7cfb\u7edf\u6765\u8bf4\u662f\u5fc5\u8981\u7684\u3002\u7814\u7a76\u8005\u4eec\u53ef\u4ee5\u7ed3\u5408\u7edf\u8ba1\u7269\u7406\u62d3\u5c55\u6a21\u578b\u3001\u6574\u5408<\/span>\uff08\u6b63\u8d1f\uff09<\/span>\u53cd\u9988\u7684\u6982\u5ff5\u548c\u62d3\u5c55\u63a7\u5236\u7406\u8bba\u516c\u5f0f\uff0c\u4ece\u4ecb\u89c2\u89d2\u5ea6\u8fdb\u884c\u5206\u6790<\/span>\uff08mesoscopic analysis\uff09<\/span>\u4ee5\u8ba1\u7b97\u6574\u4f53\u81ea\u7531\u5ea6\u7684\u5e73\u5747\u503c\u3002\u540c\u65f6\uff0c\u8fd8\u9700\u8981\u6574\u5408\u7406\u8bba\u6a21\u578b\u3001\u673a\u5668\u5b66\u4e60\u548c\u6570\u636e\u9a71\u52a8\u7b49\u63a7\u5236\u65b9\u6cd5\u3002\u672c\u7efc\u8ff0\u56de\u987e\u4e86\u6700\u65b0\u7684\u8fdb\u5c55\uff0c\u5e76\u53d1\u73b0\u4e86\u6709\u52a9\u4e8e\u7406\u89e3\u548c\u63a7\u5236\u771f\u5b9e\u7cfb\u7edf<\/span>\uff08\u4ece\u632f\u8361\u5668\u7f51\u7edc\u548c\u793e\u4f1a\u7f51\u7edc\u5230\u751f\u7269\u548c\u6280\u672f\u7f51\u7edc\uff09<\/span>\u7684\u65b0\u5951\u673a\u3002<\/span><\/section>\n

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\u76f8\u53cd\uff0c\u4f20\u7edf\u7684\u63a7\u5236\u7406\u8bba<\/strong>\u9010\u6e10\u6f14\u53d8\u4e3a\u52a8\u529b\u7cfb\u7edf\u548c\u5de5\u7a0b\u7684\u4e00\u4e2a\u5206\u652f\uff0c\u81f4\u529b\u4e8e\u6309\u7167\u9884\u671f\u81ea\u52a8\u5730\u63a7\u5236\u7cfb\u7edf\u6216\u8bbe\u5907\uff0c\u4f7f\u5176\u80fd\u591f\u5ffd\u7565\u566a\u58f0\u3001\u5ef6\u8fdf\u548c\u6270\u52a8\u3002\u8fd9\u6d89\u53ca\u5230\u8bbe\u8ba1\u53cd\u9988\u7b56\u7565\uff0c\u5728\u7406\u60f3\u60c5\u51b5\u4e0b\u5e0c\u671b\u901a\u8fc7\u5f71\u54cd\u76f8\u5bf9\u8f83\u5c11\u7684\u5fae\u89c2\u81ea\u7531\u5ea6\uff0c\u5f15\u5bfc\u76ee\u6807\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u884c\u4e3a\u4e0e\u671f\u671b\u6f14\u53d8\u540c\u6b65\u3002<\/span><\/section>\n
\u7136\u800c\u73b0\u4ee3\u7f51\u7edc\u89c4\u6a21\u5de8\u5927<\/span>\uff08\u5982\u4e92\u8054\u7f51\u6216\u4eba\u7c7b\u4ea4\u4e92\u7f51\u7edc\uff09<\/span>\uff0c\u4eba\u4eec\u65e0\u6cd5\u5b8c\u5168\u4e86\u89e3\u6bcf\u4e00\u4e2a\u81ea\u7531\u5ea6\u53ca\u5176\u76f8\u4e92\u8054\u7cfb\uff0c\u66f4\u4e0d\u7528\u8bf4\u5bf9\u6240\u6709\u81ea\u7531\u5ea6\u8fdb\u884c\u63a7\u5236\u3002\u56e0\u6b64\uff0c\u4e9f\u9700\u67b6\u8d77\u5b8f\u89c2\u548c\u5fae\u89c2\u7684\u6865\u6881\uff0c\u5efa\u7acb\u5e73\u8861\u548c\u52a8\u529b\u5b66\u65b9\u6cd5\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u4ee5\u63a7\u5236\u5177\u6709\u590d\u6742\u8282\u70b9\u7684\u590d\u6742\u7f51\u7edc<\/strong><\/span>\uff08complex networks with complex nodes\uff09<\/span>\u3002\u672c\u6587\u5f3a\u8c03\u201c\u590d\u6742\u201d\u8fd9\u4e00\u5f62\u5bb9\u8bcd\uff0c\u4e0e\u590d\u6742\u7cfb\u7edf<\/span>\uff08complex systems\uff09<\/span>\u610f\u4e49\u4e0a\u7684\u201c\u590d\u6742\u201d\u76f8\u540c\uff0c\u8fd9\u610f\u5473\u7740\u6b64\u7cfb\u7edf\u662f\u5177\u6709\u975e\u7ebf\u6027\u884c\u4e3a\u7684\u6f5c\u5728\u5f02\u6784\u7cfb\u7edf\u3002\u5177\u4f53\u800c\u8a00\uff0c\u201c\u590d\u6742\u7f51\u7edc\u201d\u662f\u6307\u8282\u70b9\u4e4b\u95f4\u7684\u8fde\u63a5\u6a21\u5f0f\uff0c\u201c\u590d\u6742\u8282\u70b9\u201d\u662f\u6307\u5355\u4e2a\u8282\u70b9\u6709\u975e\u7ebf\u6027\u884c\u4e3a<\/strong>\u3002<\/span><\/section>\n

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\u6700\u540e\uff0c\u4f5c\u8005\u603b\u7ed3\u4e86\u4e00\u5957\u7814\u7a76\u6307\u5357\uff0c\u4ee5\u4fc3\u8fdb\u672a\u6765\u8de8\u5b66\u79d1\u53d1\u5c55\u3002<\/span><\/section>\n
\u5728\u6b64\u660e\u786e\u8d2f\u7a7f\u5168\u6587\u7684\u4e24\u4e2a\u63a7\u5236\u7406\u8bba\u4e2d\u7684\u57fa\u672c\u6982\u5ff5\uff1a\u53ef\u63a7\u6027<\/span>\uff08controllability\uff09<\/span>\u548c\u53ef\u89c2\u6d4b\u6027<\/span>\uff08observability\uff09<\/span>\u3002<\/span><\/section>\n
\u53ef\u63a7\u6027<\/strong>\u662f\u6307\u63a7\u5236\u8f93\u5165\u7684\u5b58\u5728\u6027\uff0c\u63cf\u8ff0\u4e86\u4eba\u4eec\u5728\u6709\u9650\u65f6\u95f4\u5185\u901a\u8fc7\u5408\u9002\u7684\u8f93\u5165\u9009\u62e9\uff0c\u5f15\u5bfc\u52a8\u529b\u7cfb\u7edf\u4ece\u4efb\u4f55\u521d\u59cb\u72b6\u6001\u5230\u4efb\u4f55\u671f\u671b\u7684\u6700\u7ec8\u72b6\u6001\u7684\u80fd\u529b\u3002<\/span><\/section>\n
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2.1 \u7edf\u8ba1\u7269\u7406\u4e0e\u7ed3\u6784\u53ef\u63a7\u6027<\/strong><\/span><\/section>\n
1990\u5e74\u4ee3\u540e\u671f\uff0c\u968f\u7740\u4e92\u8054\u7f51\u548c\u4e07\u7ef4\u7f51\u8fc5\u901f\u53d1\u5c55\u3001\u57fa\u56e0\u7ec4\u6570\u636e\u548c\u57fa\u7840\u8bbe\u65bd\u7cfb\u7edf\u9010\u6b65\u5b8c\u5584\u3001\u7ecf\u6d4e\u5168\u7403\u5316\u52bf\u4e0d\u53ef\u6321\uff0c\u7f51\u7edc\u79d1\u5b66[1]\u5e94\u8fd0\u800c\u751f\u3002\u7edf\u8ba1\u7269\u7406\u7684\u5de5\u5177<\/span>\uff08\u5982\uff1a\u968f\u673a\u56fe\u6a21\u578b\u3001\u751f\u6210\u51fd\u6570\u548c\u901f\u7387\u65b9\u7a0b\u7b49\uff09<\/span>\u6709\u52a9\u4e8e\u4eba\u4eec\u66f4\u597d\u5730\u7406\u89e3\u590d\u6742\u7f51\u7edc\u7684\u6027\u8d28\u548c\u884c\u4e3a\u2014\u2014\u901a\u5e38\u88ab\u63cf\u8ff0\u4e3a\u5177\u6709\u5e7f\u6cdb\u89c4\u6a21\u3001\u8de8\u8d8a\u51e0\u4e2a\u6570\u91cf\u7ea7\u7684\u6f5c\u5728\u5ea6\u5206\u5e03\u3002\u7f51\u7edc\u7ed3\u6784\u5e26\u6765\u7684\u5173\u952e\u5f71\u54cd\u662f\u5bf9\u968f\u673a\u5e72\u6270\u9c81\u68d2\u3001\u5bf9\u9488\u5bf9\u653b\u51fb\u8106\u5f31\u4ee5\u53ca\u6f5c\u5728\u7684\u7f3a\u4e4f\u4f20\u67d3\u9608\u503c\u3002\u9664\u4e86\u5ea6\u5206\u5e03\uff0c\u7f51\u7edc\u7684\u663e\u8457\u7ed3\u6784\u7279\u5f81\u5305\u62ec\u5c0f\u4e16\u754c\u6027\u3001\u6a21\u5757\u6027\u548c\u4e09\u5143\u95ed\u5305[2]<\/span>\uff08\u56fe1\uff09<\/span>\u3002<\/span><\/section>\n

<\/p>\n

\u56fe1. \u590d\u6742\u7f51\u7edc\u4e2d\u7684\u5e38\u89c1\u6307\u6807\u3002a.\u8282\u70b9\u5ea6\uff08k\uff09\u5728\u8f83\u5927\u5c3a\u5ea6\u4e0a\u7684\u5206\u5e03\uff08P\uff09\uff1bb.\u96c6\u805a\u7cfb\u6570\uff1bc.\u793e\u533a\u7ed3\u6784\uff1a\u8282\u70b9\u53ef\u4ee5\u88ab\u5206\u914d\u5230\u7ec4\u5185\u7684\u8fde\u63a5\u5bc6\u5ea6\u9ad8\u4e8e\u7ec4\u4e4b\u95f4\u7684\u8fde\u63a5\u5bc6\u5ea6\u7684\u7ec4\u3002d.\u5c0f\u4e16\u754c\u5c5e\u6027\uff1a\u5927\u591a\u6570\u8282\u70b9\u4e0d\u76f4\u63a5\u76f8\u8fde\uff0c\u800c\u662f\u901a\u8fc7\u7f51\u7edc\u4e0a\u7684\u77ed\u8def\u5f84\u94fe\u63a5\u3002e.\u76f8\u53d8\uff0c\u4f8b\u5982\u6e17\u6d41\u76f8\u53d8\uff0c\u5176\u4e2d\u7f51\u7edc\u7684\u6700\u5927\u8fde\u901a\u7247\u5927\u5c0fS\u968f\u7740\u5e73\u5747\u5ea6\u7684\u589e\u52a0\u800c\u8868\u73b0\u51fa\u76f8\u53d8\u3002<\/span><\/p>\n

2011\u5e74\uff0c\u7edf\u8ba1\u7269\u7406\u4e0e\u590d\u6742\u7f51\u7edc\u63a7\u5236\u4e4b\u95f4\u5efa\u7acb\u4e86\u91cd\u8981\u8054\u7cfb\uff0c\u4ee5\u5206\u6790\u7814\u7a76\u5177\u6709\u7ebf\u6027\u52a8\u529b\u5b66\u548c\u4efb\u610f\u5ea6\u5206\u5e03\u7684\u7f51\u7edc\u7cfb\u7efc<\/span>\uff08network ensemble\uff09<\/span>\u7684\u53ef\u63a7\u6027[3]\u3002\u8fd9\u79cd\u8054\u7cfb\u5efa\u7acb\u5728\u7ed3\u6784\u63a7\u5236\u7684\u6846\u67b6\u4e0a\uff0c20\u4e16\u7eaa70\u5e74\u4ee3\u7684\u4e00\u7bc7\u6587\u7ae0[4]\uff0c\u901a\u8fc7\u56fe\u8bba\u65b9\u6cd5\u89e3\u51b3\u4e86\u7ebf\u6027\u52a8\u529b\u5b66\u7f51\u7edc\u4e0a\u7684\u53ef\u63a7\u6027\u95ee\u9898\u3002\u95ee\u9898\u5728\u4e8e\uff0c\u5f53\u5e94\u7528\u5728\u7279\u5b9a\u8282\u70b9<\/span>\uff08[3]\u4e2d\u7684\u201c\u9a71\u52a8\u8282\u70b9\u201d(driver nodes)\uff09<\/span>\u65f6\uff0c\u5982\u4f55\u786e\u5b9a\u662f\u5426\u5b58\u5728\u63a7\u5236\u8f93\u5165\u80fd\u5728\u6709\u9650\u65f6\u95f4\u5185\u5f15\u5bfc\u52a8\u529b\u7cfb\u7edf\u4ece\u4efb\u4f55\u521d\u59cb\u72b6\u6001\u5230\u4efb\u4f55\u671f\u671b\u7684\u6700\u7ec8\u72b6\u6001\uff0c\u5373\u4f7f\u5176\u53ef\u63a7\u3002\u89e3\u51b3\u6b64\u95ee\u9898\u7684\u5173\u952e\u7075\u611f\u6765\u81ea\u4e8e\u5c06\u8bc6\u522b\u6700\u5c0f\u9a71\u52a8\u8282\u70b9\u96c6\u7684\u95ee\u9898\u6620\u5c04\u5230\u7f51\u7edc\u4e0a\u7684\u6700\u5927\u5339\u914d\u95ee\u9898<\/span>\uff08\u56fe2\uff09<\/span>\uff0c\u7136\u540e\u4f7f\u7528\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u7a7a\u8154\u65b9\u6cd5<\/span>\uff08\u5728\u201c\u7edf\u8ba1\u7269\u7406\u65b9\u6cd5\u201d\u4e00\u8282\u4e2d\u6df1\u5165\u8ba8\u8bba\uff09<\/span>\u8fdb\u884c\u5206\u6790\u89e3\u51b3\u3002<\/span><\/section>\n

<\/p>\n

\u56fe2. \u7ed3\u6784\u63a7\u5236\u6846\u67b6\u4e2d\u7684\u9a71\u52a8\u8282\u70b9\u7684\u8bc6\u522b\u548c\u76f8\u53d8\u3002<\/span><\/section>\n
a. \u7ebf\u6027\u8282\u70b9\u52a8\u529b\u5b66\uff08\u72b6\u6001\u53d8\u91cf<\/sub>\uff09\u6709\u5411\u7f51\u7edc\u4e0a\u6700\u5927\u5339\u914d\u95ee\u9898\u7684\u6c42\u89e3\u3002\u80fd\u591f\u8bc6\u522b\u6700\u5c0f\u9a71\u52a8\u8282\u70b9\u96c6\uff0c\u4fdd\u8bc1\u6574\u4e2a\u7cfb\u7edf\u7684\u7ed3\u6784\u53ef\u63a7\u6027\u3002\u5bf9\u4e8e\u4e00\u822c\u6709\u5411\u7f51\u7edc\uff08\u5982\u56fe\uff09\uff0c\u53ef\u80fd\u6709\u591a\u4e2a\u6700\u5927\u5339\u914d\uff08\u7ea2\u8272\u8fde\u8fb9\u96c6\uff09\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u8bc6\u522b\u591a\u4e2a\u6700\u5c0f\u9a71\u52a8\u8282\u70b9\u96c6\u5408\uff08\u84dd\u8272\u8282\u70b9\uff09\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u9a71\u52a8\u5668\u8282\u70b9\uff0c\u5fc5\u987b\u65bd\u52a0\u786e\u4fdd\u7ed3\u6784\u53ef\u63a7\u6027\u6240\u5fc5\u9700\u7684\u552f\u4e00\u63a7\u5236\u4fe1\u53f7\uff08ui<\/sub>\uff0c\u84dd\u8272\u6ce2\u6d6a\u5f62\u7bad\u5934\uff09\u3002<\/span><\/section>\n
b. \u63a7\u5236\u9c81\u68d2\u6027\uff08robustness\uff09\u548c\u6838\u5fc3\u6e17\u6d41\uff08core percolation\uff09\u3002\u91cf\u5316\u4e0d\u53ef\u907f\u514d\u7684\u8fb9\u6545\u969c\u4e0b\u63a7\u5236\u7684\u9c81\u68d2\u6027\uff0c\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u8fde\u8fb9l\u7684\u7c7b\u578b\uff1a<\/span><\/section>\n
1\uff09\u4e34\u754c\uff08critical\uff0clc\uff09<\/strong>\uff0c\u82e5\u5176\u4e0d\u5b58\u5728\uff0c\u5219\u5fc5\u987b\u589e\u52a0\u9a71\u52a8\u8282\u70b9\u7684\u6570\u91cf\u4ee5\u4fdd\u6301\u5bf9\u7cfb\u7edf\u7684\u5b8c\u5168\u63a7\u5236\u3002\u6362\u53e5\u8bdd\u8bf4\uff0clc\u662f\u7f51\u7edc\u7684\u6240\u6709\u6700\u5927\u5339\u914d\u7684\u4e00\u90e8\u5206\u3002<\/span><\/section>\n
2\uff09\u5197\u4f59\uff08redundant\uff0clr\uff09<\/strong>\uff0c\u79fb\u9664\u6b64\u7c7b\u8fb9\u4e0d\u5f71\u54cd\u5f53\u524d\u7684\u9a71\u52a8\u8282\u70b9\u96c6\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u4e0d\u5c5e\u4e8e\u4efb\u4f55\u6700\u5927\u5339\u914d\u3002<\/span><\/section>\n
3\uff09\u4e00\u822c\uff08ordinary\uff0clo\uff09<\/strong>\uff0c\u65e2\u975e\u5173\u952e\uff0c\u4e5f\u4e0d\u5197\u4f59\u3002<\/span><\/section>\n
lr\u4f5c\u4e3a\u5e73\u5747\u5ea6\u51fd\u6570\u7684\u975e\u5355\u8c03\u884c\u4e3a\uff08\u4e0a\u534a\u90e8\u5206\uff09\u4e0e\u7f51\u7edc\u4e2d\u7684\u6838\u5fc3\u6e17\u6d41\u8dc3\u8fc1\uff08\u4e0b\u534a\u90e8\u5206\uff09\u5bc6\u5207\u76f8\u5173\uff0c\u5176\u4e2dncore<\/sub>\u662f\u6838\u4e2d\u8282\u70b9\u7684\u6bd4\u4f8b\u3002\u5f53\u4e0d\u540c\u7684\u6700\u5927\u5339\u914d\u7684\u6570\u91cf\u5f00\u59cb\u5448\u6307\u6570\u589e\u52a0\u65f6\uff0c\u53d1\u751f\u6838\u5fc3\u6e17\u6d41\uff0c\u8fd9\u4f7f\u5f97\u5197\u4f59\u8fde\u8fb9\u7684\u6bd4\u4f8b\u4e0b\u964d\u3002<\/span><\/section>\n
\u5bf9\u4e8e\u6709\u5411ER\u968f\u673a\u7f51\u7edc\uff0c\u6838\u5fc3\u6e17\u6d41\u53d1\u751f\u5728\u5e73\u5747\u5ea6=2e\u65f6\uff08\u4e0b\u534a\u90e8\u5206\uff09\u3002\u56fe\u7ecf\u8bb8\u53ef\u6539\u7f16\u81ea\u53c2\u8003\u6587\u732e[3]\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5728\u7ed3\u6784\u63a7\u5236\u4e2d\uff0c\u8fde\u8fb9\u662f\u5426\u5b58\u5728<\/span>\uff08\u5373\u7ed3\u6784\uff09<\/span>\u6bd4\u8fde\u8fb9\u7684\u6743\u91cd\u66f4\u91cd\u8981\u3002\u4f20\u7edf\u4e0a\uff0c\u7ed3\u6784\u63a7\u5236\u6846\u67b6\u5047\u8bbe\u8282\u70b9\u6839\u636e\u7ebf\u6027\u975e\u65f6\u53d8\u52a8\u529b\u5b66\u6f14\u5316\uff1a<\/sub><\/span>\uff08\u6709\u5173\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7684\u8be6\u7ec6\u4fe1\u606f\u548c\u6269\u5c55\uff0c\u8bf7\u53c2\u89c1\u201c\u65b0\u8303\u5f0f\u548c\u5efa\u6a21\u6280\u672f\u201d\u4e00\u8282\uff09<\/span>\u3002\u8fd9\u79cd\u7ebf\u6027\u610f\u5473\u7740\uff1a\u53ef\u4ee5\u7528\u7ebf\u6027\u4ee3\u6570\u7684\u5de5\u5177\u6765\u9610\u660e\u7f51\u7edc\u7ed3\u6784\u548c\u53ef\u63a7\u6027\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u5305\u62ec\u7f51\u7edc\u7ed3\u6784\u4e2d\u7684\u76f8\u53d8\u8fde\u63a5[5\uff0c6]\u3002\u6b64\u5916\uff0c\u8fd8\u5efa\u7acb\u4e86\u53ef\u63a7\u6027\u8f6c\u53d8\u548c\u63a7\u5236\u72b6\u6001\u8f68\u8ff9\u7684\u975e\u5c40\u90e8\u6027\u548c\u63a7\u5236\u8f93\u5165\u7684\u975e\u5c40\u90e8\u6027\u4e4b\u95f4\u7684\u5e73\u8861\u3002<\/span><\/section>\n
\u9664\u4e86\u7ed3\u6784\u63a7\u5236\u4e4b\u5916\uff0c\u8bb8\u591a\u7814\u7a76\u5df2\u7ecf\u6df1\u5165\u7406\u89e3\u4e86\u63a7\u5236\u80fd\u91cf<\/span>\uff08control energy\uff09<\/span>[8]\u3001\u63a7\u5236\u914d\u7f6e\u6587\u4ef6<\/span>\uff08control profiles\uff09\uff08\u57fa\u4e8e\u63a7\u5236\u6d41\u6a21\u5f0f\uff09<\/span>[9]\u548c\u6765\u81ea\u73b0\u5b9e\u4e16\u754c\u7cfb\u7edf\u7684\u7ea6\u675f[10]\u3002\u76f8\u5173\u66f4\u5168\u9762\u7684\u7efc\u8ff0\uff0c\u8bf7\u53c2\u89c1\u53c2\u8003\u6587\u732e[11\uff0c12]\u3002\u7269\u7406\u5b66\u5bb6\u7684\u63a7\u5236\u7406\u8bba\u7efc\u5408\u5165\u95e8\uff0c\u89c1\u53c2\u8003\u6587\u732e13\u3002\u7136\u800c\uff0c\u5982\u4f55\u4ece\u7edf\u8ba1\u7269\u7406\u7684\u65b9\u6cd5\u6269\u5c55\u5230\u52a8\u6001\u3001\u975e\u5e73\u8861\u3001\u975e\u7ebf\u6027\u7684\u7cfb\u7edf\uff1f<\/strong>\u8fd9\u4e2a\u95ee\u9898\u4ecd\u7136\u60ac\u800c\u672a\u51b3\u3002<\/span><\/section>\n

<\/span><\/section>\n
2.2 \u63a7\u5236\u7406\u8bba\u7efc\u8ff0<\/strong><\/span><\/section>\n
\u5728\u7ecf\u5178\u7684\u63a7\u5236\u8303\u5f0f\u4e2d\uff0c\u4eba\u4eec\u611f\u6d4b\u548c\u63a7\u5236\u611f\u5174\u8da3\u7684\u7279\u5b9a\u7cfb\u7edf\u6216\u8bbe\u5907\u7684\u884c\u4e3a\uff0c\u4f8b\u5982\u6c7d\u8f66\u3001\u98de\u673a\u6216\u673a\u5668\u4eba\u3002\u63a7\u5236\u8bbe\u8ba1\u901a\u5e38\u4ece\u611f\u5174\u8da3\u7684\u7cfb\u7edf\u7684\u7ed3\u6784\u548c\u52a8\u529b\u5b66\u7684\u6570\u5b66<\/span>\uff08\u6216\u8ba1\u7b97\uff09<\/span>\u8868\u793a\u5f00\u59cb\uff0c\u5e76\u4e14\u5305\u62ec\u5408\u6210\u53cd\u9988\u63a7\u5236\u7b56\u7565\uff0c\u8be5\u53cd\u9988\u63a7\u5236\u7b56\u7565\u901a\u8fc7\u611f\u77e5\u7cfb\u7edf\u884c\u4e3a\u6765\u8ba1\u7b97\u6240\u9700\u7684\u8f93\u5165\u4ee5\u9a71\u52a8\u7cfb\u7edf\u8fbe\u5230\u671f\u671b\u7684\u72b6\u6001\u3002\u8d1f\u53cd\u9988\u63d0\u4f9b\u4e86\u7a33\u5b9a\u884c\u4e3a\u7684\u80fd\u529b\uff0c\u5373\u4f7f\u5728\u5b58\u5728\u566a\u58f0\u3001\u5ef6\u8fdf\u6216\u6270\u52a8\u7684\u60c5\u51b5\u4e0b\uff0c\u4e5f\u5177\u6709\u4fdd\u8bc1\u9c81\u68d2\u6027\u7684\u4e00\u4e9b\u671f\u671b\u6027\u80fd\u3002\u76f8\u53cd\uff0c\u6b63\u53cd\u9988\u53ef\u4ee5\u7528\u4e8e\u5728\u975e\u7ebf\u6027\u7cfb\u7edf\u4e2d\u5b9e\u73b0\u53cc\u7a33\u5b9a\u6027\u548c\u5206\u53c9\uff0c\u9a71\u52a8\u7cfb\u7edf\u80fd\u8fbe\u5230\u591a\u4e2a\u7a33\u5b9a\u72b6\u6001\u3002<\/span><\/section>\n
\u987a\u7740\u63a7\u5236\u7b56\u7565\u7684\u601d\u60f3\uff0c\u5df2\u7ecf\u53d1\u5c55\u4e86\u8bb8\u591a\u9488\u5bf9\u7ebf\u6027\u548c\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u6570\u5b66\u516c\u5f0f[14]\u3002\u8fd9\u4e9b\u65b9\u6cd5\u4e2d\uff0c\u8bb8\u591a\u662f\u5206\u5e03\u5f0f\u6216\u5206\u6563\u5f0f\u7684\uff0c\u5e76\u4e14\u6709\u4e9b\u4f7f\u7528\u4e86\u590d\u6742\u7684\u975e\u7ebf\u6027\u3001\u81ea\u9002\u5e94\u3001\u8ba1\u7b97\u548c\u65f6\u53d8\u65b9\u6cd5[15]\u3002\u591a\u6570\u65b9\u6cd5\u96c6\u4e2d\u5728\u5355\u4e2a\u7cfb\u7edf\u4e0a\uff0c\u8fd9\u610f\u5473\u7740\u6240\u6709\u76f8\u5173\u7684\u81ea\u7531\u5ea6\u53ca\u5176\u52a8\u529b\u5b66\u548c\u8026\u5408\u90fd\u662f\u5df2\u77e5\u7684<\/span>\uff08\u56fe3a\uff09<\/span>\u3002\u7136\u800c\uff0c\u8fd9\u4e00\u7ecf\u5178\u8303\u5f0f\u9762\u4e34\u7740\u65b0\u5174\u5e94\u7528\u7684\u6311\u6218\u2014\u2014\u5982\u4f55\u5e94\u7528\u5230\u5927\u89c4\u6a21\u3001\u901a\u8fc7\u590d\u6742\u7684\u7f51\u7edc\u5173\u7cfb\u76f8\u4e92\u4f5c\u7528\u7684\u52a8\u529b\u5b66\u7cfb\u7edf\u4e2d<\/strong><\/span>\uff08\u56fe3b\uff09<\/span>\u3002\u5f53\u4e0b\uff0c\u63a7\u5236\u8fd9\u79cd\u590d\u6742\u7684\u7f51\u7edc\u6765\u534f\u8c03\u5b83\u4eec\u7684\u96c6\u4f53\u884c\u4e3a\u662f\u63a7\u5236\u7406\u8bba\u7684\u6838\u5fc3\u95ee\u9898\u548c\u70ed\u95e8\u7814\u7a76\u4e3b\u9898\uff0c\u6700\u65e9\u53ef\u4ee5\u8ffd\u6eaf\u5230\u0160iljak\u572820\u4e16\u7eaa70\u5e74\u4ee3\u540e\u671f\u7684\u5f00\u521b\u6027\u5de5\u4f5c[16]\u3002<\/span><\/section>\n

<\/p>\n

\u56fe3. \u63a7\u5236\u8303\u5f0f\u3002<\/span><\/section>\n
a\uff09\u7ecf\u5178\u53cd\u9988\u63a7\u5236\u8303\u5f0f\u3002\u7cfb\u7edf\u7684\u63a7\u5236\u8f93\u51fay\u88ab\u4f20\u611f\u5668\u6d4b\u91cf\u6216\u4f30\u8ba1\uff1b\u6d4b\u91cf\u8f93\u51fa<\/sub>\u53cd\u9988\u56de\u6bd4\u8f83\u8282\u70b9\uff08\u9ed1\u7070\u8272\uff09\uff0c\u6d4b\u91cf<\/sub>\u548c\u53c2\u8003\u4fe1\u53f7\uff08Ref\uff09\u7684\u5dee\uff1b\u63a7\u5236\u8bef\u5deee\u88ab\u9988\u9001\u5230\u63a7\u5236\u5668\uff0c\u8be5\u63a7\u5236\u5668\u518d\u6839\u636e\u67d0\u4e2a\u63a7\u5236\u89c4\u5219\u8ba1\u7b97\u63a7\u5236\u8f93\u5165\uff08u1<\/sub>\uff09\uff1b\u8ba1\u7b97\u7684\u8f93\u5165\u901a\u8fc7\u4e00\u7ec4\u9a71\u52a8\u5668\u5728\u7cfb\u7edf\u7684\u5b9e\u9645\u8f93\u5165\uff08u\uff09\u4e2d\u5b9e\u73b0\uff1b\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6240\u6709\u76f8\u5173\u7684\u81ea\u7531\u5ea6\u53ca\u5176\u8026\u5408\u90fd\u662f\u5df2\u77e5\u7684\u3002<\/span><\/section>\n
b\uff09\u5206\u5e03\u5f0f\u5206\u6563\u7275\u5236\u63a7\u5236\u7b56\u7565\u3002\u4e00\u4e9b\u7f51\u7edc\u8282\u70b9\uff08\u9ec4\u8272\u5706\u5708\uff09\u5411\u63a7\u5236\u5668\uff08\u7c89\u8272\u65b9\u5757\uff09\u53d1\u9001\u5305\u542b\u5176\u72b6\u6001\u6216\u8f93\u51fa\u7684\u4fe1\u606f\uff08\u84dd\u8272\u7bad\u5934\uff09\u3002\u63a7\u5236\u5668\u5408\u4f5c\uff08\u9ed1\u8fb9\uff09\u5236\u5b9a\u7f51\u7edc\u63a7\u5236\u7b56\u7565\uff0c\u7136\u540e\u9009\u62e9\u6027\u5730\u5e72\u9884\u7f51\u7edc\u4e2d\u90e8\u5206\u8282\u70b9\uff08\u7ea2\u8272\u7bad\u5934\uff09\u7684\u884c\u4e3a\uff0c\u4ee5\u5b9e\u73b0\u4e00\u4e9b\u671f\u671b\u7684\u96c6\u4f53\u884c\u4e3a\u3002<\/span><\/section>\n
\u56fe\u7247\u7531Davide Salzano\u63d0\u4f9b\u3002<\/span><\/section>\n
\u4ece\u63a7\u5236\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u590d\u6742\u7f51\u7edc\u662f\u7531\u8bb8\u591a\u8fde\u7eed\u65f6\u95f4\u6216\u79bb\u6563\u65f6\u95f4\u5355\u5143\u7ec4\u6210\u7684\u5927\u89c4\u6a21\u52a8\u6001\u7cfb\u7edf\u7684\u4f8b\u5b50\uff0c\u8fd9\u4e9b\u4e2a\u4f53\u53ef\u4ee5\u901a\u8fc7\u9759\u6001\u6216\u65f6\u53d8\u7684\u4e92\u8fde\u7f51\u7edc\u8fdb\u884c\u4ea4\u4e92[16,17]\u3002<\/span><\/section>\n
\u56e0\u4e3a\u9700\u8981\u5728\u6211\u4eec\u611f\u5174\u8da3\u7684\u5b8f\u89c2\u884c\u4e3a<\/span>\uff08\u5982\u5171\u8bc6\u6216\u540c\u6b65\uff09<\/span>\u4e0e\u5fae\u89c2\u884c\u52a8\u4e4b\u95f4\u5efa\u7acb\u53cd\u9988\u8054\u7cfb\uff0c\u4ee5\u8bbe\u8ba1\u6240\u9700\u7684\u96c6\u4f53\u52a8\u529b\u5b66\u673a\u5236\uff0c\u6240\u4ee5\u5173\u952e\u95ee\u9898\u5c31\u6210\u4e86<\/span><\/section>\n
1.\u5224\u65ad\u7ed9\u5b9a\u7f51\u7edc\u662f\u5426\u6ee1\u8db3\u57fa\u672c\u7684\u63a7\u5236\u5c5e\u6027<\/span>\uff08\u4f8b\u5982\u53ef\u63a7\u6027\u548c\u53ef\u89c2\u6d4b\u6027\uff09<\/span>\uff1b<\/span><\/section>\n
2.\u5982\u4f55\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u95ed\u5408\u53cd\u9988\u56de\u8def<\/span>\uff08\u56fe4\uff09<\/span>\uff1f<\/span><\/section>\n
\u5b9e\u73b0\u63a7\u5236\u7684\u65b9\u6cd5\u6709\uff1a\u63a7\u5236\u7f51\u7edc\u8282\u70b9\u3001\u8d4b\u4e88\u8fb9\u52a8\u529b\u5b66\u5c5e\u6027\u3001\u901a\u8baf\u534f\u5b9a<\/span>\uff08communication protocol\uff09<\/span>\u3001\u63a7\u5236\u7f51\u7edc\u672c\u8eab\u7684\u7ed3\u6784\u6216\u7ec4\u5408\u4ee5\u4e0a\u65b9\u6cd5\u3002\u4e00\u4e2a\u7a81\u51fa\u7684\u4f8b\u5b50\u662f\u7275\u5236\u63a7\u5236<\/span>\uff08pinning control\uff09<\/span>[18 -21]\uff0c\u5176\u4e2d\u53ea\u9700\u63a7\u5236\u76f8\u5bf9\u5c0f\u90e8\u5206\u7684\u7f51\u7edc\u8282\u70b9\u6216\u8fb9\u7f18\u5c31\u80fd\u591f\u63a7\u5236\u7cfb\u7edf\u7684\u96c6\u4f53\u884c\u4e3a\u671d\u4e00\u4e9b\u53c2\u8003\u5e73\u8861\u6216\u6e10\u8fd1\u8f68\u8ff9[22\uff0c23]\u53d1\u5c55\u3002\u7136\u800c\uff0c\u6211\u4eec\u8fd8\u60f3\u8981\u8bbe\u8ba1\u7b56\u7565\u63a7\u5236\u66f4\u4e00\u822c\u7684\u3001\u6709\u66f4\u5e7f\u6cdb\u8282\u70b9\u52a8\u529b\u5b66\u7684\u7cfb\u7edf<\/span>\uff08\u5982\uff0c\u7f51\u7edc\u7ed3\u6784\u968f\u65f6\u95f4\u6216\u662f\u8282\u70b9\u52a8\u529b\u5b66\u51fd\u6570\u6f14\u53d8\uff09<\/span>\u3002<\/span><\/section>\n

<\/p>\n

\u56fe4. \u590d\u6742\u7f51\u7edc\u4e2d\u7684\u95ed\u5408\u53cd\u9988\u56de\u8def\u9700\u8981\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u8fdb\u884c\u611f\u6d4b\u3001\u8ba1\u7b97\u548c\u9a71\u52a8\uff08actuation\uff09\u3002\u611f\u6d4b\u548c\u5236\u52a8\u53ef\u4ee5\u5728\u56fe\u4e2d\u63cf\u7ed8\u7684\u4efb\u4f55\u5c3a\u5ea6\u4e0b\u6267\u884c\u3002\u5728\u8be5\u56fe\u4e2d\uff0c\u4e3a\u4e86\u7b80\u5355\u8d77\u89c1\uff0c\u6211\u4eec\u63cf\u7ed8\u4e86\u96c6\u4e2d\u5f0f\u63a7\u5236\u7b56\u7565\uff1b\u7136\u800c\uff0c\u5f53\u5904\u7406\u7f51\u7edc\u7cfb\u7edf\u65f6\uff0c\u63a7\u5236\u7b56\u7565\u901a\u5e38\u662f\u5206\u5e03\u5f0f\u548c\u5206\u6563\u5f0f\u7684\u3002\u6ce8\u610fr\u662f\u8868\u793a\u7cfb\u7edf\u7684\u671f\u671b\u884c\u4e3a\u7684\u53c2\u8003\u4fe1\u53f7\u3002\u56fe\u7247\u7531Marco Coraggio\u63d0\u4f9b\u3002<\/span><\/p>\n


<\/span><\/section>\n
2.3 \u590d\u6742\u7f51\u7edc\u80cc\u666f\u4e0b\u7684\u63a7\u5236<\/strong><\/span><\/section>\n
\u4ea4\u53c9\u5b66\u79d1\u771f\u5b9e\u4e16\u754c\u7f51\u7edc\u5bf9\u63a7\u5236\u4e3b\u8981\u63d0\u51fa\u4e86\u4e09\u70b9\u6311\u6218\uff1a<\/span><\/section>\n
\u4e00\u3001\u53ef\u80fd\u5b58\u5728\u591a\u4e2a\u957f\u5ea6\u5c3a\u5ea6\u548c\u65f6\u95f4\u5c3a\u5ea6\u7684\u884c\u4e3a\u548c\u4ea4\u4e92\uff0c\u5305\u62ec\u4e2a\u4f53\u4e4b\u95f4\u4f1a\u76f8\u4e92\u5f71\u54cd\u7684\u81ea\u7ec4\u7ec7\u884c\u4e3a\u3002<\/strong>\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u53ea\u5173\u6ce8\u96c6\u4f53\u884c\u4e3a<\/span>\uff08\u4f8b\u5982\uff0c\u611f\u67d3\u603b\u4eba\u6570\uff09<\/span>\u3002\u7136\u800c\u5728\u5176\u4ed6\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u6709\u53ef\u80fd\u5bf9\u5fae\u89c2\u7ec6\u8282\u611f\u5174\u8da3<\/span>\uff08\u4f8b\u5982\uff0c\u54ea\u4e9b\u7279\u5b9a\u7684\u4eba\u88ab\u611f\u67d3\uff09<\/span>\u3002\u540c\u6837\u5730\uff0c\u5bf9\u4e8e\u6d4b\u91cf\u548c\u8f93\u5165\u63a7\u5236\u4fe1\u53f7\u4e0e\u81ea\u7531\u5ea6\u76f8\u4e92\u4f5c\u7528\u7684\u80fd\u529b\uff0c\u53ef\u80fd\u5b58\u5728\u7ea6\u675f\u3002\u6b64\u5916\uff0c\u6709\u65f6\u6211\u4eec\u6216\u8bb8\u4e0d\u9700\u8981\u975e\u5f97\u5c06\u7cfb\u7edf\u63a7\u5236\u5230\u7279\u5b9a\u72b6\u6001\uff0c\u53ea\u9700\u8981\u7b80\u5355\u5730\u63a7\u5236\uff0c\u4f7f\u7cfb\u7edf\u8fdc\u79bb\u4e0d\u671f\u671b\u7684\u72b6\u6001<\/span>\uff08\u4f8b\u5982\u7cfb\u7edf\u5d29\u6e83\uff09<\/span>\u6216\u671d\u5411\u671f\u671b\u72b6\u6001\u53ef\u80fd\u5c31\u8db3\u591f\u4e86\u3002\u53c2\u8003\u6587\u732e[10\uff0c24\uff0c25]\u4e2d\u6709\u5bf9\u771f\u5b9e\u7cfb\u7edf\u7684\u5e72\u9884\u4e2d\u7684\u9ad8\u7ef4\u6027\uff0c\u975e\u7ebf\u6027\u548c\u7ea6\u675f\u6240\u5e26\u6765\u7684\u6311\u6218\u7684\u6df1\u5165\u8ba8\u8bba\u3002<\/span><\/section>\n
\u4e8c\u3001\u7f51\u7edc\u672c\u8eab\u5177\u6709\u6a21\u7cca\u6027\u3002\u5728\u5927\u8111\u7f51\u7edc\u4e2d\uff0c\u8282\u70b9\u53ef\u4ee5\u662f\u5355\u4e2a\u795e\u7ecf\u5143\u3001\u795e\u7ecf\u5143\u5757\u3001\u751a\u6216\u662f\u8de8\u8d8a\u5927\u91cf\u795e\u7ecf\u5143\u7684\u8111\u533a\u3002<\/strong>\u7814\u7a76\u8282\u70b9\u4e4b\u95f4\u7684\u4ea4\u4e92\uff0c\u5b66\u4e60\u8fde\u63a5\u6a21\u5f0f<\/span>\uff08\u5982\u201c\u7ebf\u8def\u56fe\uff0cwiring diagram\u201d\uff09<\/span>\u6b64\u7c7b\u7684\u5b9e\u9a8c\u6210\u672c\u5f88\u9ad8\uff0c\u5e76\u4e14\u65e0\u6cd5\u5b66\u4e60\u5230\u5b8c\u6574\u7684\u8fde\u63a5\u6a21\u5f0f\u3002\u6ce8\u610f\uff0c\u5355\u4e2a\u8fb9\u7684\u5b58\u5728\u4e0e\u5426\u5bf9\u4ecb\u6570\u4e2d\u5fc3\u6027\u4e4b\u7c7b\u7684\u5c5e\u6027\u6709\u660e\u663e\u7684\u5f71\u54cd\u3002\u6b64\u5916\uff0c\u7f51\u7edc\u4e0a\u53d1\u751f\u7684\u52a8\u529b\u5b66\u6d3b\u52a8\u4e0e\u62d3\u6251\u7ed3\u6784\u540c\u6837\u91cd\u8981\u3002\u4f8b\u5982\uff0c\u5728\u4ea4\u901a\u7f51\u7edc\u4e2d\uff0c\u786e\u5b9a\u62e5\u5835\u6a21\u5f0f\u7684\u662f\u7f51\u7edc\u6d41\u548c\u7f51\u7edc\u62d3\u6251\u3002\u957f\u7a0b\u5e8f\u5c31\u8fd9\u6837\u4ece\u8282\u70b9\u52a8\u529b\u5b66\u548c\u7f51\u7edc\u7ed3\u6784\u7684\u76f8\u4e92\u4f5c\u7528\u4e2d\u6d8c\u73b0\u800c\u51fa[26\uff0c27]\u3002<\/span><\/section>\n
\u4e09\u3001\u5c06\u5f02\u8d28\u6027<\/strong><\/span>\uff08heterogeneity\uff09<\/span>\u548c\u591a\u5c3a\u5ea6\u7ed3\u5408\u8d77\u6765\u610f\u5473\u7740\uff0c\u7cfb\u7edf\u7684\u4e0d\u540c\u90e8\u5206\u53ef\u80fd\u9700\u8981\u4e0d\u540c\u7c7b\u578b\u7684\u8868\u5f81\u3002<\/strong>\u5176\u4e2d\u4e00\u4e9b\u80fd\u591f\u7528\u79bb\u6563\u65f6\u95f4\u52a8\u529b\u5b66\u5efa\u6a21\uff0c\u800c\u53e6\u4e00\u4e9b\u53ef\u80fd\u9700\u8981\u57fa\u4e8e\u8fde\u7eed\u65f6\u95f4\uff1b\u67d0\u4e9b\u65b9\u9762\u53ef\u80fd\u9700\u8981\u7528\u5e38\u5fae\u5206\u65b9\u7a0b<\/span>\uff08ODE\uff09<\/span>\u63cf\u8ff0\uff0c\u53e6\u4e00\u4e9b\u65b9\u9762\u5219\u9700\u8981\u7528\u504f\u5fae\u5206\u65b9\u7a0b<\/span>\uff08PDE\uff09<\/span>\u63cf\u8ff0\u3002\u4f8b\u5982\uff0c\u5728\u4ea4\u901a\u7ba1\u7406\u5e94\u7528\u4e2d\uff0cODE\u80fd\u5f88\u597d\u5730\u63cf\u8ff0\u8f66\u6d41\u7684\u8fd0\u52a8\uff1b\u800cPDE\u5728\u63cf\u8ff0\u4e2a\u4f53\u7ea7\u522b\u7684\u8f66\u8f86\u63a5\u53d7\u4fe1\u53f7\u706f\u6216\u5176\u4ed6\u4fe1\u53f7\u7684\u5efa\u6a21\u4e2d\uff0c\u66f4\u5177\u4f18\u52bf\u3002\u5982\u4f55\u6574\u5408\u8fd9\u79cd\u5206\u6790\u4ecd\u7136\u60ac\u800c\u672a\u51b3\uff0c\u8fd8\u6709\u566a\u97f3\u548c\u4e0d\u786e\u5b9a\u6027\u5728\u65c1\u201c\u8822\u8822\u6b32\u52a8\u201d\u3002\u6700\u540e\uff0c\u6b64\u5e94\u7528\u9886\u57df\u7684\u8de8\u5ea6\u4e5f\u5f88\u5927\uff0c\u4ece\u7535\u7f51\u5230\u793e\u4f1a\u7f51\u7edc\u5230\u751f\u7269\u7cfb\u7edf\uff0c\u5404\u81ea\u6709\u4e0d\u540c\u7684\u76ee\u6807\u548c\u7ea6\u675f\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u6211\u4eec\u5fc5\u987b\u8c28\u614e\u5730\u9009\u62e9\u4e00\u4e2a\u6070\u5f53\u7684\u5efa\u6a21\u8303\u5f0f\u3002<\/span><\/section>\n

\u5efa\u6a21\u65f6\u7684\u5173\u952e\u95ee\u9898\u662f\uff1a<\/span><\/p>\n

1.\u6211\u4eec\u6d4b\u91cf\u4ec0\u4e48\uff1f<\/span><\/p>\n

2.\u4ec0\u4e48\u56e0\u7d20\u6709\u5f71\u54cd\uff1f<\/span><\/p>\n

3.\u4f55\u65f6\u5f71\u54cd\uff1f<\/span><\/p>\n

4.\u5982\u4f55\u5f71\u54cd\uff1f<\/span><\/section>\n
\u6b64\u5916\uff0c\u7814\u7a76\u5982\u4f55\u6536\u655b\u5230\u76ee\u6807\u72b6\u6001\u4e0e\u4fdd\u6301\u590d\u6742\u7f51\u7edc\u63a7\u5236\u7b56\u7565\u9c81\u68d2\u6027\u548c\u5f39\u6027\u7684\u6070\u5f53\u65b9\u6cd5\u4e5f\u81f3\u5173\u91cd\u8981\u3002<\/span><\/section>\n


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3. \u73b0\u6709\u5efa\u6a21\u8303\u5f0f<\/strong><\/strong><\/strong><\/p>\n<\/section>\n

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 <\/span><\/section>\n
3.1 \u7edf\u8ba1\u7269\u7406\u65b9\u6cd5<\/strong><\/span><\/section>\n
\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u6982\u5ff5\u548c\u6280\u672f\u5df2\u5e7f\u6cdb\u7528\u4e8e\u7814\u7a76\u590d\u6742\u7f51\u7edc\u7684\u7ed3\u6784\u548c\u52a8\u529b\u5b66\u7279\u6027[2\uff0c28\uff0c29]\uff0c\u7814\u7a76\u9886\u57df\u8986\u76d6\u7f51\u7edc\u751f\u957f<\/span>\uff08network growth\uff09<\/span>\uff0c\u76f8\u53d8\u548c\u7ea7\u8054\u6545\u969c<\/span>\uff08cascading failures\uff09<\/span>\u7b49\u590d\u6742\u7f51\u7edc\u57fa\u672c\u884c\u4e3a\u3002\u4ece\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u89d2\u5ea6\u7814\u7a76\u63a7\u5236\u8fd9\u4e9b\u884c\u4e3a\u5e76\u4e0d\u662f\u4e3a\u4e86\u4e25\u683c\u6ee1\u8db3\u53ef\u63a7\u5c5e\u6027\uff0c\u66f4\u50cf\u662f\u5728\u63a7\u5236\u7cfb\u7edf\uff1a\u4f8b\u5982\uff0c\u5f15\u5bfc\u5b83\u8fdc\u79bb\u4e34\u754c\u70b9\u6216\u51cf\u5c11\u6545\u969c\u53d1\u751f\u3002\u76f4\u63a5\u5e94\u7528\u7edf\u8ba1\u7269\u7406\u5de5\u5177\u6765\u7814\u7a76\u590d\u6742\u7f51\u7edc\u7684\u4f20\u7edf\u63a7\u5236\u6027\u8d28\u4e3b\u8981\u6d89\u53ca\u5230\u53ef\u63a7\u6027\u548c\u53ef\u89c2\u6d4b\u6027\u3002\u6211\u4eec\u5c06\u5728\u63a5\u4e0b\u6765\u8ba8\u8bba\u8fd9\u4e9b\u4e3b\u9898\uff0c\u5e76\u5c06\u65b9\u6cd5\u603b\u7ed3\u5728\u88681\u4e2d\u3002<\/span><\/section>\n
<\/section>\n

\u88681. \u57fa\u4e8e\u7edf\u8ba1\u7269\u7406\u7684\u6982\u5ff5\u548c\u65b9\u6cd5\uff0c\u7528\u4e8e\u7814\u7a76\u590d\u6742\u7f51\u7edc\u7684\u7ed3\u6784\u3001\u52a8\u529b\u5b66\u6216\u63a7\u5236\u7279\u6027<\/span><\/p>\n

\u4e3a\u4e86\u7814\u7a76\u590d\u6742\u7f51\u7edc\u7684\u751f\u957f<\/strong>\uff0c\u7279\u522b\u662f\u4ee5\u5e42\u5f8b\u5206\u5e03\u800c\u95fb\u540d\u7684\u65e0\u6807\u5ea6\u7f51\u7edc[30]\uff0c\u5df2\u7ecf\u6709\u4e86\u8bb8\u591a\u5177\u6709\u5f3a\u70c8\u7edf\u8ba1\u7269\u7406\u8272\u5f69\u7684\u5206\u6790\u65b9\u6cd5\uff0c\u4f8b\u5982\u8fde\u7eed\u7edf\u7406\u8bba[31]\u3001\u4e3b\u65b9\u7a0b\u65b9\u6cd5[32]\u548c\u901f\u7387\u65b9\u7a0b\u65b9\u6cd5[33]\u3002<\/span><\/section>\n
\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u4e00\u4e2a\u6838\u5fc3\u7814\u7a76\u70b9\u662f\u76f8\u53d8<\/strong><\/span>\uff08\u4e34\u754c\u70b9\u5916\u90e8\u63a7\u5236\u53c2\u6570\u7684\u5c0f\u6270\u52a8\uff0c\u4f7f\u7cfb\u7edf\u5b8f\u89c2\u884c\u4e3a\u53d1\u751f\u5267\u70c8\u53d8\u5316\u7684\u73b0\u8c61\uff09<\/span>[34]\u3002\u5728\u7f51\u7edc\u7684\u80cc\u666f\u4e0b\uff0c\u6709\u4e00\u4e2a\u8457\u540d\u7684\u76f8\u53d8\uff0c\u5c31\u662f\u6e17\u6d41\u76f8\u53d8<\/span>\uff08\u56fe1e\uff09<\/span>\uff0c\u53ef\u4ee5\u4f7f\u7528\u968f\u673a\u56fe\u6a21\u578b\u8fdb\u884c\u5206\u6790[35]\u3002\u8fd9\u4e9b\u6a21\u578b\u57fa\u4e8e\u7edf\u8ba1\u7cfb\u7efc\u7684\u6982\u5ff5\uff0c\u662f\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u57fa\u7840\u3002<\/span><\/section>\n
\u7f51\u7edc\u7684\u7edf\u8ba1\u7cfb\u7efc<\/span><\/strong>\u8003\u8651\u7ed9\u5b9a\u7684\u4e00\u7ec4\u5c5e\u6027\uff0c\u4f8b\u5982\u6307\u5b9a\u7684\u5ea6\u5206\u5e03\u3002\u7cfb\u7efc\u4e2d\u7684\u6bcf\u4e2a\u4f53\u7cfb\u662f\u5177<\/strong>\u6709\u7279\u5b9a\u8282\u70b9\u548c\u8fde\u8fb9\u6784\u578b\u7684\u7f51\u7edc\u5b9e\u73b0\uff0c\u5e76\u6709\u5176\u51fa\u73b0\u7684\u6982\u7387\uff08\u5373\uff0c\u7edf\u8ba1\u6743\u91cd\uff09\u3002\u9664\u4e86\u7ed9\u5b9a\u7684\u5c5e\u6027\u96c6\u4e4b\u5916\uff0c\u6211\u4eec\u5047\u8bbe\u5176\u4ed6\u5c5e\u6027\u90fd\u662f\u5b8c\u5168\u968f\u673a\u7684\uff0c\u56e0\u6b64\u5b83\u4eec\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u4e00\u4e9b\u5e73\u5747\u573a\u65b9\u6cd5\u5728\u6574\u4e2a\u7cfb\u7efc\u4e0a\u5e73\u5747\uff0c\u4f8b\u5982\u57fa\u4e8e\u5206\u652f\u8fc7\u7a0b\u548c\u6811\u5047\u8bbe\u7684\u751f\u6210\u51fd\u6570\u5f62\u5f0f[36\uff0c37]\u3002<\/span><\/section>\n
\u6e17\u6d41\u76f8\u53d8\u63cf\u8ff0\u4e86\u7f51\u7edc\u4e2d\u5927\u89c4\u6a21\u8fde\u901a\u7247\u7684\u7a81\u73b0\uff0c\u9010\u6e10\u8fde\u901a\u8fc7\u7a0b\u4e2d\u7684\u5c0f\u6270\u52a8\u53ef\u4ee5\u63a7\u5236\u4e34\u754c\u70b9\u7684\u4f4d\u7f6e\uff0c\u5e76\u53ef\u80fd\u5bfc\u81f4\u7206\u70b8\u6027\u6e17\u6d41[38\uff0c39]\u3002\u5bf9\u4e8e\u4e34\u754c\u8f6c\u53d8\uff0c\u5df2\u6709\u7814\u7a76\u8868\u660e\uff0c\u7cfb\u7edf\u5230\u8fbe\u4e34\u754c\u70b9\u65f6\uff0c\u9884\u6d4b\u7684\u6da8\u843d\u548c\u81ea\u76f8\u5173\u65f6\u95f4\u4f1a\u589e\u52a0\uff0c\u8fd9\u53ef\u4ee5\u4f5c\u4e3a\u65e9\u671f\u7684\u9884\u8b66\u4fe1\u53f7[40\uff0c41]\u3002<\/span><\/section>\n
\u7edf\u8ba1\u7269\u7406\u5b66\u4e2d\u81ea\u7ec4\u7ec7\u7814\u7a76\u7684\u7406\u8bba\u57fa\u7840\u662f\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027<\/span>\uff08self-organized criticality, SOC\uff09<\/span>\u7684\u8303\u5f0f[42]\u3002\u5728SOC\u4e2d\uff0c\u7ade\u4e89\u529b\u7684\u5e73\u8861<\/span>\uff08\u4f8b\u5982\u9a71\u52a8\u548c\u8017\u6563\uff09<\/span>\u4f1a\u5bfc\u81f4\u7cfb\u7edf\u63a5\u8fd1\u4e34\u754c\u70b9\uff0c\u4ece\u800c\u5f15\u53d1\u9075\u5faa\u5e42\u5f8b\u5206\u5e03\u7684\u7ea7\u8054\u6545\u969c\u3002\u8fd9\u79cd\u7ea7\u8054\u6545\u969c\u5728\u590d\u6742\u7f51\u7edc<\/span>\uff08\u5982\u7535\u7f51\u548c\u8111\u7f51\u7edc\uff09<\/span>\u4e2d\u65f6\u6709\u53d1\u751f[43]\u3002\u901a\u8fc7\u9a71\u52a8\u529b\u7684\u6027\u8d28\u6765\u63a7\u5236SOC\u662f\u7edf\u8ba1\u7269\u7406\u5b66\u6587\u732e\u4e2d\u7684\u4e00\u4e2a\u91cd\u8981\u4e3b\u9898[44 -47]\uff0c\u6b63\u5982\u6700\u8fd1\u201c\u9f99\u738b\u201d\u4e8b\u4ef6[48 -51]\u5907\u53d7\u5173\u6ce8<\/span>\uff08\u2018dragon king\u2019 events\uff0c\u707e\u96be\u8f6c\u53d8\u524d\u5146\uff09<\/span>\u3002<\/span><\/section>\n
\u7edf\u8ba1\u7269\u7406\u5de5\u5177\u5728\u53ef\u63a7\u6027\u548c\u53ef\u89c2\u6d4b\u6027\u65b9\u9762\u7684\u76f4\u63a5\u5e94\u7528<\/strong>\u662f\u5b58\u5728\u7684\u3002\u4e0b\u9762\uff0c\u6211\u4eec\u5c06\u4ecb\u7ecd\u51e0\u4e2a\u5b8c\u5168\u4ece\u7f51\u7edc\u7ed3\u6784<\/span>\uff08\u6216\u8fde\u63a5\u6a21\u5f0f\uff09<\/span>\u7684\u89d2\u5ea6\uff0c\u7814\u7a76\u63a7\u5236\u7279\u6027\u7684\u5178\u578b\u6848\u4f8b\u3002<\/span><\/section>\n
\u5176\u4e00\u662f\u5e94\u7528\u7a7a\u8154\u6cd5<\/strong><\/span>\uff08cavity method\uff09<\/span>\u6765\u89e3\u51b3\u7ed3\u6784\u63a7\u5236\u95ee\u9898<\/strong>[3]\u3002\u7531\u4e8e\u7ed3\u6784\u53ef\u63a7\u6027\u5b9a\u7406[4]\u7684\u56fe\u5f62\u89e3\u91ca\uff0c\u4eba\u4eec\u53ef\u4ee5\u7b80\u5355\u5730\u68c0\u67e5\u7f51\u7edc\u7ed3\u6784\uff0c\u6765\u68c0\u67e5\u7f51\u7edc\u7ed3\u6784\u662f\u5426\u53ef\u63a7\uff0c\u800c\u907f\u514d\u4f9d\u8d56\u590d\u6742\u7684\u8fb9\u6743\u77e9\u9635\u8fd0\u7b97\u3002\u7279\u522b\u5730\uff0c\u6211\u4eec\u53ef\u4ee5\u8bc6\u522b\u52a8\u529b\u8282\u70b9<\/span>\uff08driver nodes\uff09<\/span>\u7684\u6700\u5c0f\u96c6\u5408\uff0c\u5176\u65f6\u95f4\u76f8\u5173\u63a7\u5236<\/span>\uff08time-dependent control\uff09<\/span>\u8db3\u4ee5\u63a7\u5236\u7cfb\u7edf\u7684\u6574\u4e2a\u52a8\u529b\u5b66\u3002\u8fd9\u79cd\u8bc6\u522b\u53ef\u4ee5\u901a\u8fc7\u5c06\u7ed3\u6784\u63a7\u5236\u95ee\u9898\u6620\u5c04\u6210\u4e3a\u6700\u5927\u5339\u914d\u7684\u7eaf\u56fe\u8bba\u95ee\u9898\u6765\u5b9e\u73b0[52 -54]\u3002\u5229\u7528\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u7a7a\u8154\u65b9\u6cd5[55 -57]<\/span>\uff08\u53ca\u5176\u5728\u89e3\u51b3\u6700\u5927\u5339\u914d\u95ee\u9898[58]\u4e2d\u7684\u8fdb\u4e00\u6b65\u5e94\u7528\uff09<\/span>\uff0c\u53ef\u4ee5\u5206\u6790\u8ba1\u7b97\u5177\u6709\u6307\u5b9a\u5ea6\u5206\u5e03\u7684\u7f51\u7edc\u7cfb\u7efc\u7684\u67d0\u4e9b\u63a7\u5236\u5c5e\u6027[3]\u3002\u8fd9\u4e9b\u5c5e\u6027\u5305\u62ec\uff1a\u6700\u5927\u5339\u914d\u7684\u5927\u5c0f\uff0c\u5b83\u4e0e\u786e\u4fdd\u7ed3\u6784\u53ef\u63a7\u6027\u7684\u9a71\u52a8\u5668\u8282\u70b9<\/span>\uff08\u6216\u63a7\u5236\u8f93\u5165\uff09<\/span>\u7684\u6700\u5c0f\u6570\u76ee\u76f4\u63a5\u76f8\u5173\uff1b\u4ee5\u53ca\u4e0d\u540c\u6700\u5927\u5339\u914d\u7684\u603b\u6570\uff0c\u5b83\u4e0e\u4e0d\u540c\u63a7\u5236\u914d\u7f6e\u7684\u6570\u91cf\u76f4\u63a5\u76f8\u5173\uff0c\u5e76\u4e14\u4f1a\u56e0\u6b64\u5f71\u54cd\u63a7\u5236\u9c81\u68d2\u6027\u3002<\/span><\/section>\n
\u53e6\u4e00\u5178\u4f8b\u662f\u7535\u7f51\u7684\u53ef\u89c2\u6d4b\u6027\u7814\u7a76<\/strong>\u3002\u5728\u8be5\u7cfb\u7edf\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u76f8\u91cf\u6d4b\u91cf\u5355\u5143<\/span>\uff08phasor measurement units\uff0cPMU\uff09<\/span>\u6765\u786e\u5b9a\u8282\u70b9\u7684\u7535\u538b<\/span>\uff08\u8fd8\u53ef\u770b\u4f5c\u72b6\u6001\u53d8\u91cf\uff09<\/span>\u3002PMU\u80fd\u591f\u6d4b\u91cf\u5176\u5bf9\u5e94\u8282\u70b9\u7684\u5b9e\u65f6\u7535\u538b\u548c\u7ebf\u8def\u7535\u6d41\uff0c\u56e0\u6b64PMU\u4e0d\u4ec5\u80fd\u786e\u5b9a\u5176\u6240\u653e\u7f6e\u7684\u8282\u70b9\u7684\u72b6\u6001\u53d8\u91cf\uff0c\u8fd8\u80fd\u786e\u5b9a\u5176\u6240\u6709\u6700\u8fd1\u90bb\u5c45\u7684\u72b6\u6001\u53d8\u91cf\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u53ef\u89c2\u6d4b\u6027\u95ee\u9898\u53ef\u4ee5\u6620\u5c04\u6210\u4e00\u4e2a\u7eaf\u7cb9\u7684\u56fe\u8bba\u95ee\u9898\u3002\u4e8b\u5b9e\u4e0a\uff0cPMU\u7684\u968f\u673a\u653e\u7f6e\u4f1a\u5bfc\u81f4\u7f51\u7edc\u53ef\u89c2\u6d4b\u6027\u8f6c\u6362[59]\uff0c\u53ef\u4ee5\u4f7f\u7528\u6bcd\u51fd\u6570\u5f62\u5f0f<\/span>\uff08generating function formalism\uff09<\/span>\u8fdb\u884c\u5206\u6790\u7814\u7a76[36\uff0c37]\u3002\u6b64\u5916\uff0c\u8bc6\u522b\u7535\u7f51\u4e2d\u4f20\u611f\u5668\u8282\u70b9<\/span>\uff08\u5373PMU\uff09<\/span>\u7684\u6700\u5c0f\u96c6\u5408\u95ee\u9898\u53ef\u4ee5\u6620\u5c04\u6210\u4e3a\u7ecf\u5178\u7684\u56fe\u8bba\u95ee\u9898\uff1a\u5c3d\u7ba1\u5b83\u901a\u5e38\u6c42\u89e3\u56f0\u96be\uff0c\u4f46\u6700\u5c0f\u652f\u914d\u96c6\u95ee\u9898\u53ef\u4ee5\u901a\u8fc7\u6d88\u606f\u4f20\u9012\u7b97\u6cd5<\/span>\uff08\u6e90\u4e8e\u81ea\u65cb\u73bb\u7483\u7406\u8bba\uff09<\/span>\u6765\u89e3\u51b3\uff0c\u8be5\u7b97\u6cd5\u63d0\u4f9b\u4e86\u63a5\u8fd1\u6700\u4f18\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u5e76\u4e14\u5728\u771f\u5b9e\u7f51\u7edc\u4e2d\u8868\u73b0\u826f\u597d[60]\u3002<\/span><\/section>\n
\u5982\u4f55\u5c06\u63a7\u5236\u95ee\u9898\u6620\u5c04\u4e3a\u7eaf\u56fe\u8bba\u95ee\u9898\uff1f<\/strong>\u4efb\u4f55\u63a7\u5236\u5c5e\u6027<\/span>\uff08\u5982\u63a7\u5236\u80fd\u91cf\u6210\u672c\uff09<\/span>\uff0c\u90fd\u9700\u8981\u76f8\u5173\u9886\u57df\u7684\u5177\u4f53\u77e5\u8bc6\uff0c\u800c\u4e14\u7eaf\u7cb9\u7684\u56fe\u8bba\u89e3\u91ca\u548c\u76f8\u5e94\u7684\u7edf\u8ba1\u96c6\u6210\u65b9\u6cd5\u5728\u6b64\u65e0\u7528\u6b66\u4e4b\u5730\u3002\u968f\u673a\u77e9\u9635\u7406\u8bba[61]\u4e2d\u53ef\u4ee5\u76f4\u63a5\u5904\u7406\u590d\u6742\u7f51\u7edc\u8fb9\u6743\u91cd\u7684\u6280\u672f\uff0c\u8fd9\u5bf9\u9002\u5f53\u7684\u7f51\u7edc\u7cfb\u7efc\u7684\u5efa\u6a21\u6765\u8bf4\u5fc5\u4e0d\u53ef\u5c11\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u5177\u4f53\u7684\u7ed3\u6784\u548c\u52a8\u529b\u5b66\u90fd\u5f88\u91cd\u8981[62]\u3002<\/span><\/section>\n


<\/p>\n

3.2 \u63a7\u5236\u7406\u8bba\u65b9\u6cd5<\/strong><\/span><\/section>\n
\u4f20\u7edf\u63a7\u5236\u7406\u8bba\u65b9\u6cd5\u7684\u76ee\u7684\u662f\u5206\u6790\u548c\u64cd\u7eb5\u7279\u5b9a\u7cfb\u7edf\u7684\u884c\u4e3a\u3002\u63a7\u5236\u95ee\u9898\u53ef\u4ee5\u6982\u62ec\u6210\u5982\u4e0b\u4e09\u4e2a\uff1a\u786e\u5b9a\u9700\u8981\u611f\u6d4b\u4ec0\u4e48<\/strong>\u3001\u9700\u8981\u63a7\u5236\u4ec0\u4e48<\/strong>\u4ee5\u53ca\u5982\u4f55\u7528\u611f\u6d4b\u4fe1\u606f\u5b9e\u73b0\u63a7\u5236\u76ee\u6807<\/strong>\u3002\u56e0\u6b64\uff0c\u4efb\u4f55\u63a7\u5236\u8bbe\u8ba1\u7684\u4e09\u4e2a\u5173\u952e\u8981\u7d20\u662f\u611f\u6d4b\u3001\u8ba1\u7b97\u548c\u9a71\u52a8[14]\u3002\u88682\u4e2d\u603b\u7ed3\u4e86\u4e00\u4e9b\u65b9\u6cd5\u3002<\/span><\/section>\n
<\/section>\n

<\/section>\n

<\/section>\n
\u88682. \u63a7\u5236\u7406\u8bba\u4e2d\u7528\u4e8e\u5206\u6790\u548c\u63a7\u5236\u590d\u6742\u7f51\u7edc\u7684\u6982\u5ff5\u548c\u65b9\u6cd5\u3002<\/span><\/section>\n
\u591a\u667a\u80fd\u4f53\u7cfb\u7edf\u4e2d\u7ecf\u5178\u63a7\u5236\u76ee\u6807\u5305\u542b\u4e00\u81f4\u6027<\/strong><\/span>\uff08consensus\uff0c\u5373\u6240\u6709\u5355\u5143\u4f1a\u671d\u7740\u540c\u4e00\u4e2a\u5e73\u8861\u70b9\u6536\u655b\uff09<\/span>[63-71]\u548c\u540c\u6b65\u6027<\/strong><\/span>\uff08synchronization\uff0c\u5373\u6536\u655b\u5230\u6e10\u8fdb\u65f6\u53d8\u89e3<\/strong>[asymptotic time-varying solution]\uff09<\/span>[72-75]\uff0c\u540c\u65f6\u4e5f\u8fd8\u5305\u62ec\u5982\u7f16\u961f\u63a7\u5236<\/span>\uff08formation control\uff09<\/span>[76 -78]\uff0c\u6a21\u5f0f\u751f\u6210<\/span>\uff08pattern formation\uff09<\/span>[79]\u548c\u591a\u667a\u80fd\u4f53\u534f\u540c\u8fd0\u52a8<\/span>\uff08\u5982\u96c6\u7fa4\uff09<\/span>[80]\u7b49\u76ee\u6807\u3002\u63a7\u5236\u76ee\u6807\u901a\u5e38\u6839\u636e\u6027\u80fd<\/span>\uff08\u4fa7\u91cd\u4e8e\u77ac\u6001\u7279\u6027\uff0c\u4f8b\u5982\u5efa\u7acb\u65f6\u95f4\u3001\u4e0a\u5347\u65f6\u95f4\u548c\u8d85\u8c03\u91cf\uff09<\/span>\u3001\u7a33\u5b9a\u6027<\/span>\uff08\u4f8b\u5982\u6536\u655b\u5230\u72b6\u6001\u7a7a\u95f4\u4e2d\u7684\u5e73\u8861\u6216\u6d41\u5f62\uff09<\/span>\u4ee5\u53ca\u5bf9\u566a\u58f0\u548c\u5916\u90e8\u6270\u52a8\u7684\u9c81\u68d2\u6027\u6765\u5236\u5b9a[14]\u3002<\/span><\/section>\n
\u4ece\u7cfb\u7edf\u7684\u6570\u5b66<\/span>\uff08\u6216\u6570\u636e\u9a71\u52a8\uff09<\/span>\u6a21\u578b\u548c\u63a7\u5236\u76ee\u6807\u51fa\u53d1\uff0c\u6211\u4eec\u53ef\u4ee5\u5c1d\u8bd5\uff1a1.\u5efa\u7acb\u7cfb\u7edf\u7684\u53ef\u63a7\u6027\u548c\u53ef\u89c2\u6d4b\u6027\uff1b2.\u8bbe\u8ba1\u63a7\u5236\u7b56\u7565\uff0c\u5e76\u901a\u8fc7\u5bf9\u95ed\u73af\u7f51\u7edc\u7cfb\u7edf\u4e2d\u7684\u8fd9\u4e9b\u7279\u6027\u8fdb\u884c\u9002\u5f53\u7684\u4e25\u683c\u8bc1\u660e\uff0c\u8bc1\u660e\u8be5\u63a7\u5236\u7b56\u7565\u80fd\u4fdd\u8bc1\u6240\u9700\u884c\u4e3a\u7684\u6536\u655b\u6027\u548c\u7a33\u5b9a\u6027<\/span>\uff08\u56fe5\uff09<\/span>\u3002<\/span><\/section>\n

<\/p>\n

\u56fe5. \u7ecf\u5178\u95ed\u73af\u63a7\u5236\u5668\u8bbe\u8ba1\u7684\u4e3b\u8981\u9636\u6bb5\u3002\u59cb\u4e8e\u771f\u5b9e\u7cfb\u7edf\uff0c\u5148\u5efa\u6a21\u5206\u6790\u5176\u5728\u6ca1\u6709\u63a7\u5236\u7684\u60c5\u51b5\u4e0b\u7684\u6027\u8d28\u3002\u7136\u540e\u8bbe\u8ba1\u63a7\u5236\u7b56\u7565\u4ee5\u6ee1\u8db3\u76ee\u6807\u8981\u6c42\uff0c\u987b\u5728\u5b9e\u65bd\u4e4b\u524d\u8fdb\u884c\u9a8c\u8bc1\u3002\u901a\u5e38\uff0c\u8fd9\u79cd\u8bbe\u8ba1\u65b9\u6cd5\u5728\u5b9e\u73b0\u7cbe\u786e\u7684\u63a7\u5236\u4e4b\u524d\u9700\u8981\u591a\u6b21\u8fed\u4ee3\u3002\u4e28<\/span>\u56fe\u50cf\u6765\u6e90\uff1aGian Carlo Maffettone<\/span><\/p>\n

\u6211\u4eec\u5e38\u5e0c\u671b\u8bbe\u8ba1\u5206\u5e03\u5f0f\u548c\u5206\u6563\u5f0f\u7b56\u7565\u6765\u5904\u7406\u591a\u667a\u80fd\u4f53\u7cfb\u7edf\uff0c\u4e0d\u5fc5\u4ee5\u96c6\u4e2d\u7684\u65b9\u5f0f\u51b3\u5b9a\u611f\u6d4b\u3001\u5236\u52a8\u548c\u63a7\u5236\u8f93\u5165\u3002\u67d0\u4e9b\u63a7\u5236\u95ee\u9898\u4e5f\u7528\u65e0\u9700\u53cd\u9988\u7684\u5f00\u73af\u7b56\u7565\u6765\u89e3\u51b3\uff0c\u4f46\u4e00\u65e6\u5b58\u5728\u6270\u52a8\uff0c\u7a33\u5b9a\u6027\u548c\u6027\u80fd\u8981\u6c42\u5c31\u65e0\u6cd5\u88ab\u6ee1\u8db3\uff0c\u5c31\u4e0d\u591f\u9c81\u68d2\u3002\u56e0\u6b64\u5728\u6b64\u5904\uff0c\u6211\u4eec\u53ea\u5173\u6ce8\u95ed\u73af\u53cd\u9988\u63a7\u5236\u7b56\u7565\u3002<\/span><\/section>\n
\u53ef\u63a7\u6027\u95ee\u9898<\/span><\/strong>\u662f\u4e00\u4e2a\u5b58\u5728\u6027\u95ee\u9898\uff0c\u5173\u6ce8\u5728\u7ed9\u5b9a\u7f51\u7edc\u7ed3\u6784\u3001\u4e3b\u4f53\u7684\u52a8\u529b\u5b66\u548c\u8fde\u8fb9\u4ea4\u4e92\u7684\u60c5\u51b5\u4e0b\uff0c\u5f15\u5bfc\u96c6\u4f53\u884c\u4e3a\u9700\u8981\u63a7\u5236\u54ea\u4e9b\u8282\u70b9<\/strong>\u3002\u5728\u590d\u6742\u7f51\u7edc\u7684\u80cc\u666f\u4e0b\uff0c\u65e0\u6cd5\u901a\u8fc7\u79e9\u6765\u5224\u65ad\u662f\u5426\u7cfb\u7edf\u662f\u5426\u80fd\u63a7\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528\u7ed3\u6784\u53ef\u63a7\u6027\u7684\u548cGramians\u53ef\u63a7\u6027\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898[81-85]\u3002\u5c3d\u7ba1\u8fc7\u53bb\u5341\u5e74\u53ef\u63a7\u6027\u95ee\u9898\u53d6\u5f97\u4e86\u663e\u8457\u8fdb\u5c55\uff0c\u4f46\u4ecd\u7136\u5b58\u5728\u8bb8\u591a\u672a\u51b3\u7684\u95ee\u9898\uff0c\u5305\u62ec\u7406\u89e3\u975e\u7ebf\u6027\u6216\u65f6\u53d8\u7cfb\u7edf\u7f51\u7edc\u4e2d\u7684\u53ef\u63a7\u6027\uff0c\u6216\u8005\u5f53\u7f51\u7edc\u7ed3\u6784\u968f\u65f6\u95f4\u6216\u52a8\u529b\u5b66\u51fd\u6570<\/span>\uff08\u72b6\u6001\u4f9d\u8d56\u7f51\u7edc\u6f14\u5316\uff09<\/span>\u6f14\u5316\u65f6\u7684\u53ef\u63a7\u6027\u3002<\/span><\/section>\n
\u7814\u7a76\u53ef\u89c2\u6d4b\u6027\u95ee\u9898<\/strong>\u662f\u4e3a\u4e86\u53d1\u73b0\u54ea\u4e9b\u53d8\u91cf\u7684\u4fe1\u606f\u91cf\u8db3\u4ee5\u91cd\u73b0\u6574\u4e2a\u7cfb\u7edf\u884c\u4e3a<\/strong>\u3002\u5f53\u5e94\u7528\u4e8e\u5927\u89c4\u6a21\u590d\u6742\u7f51\u7edc\u65f6\uff0c\u53ef\u89c2\u6d4b\u6027\u7684\u8bc4\u4f30\u4e5f\u53d8\u5f97\u590d\u6742\u7e41\u7410\uff0c\u56e0\u4e3a\u5b83\u53d6\u51b3\u4e8e\u80fd\u91cd\u5851\u6574\u4f53\u7f51\u7edc\u52a8\u529b\u5b66\u7684\u53d8\u91cf\u3002\u540c\u6837\uff0c\u63a7\u5236\u7684\u65b9\u6cd5<\/span>\uff08\u5982\u7ed3\u6784\u53ef\u89c2\u6027\u7406\u8bba\uff09<\/span>\u4e5f\u662f\u4e3a\u4e86\u8fd9\u4e00\u76ee\u7684[82\uff0c86-88]\u3002\u7136\u800c\u73b0\u5728\u4ecd\u6709\u8bb8\u591a\u53ef\u89c2\u6d4b\u6027\u95ee\u9898\u6709\u5f85\u89e3\u51b3<\/span>\uff08\u5982\u7814\u7a76\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u7684\u65f6\u53d8\u7f51\u7edc\u7ed3\u6784\u7684\u53ef\u89c2\u6d4b\u6027\uff09<\/span>\u3002<\/span><\/section>\n
\u7531\u4e8e\u56fe\u8bba\u5de5\u5177\u53ef\u4ee5\u8865\u5145\u548c\u589e\u5f3a\u4ee3\u6570\u6216\u51e0\u4f55\u57fa\u7840\u7406\u8bba\uff0c\u590d\u6742\u7f51\u7edc\u7684\u53ef\u63a7\u6027\u548c\u53ef\u89c2\u6d4b\u6027\u65b9\u6cd5\u4e0e\u4f20\u7edf\u7684\u63a7\u5236\u7406\u8bba\u65b9\u6cd5\u76f8\u6bd4\u6709\u660e\u663e\u53d8\u5316\u3002\u8fd9\u4e00\u91cd\u8981\u7814\u7a76\u65b9\u5411\u572820\u4e16\u7eaa70\u5e74\u4ee3\u672b\u7531\u0160iljak\u7684\u65e9\u671f\u5de5\u4f5c[16]\u4e2d\u9996\u6b21\u5f97\u5230\u627f\u8ba4\uff0c\u5e76\u5728\u540e\u6765\u7684\u5de5\u4f5c\u4e2d\u5f97\u5230\u8fdb\u4e00\u6b65\u53d1\u5c55[82]\uff0c\u5b83\u4f7f\u5f97\u5904\u7406\u5927\u91cf\u76f8\u4e92\u4f5c\u7528\u7684\u52a8\u6001\u53d8\u91cf\u5177\u6709\u53ef\u884c\u6027\u3002<\/span>\uff08\u6211\u4eec\u6ce8\u610f\u5230\uff0c\u4f7f\u7528\u56fe\u8bba\u65b9\u6cd5\u6765\u7814\u7a76\u7f51\u7edc\u95ee\u9898\u81f3\u5c11\u53ef\u4ee5\u8ffd\u6eaf\u523020\u4e16\u7eaa60\u5e74\u4ee3\u7684\u6570\u5b66\u793e\u4f1a\u5b66\u793e\u7fa4\u3002[89]\uff09<\/span><\/section>\n
\u5982\u679c\u5df2\u7ecf\u5206\u6790\u4e86\u76ee\u6807\u7cfb\u7edf\u7684\u57fa\u672c\u7279\u6027\uff0c\u5c31\u53ef\u4ee5\u8bbe\u8ba1\u53cd\u9988\u63a7\u5236\u7b56\u7565<\/span>\uff08\u95ed\u73af\u7b56\u7565\uff09<\/span>\u4e86\u3002\u901a\u8fc7\u89c2\u6d4b\u4fe1\u606f\u548c\u63a7\u5236\u8f93\u5165\uff0c\u6765\u64cd\u7eb5\u7cfb\u7edf\u4ee5\u5b9e\u73b0\u63a7\u5236\u76ee\u6807\u3002\u9a8c\u8bc1\u63a7\u5236\u7b56\u7565\u7684\u4e00\u4e2a\u57fa\u672c\u95ee\u9898\u662f\u5206\u6790\u548c\u8bc1\u660e\u53d7\u63a7\u7f51\u7edc\u7cfb\u7edf\u4ece\u4e0d\u540c\u7684\u521d\u59cb\u6761\u4ef6<\/span>\uff08\u7a33\u5b9a\u6027\uff09<\/span>\u548c\u5916\u90e8\u6270\u52a8<\/span>\uff08\u9c81\u68d2\u6027\uff09<\/span>\u4e0b\u7684\u6536\u655b\u6027\u3002\u901a\u8fc7\u501f\u9274\u540c\u7c7b\u7cfb\u7edf\u7684\u7a33\u5b9a\u6027\u548c\u9c81\u68d2\u6027\u65b9\u6cd5\uff0c\u73b0\u5df2\u63a8\u5e7f\u51fa\u8bb8\u591a\u7814\u7a76\u52a8\u529b\u7cfb\u7edf\u590d\u6742\u7f51\u7edc\u7a33\u5b9a\u6027\u548c\u9c81\u68d2\u6027\u7684\u65b9\u6cd5\u3002<\/span>\uff08\u5173\u4e8e\u53ef\u7528\u65b9\u6cd5\uff0c\u8be6\u89c1\u53c2\u8003\u6587\u732e[17\uff0c21-23\uff0c90-95]\uff09<\/span>\u3002<\/span><\/section>\n
\u5173\u4e8e\u7a33\u5b9a\u6027\uff0c\u7814\u7a76\u7ed9\u5b9a\u590d\u6742\u7f51\u7edc\u7cfb\u7edf\u7684\u5c40\u90e8\u6216\u5168\u5c40\u7a33\u5b9a\u6027\u7684\u65b9\u6cd5\u5305\u62ec\u4e24\u65b9\u9762\uff1a<\/span><\/section>\n
1.\u5c06\u7f51\u7edc\u7cfb\u7edf\u89c6\u4e3a\u4e00\u4e2a\u6574\u4f53\uff0c\u7814\u7a76\u5176\u5728\u6270\u52a8\u4e0b\u7684\u7a33\u5b9a\u6027\u7684\u65b9\u6cd5\uff1b<\/span><\/section>\n
2.\u7814\u7a76\u8282\u70b9\u4ee5\u67d0\u79cd\u65b9\u5f0f\u8026\u5408\u65f6\uff0c\u7cfb\u7edf\u4fdd\u6301\u7a33\u5b9a\u7684\u65b9\u6cd5\u3002<\/span><\/section>\n
\u8003\u8651\u6574\u4e2a\u7f51\u7edc\u7cfb\u7edf\u7684\u5206\u6790\u5de5\u5177\u5305\u62ec\uff1a\u57fa\u4e8e\u674e\u4e9a\u666e\u8bfa\u592b\u76f4\u63a5\u6cd5\u7684\u65b9\u6cd5[90]\u6216\u57fa\u4e8e\u7ebf\u6027\u5316\u5de5\u5177<\/span>\uff08\u5982\u4e3b\u7a33\u5b9a\u6027\u51fd\u6570\u65b9\u6cd5\uff0cmaster stability function\uff09<\/span>\u7684\u65b9\u6cd5[96]\u3002\u5176\u4ed6\u7684\u6709\u6548\u65b9\u6cd5\u5305\u62ec\u589e\u91cf\u7a33\u5b9a\u6027\u548c\u4f7f\u7528\u6536\u655b\u5de5\u5177\uff0c\u5982\u6536\u7f29\u7406\u8bba[23,92-95]\u6216\u589e\u91cf\u88ab\u52a8\u6027[91]\u3002\u8fd9\u4e9b\u7406\u8bba\u5de5\u5177\u4e5f\u9002\u7528\u4e8e\u7814\u7a76\u8fde\u63a5\u7a33\u5b9a\u6027[16]\u76f8\u5173\u6982\u5ff5\u7684\u5176\u4ed6\u95ee\u9898\uff0c\u8b6c\u5982\u524d\u9762\u63d0\u5230\u7684\u53e6\u4e00\u4e2a\u6838\u5fc3\u95ee\u9898\u2014\u2014\u5e95\u5c42\u7f51\u7edc\u7ed3\u6784\u5982\u4f55\u5f71\u54cd\u53d1\u751f\u5728\u5176\u4e0a\u7684\u52a8\u529b\u5b66\u3002<\/span><\/section>\n
\u63a7\u5236\u8bbe\u8ba1\u7684\u65b9\u6cd5\u5728\u6587\u732e\u4e2d\u6bd4\u6bd4\u7686\u662f\uff0c\u5404\u9886\u57df\u57fa\u4e8e\u52a8\u6001\u4f18\u5316\u63a7\u5236\u7406\u8bba\u7684\u63a7\u5236\u8bbe\u8ba1\u65b9\u6cd5\u5305\u62ec\uff1a\u6700\u4f18\u63a7\u5236\u3001\u535a\u5f08\u7406\u8bba\u3001\u81ea\u9002\u5e94\u63a7\u5236\u3001\u667a\u80fd\u63a7\u5236\u3001\u975e\u7ebf\u6027\u63a7\u5236\u3001\u6a21\u578b\u9884\u6d4b\u63a7\u5236\u548c\u9c81\u68d2\u63a7\u5236\u7b49\u7b49\u3002\u76ee\u524d\uff0c\u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u6570\u636e\u9a71\u52a8\u65b9\u6cd5\u548c\u63a7\u5236\u7b56\u7565\u4e5f\u8d8a\u6765\u8d8a\u591a\u5730\u88ab\u7528\u4e8e\u63a7\u5236\u590d\u6742\u7f51\u7edc\u7684\u884c\u4e3a\u3002\u66f4\u591a\u4fe1\u606f\u8be6\u89c1\u53c2\u8003\u6587\u732e[97\uff0c98]\uff0c\u5728\u201c\u65b0\u8303\u4f8b\u548c\u5efa\u6a21\u6280\u672f\u201d\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u4e5f\u6709\u8ba8\u8bba\u3002<\/span><\/section>\n
\u5c3d\u7ba1\u5728\u63a7\u5236\u7406\u8bba\u7684\u7814\u7a76\u9886\u57df\u6709\u8bb8\u591a\u8fdb\u5c55\uff0c\u4f46\u4ecd\u6709\u8bb8\u591a\u6311\u6218\u6709\u5f85\u89e3\u51b3\u3002\u6700\u8fd1\u63a7\u5236\u5b66\u754c\u81f4\u529b\u4e8e\u7814\u7a76\u566a\u58f0\u5bf9\u7f51\u7edc\u4e2d\u7cfb\u7edf\u96c6\u4f53\u884c\u4e3a\u7684\u5f71\u54cd\u3001\u6297\u6270\u52a8\u80fd\u529b<\/span>\uff08\u5305\u62ec\u7ed3\u6784\u6270\u52a8\uff09<\/span>\u3001\u53d1\u5c55\u534f\u540c\u548c\u5171\u8bc6\u7b56\u7565\u4ee5\u4fdd\u969c\u8282\u70b9\u7684\u9690\u79c1\uff0c\u4ee5\u53ca\u7f51\u7edc\u7cfb\u7edf\u4e2d\u6270\u52a8\u4f20\u64ad\u5206\u6790\u4e0e\u63a7\u5236[99-109]\u3002<\/span><\/section>\n


<\/p>\n

3.3 \u52a8\u529b\u7cfb\u7edf\u65b9\u6cd5<\/strong><\/span><\/section>\n
\u6b63\u5982\u7edf\u8ba1\u7269\u7406\u5b66\u5bf9\u63a7\u5236\u7b56\u7565\u7684\u542f\u53d1\uff0c\u52a8\u529b\u7cfb\u7edf\u65b9\u6cd5\u4e5f\u6253\u5f00\u4e86\u63a7\u5236\u7b56\u7565\u7684\u601d\u8def\u3002\u63a7\u5236\u7b56\u7565\u5e38\u65e8\u5728\u64cd\u7eb5\u548c\u5f71\u54cd\u7cfb\u7edf\uff0c\u800c\u4e0d\u662f\u4e25\u683c\u7684\u53ef\u63a7\u3002\u6709\u8bb8\u591a\u65b9\u6cd5\u76f4\u63a5\u5229\u7528\u7cfb\u7edf\u7684\u975e\u7ebf\u6027\u6027\u8d28\uff0c\u8fd8\u6709\u5229\u7528\u6570\u636e\u9a71\u52a8\u7684\u65b9\u6cd5<\/span>\uff08\u5982\u7cfb\u7edf\u8bc6\u522b\uff09<\/span>\u3002\u6211\u4eec\u63a5\u4e0b\u6765\u5c06\u804a\u804a\u8fd9\u4e9b\u5185\u5bb9\u3002<\/span><\/section>\n
\u7ed9\u5b9a\u52a8\u529b\u5b66\u65b9\u7a0b\u5bf9\u7cfb\u7edf\u7684\u884c\u4e3a\u53ca\u5176\u5438\u5f15\u5b50\u3001\u6781\u9650\u73af\u548c\u5438\u5f15\u76c6\u8fb9\u754c\u7684\u76f8\u7a7a\u95f4\u8fdb\u884c\u5efa\u6a21\uff0c\u53ef\u4ee5\u627e\u5230\u5229\u7528\u81ea\u7136\u8f68\u8ff9\u5c06\u7cfb\u7edf\u9a71\u52a8\u5230\u76f8\u7a7a\u95f4\u7684\u671f\u671b\u533a\u57df\u7684\u84c4\u610f\u6270\u52a8<\/strong><\/span>\uff08strategic perturbations\uff09<\/span>\u3002\u65e9\u671f\uff0c\u8fd9\u4e00\u9886\u57df\u7684\u63a7\u5236\u6df7\u6c8c\u7684\u540e\u7eed\u5de5\u4f5c[111 -113]\u8bc1\u660e\u4e86\u8fd9\u79cd\u53ef\u80fd\u6027\u662f\u6df7\u6c8c\u5438\u5f15\u5b50[110]\u3002\u6700\u8fd1\uff0c\u5b66\u8005\u4eec\u5df2\u89e3\u51b3\u4e86\u5982\u4f55\u901a\u8fc7\u4e00\u7cfb\u5217\u8003\u8651\u4e86\u6270\u52a8\u7ea6\u675f\u7684\u7b56\u7565\u6027\u53cd\u51b2\u6765\u5b9e\u73b0\u63a7\u5236[114]\u3002\u867d\u7136\u5229\u7528\u76f8\u7a7a\u95f4\u4e2d\u7684\u81ea\u7136\u8f68\u8ff9\u770b\u4e0a\u53bb\u5b8c\u7f8e\uff0c\u4f46\u5728\u5b9e\u8df5\u4e2d\u5b83\u96be\u4ee5\u63d0\u4f9b\u4f20\u7edf\u63a7\u5236\u7406\u8bba\u6240\u5fc5\u9700\u7684\u4e25\u683c\u6027\u80fd\u4fdd\u969c\u548c\u5bf9\u566a\u58f0\u7684\u9c81\u68d2\u6027\u3002\u4f8b\u5982\uff0c\u5438\u5f15\u76c6\u7684\u8fb9\u754c\u53ef\u4ee5\u662f\u7f51\u72b6\u7684\u6216\u5206\u5f62\u7684\u3002<\/span><\/section>\n
\u5728\u76f8\u5173\u6587\u732e\u4e2d\uff0c\u6709\u5927\u91cf\u5173\u4e8e\u5d4c\u5408\u4f53\u72b6\u6001<\/span>\uff08chimaera states\uff09<\/span>\u63a7\u5236\u7684\u5de5\u4f5c[115]\u3002\u5d4c\u5408\u4f53\u72b6\u6001\u7531\u5bf9\u79f0\u8026\u5408\u7684\u76f8\u540c\u632f\u8361\u5668\u7cfb\u7edf\u4e2d\u76f8\u5e72\u548c\u975e\u76f8\u5e72\u52a8\u529b\u5b66\u7684\u5171\u5b58\u6240\u5b9a\u4e49\uff0c\u6545\u663e\u793a\u51fa\u60ca\u4eba\u7684\u5bf9\u79f0\u7834\u7f3a\u6027\u8d28[116\u3001117]\u3002\u8fd9\u65b9\u9762\u7684\u7814\u7a76\u5305\u62ec\u5ef6\u65f6\u53cd\u9988\u63a7\u5236[118 -120]\u3001\u7275\u5236\u63a7\u5236[121]\u3001\u5468\u671f\u6027\u5f3a\u8feb[122]\u3001\u901a\u8fc7\u62d3\u6251\u7ed3\u6784\u63a7\u5236[123]\u6216\u8026\u5408\u4fee\u6539[124]\u4ee5\u53ca\u591a\u5c42\u7f51\u7edc\u4e2d\u5d4c\u5408\u4f53\u7684\u63a7\u5236[125]\u3002\u53c2\u8003\u6587\u732e[126]\u4ee5\u81ea\u7ec4\u7ec7\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u4e3a\u4e2d\u5fc3\u8fdb\u884c\u4e86\u7efc\u8ff0\uff0c\u867d\u7136\u8fd8\u6709\u8bb8\u591a\u65b9\u5411\u6709\u5f85\u63a2\u7d22\u3002<\/span><\/section>\n
\u901a\u5e38\uff0c\u7cfb\u7edf\u7684\u8fd0\u52a8\u65b9\u7a0b\u662f\u672a\u77e5\u7684\uff0c\u751a\u81f3\u8fde\u72b6\u6001\u7a7a\u95f4\u4e5f\u53ef\u80fd\u662f\u672a\u77e5\u7684\u3002\u4f46\u662f\u7cfb\u7edf\u4e0a\u7684\u6570\u636e\u53ef\u80fd\u5f88\u4e30\u5bcc\u3002\u5982\u679c\u4e00\u4e2a\u7cfb\u7edf\u4e0a\u7684\u6570\u636e\uff0c\u5373\u53ef\u89c2\u6d4b\u91cf\uff0c\u662f\u5b83\u72b6\u6001\u7684\u51fd\u6570\uff0c\u4eba\u4eec\u5c31\u53ef\u4ee5\u4ece\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u4e2d\u63a8\u65ad\u51fa\u7cfb\u7edf\u7684\u6f14\u5316<\/strong>\u3002\u4f8b\u5982\uff0c\u8bb8\u591a\u6587\u732e\u4e2d\u6709\u7528\u4e8e\u7cfb\u7edf\u8bc6\u522b\u6216\u7f51\u7edc\u63a8\u65ad\u7684\u6280\u672f<\/span>\uff08\u5982\u6587\u732e[127-129]\u53ca\u5176\u53c2\u8003\u6587\u732e\uff09<\/span>\u3002\u5728\u4e0b\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u57fa\u4e8e\u7b97\u5b50\u7406\u8bba\u548c\u7a00\u758f\u8bc6\u522b\u6280\u672f\u7684\u6700\u65b0\u65b9\u6cd5\u3002<\/span><\/section>\n

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4. \u65b0\u8303\u5f0f\u548c\u5efa\u6a21\u6280\u672f<\/strong><\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n
 <\/span><\/section>\n
\u672c\u8282\u8ba8\u8bba\u5982\u4f55\u6539\u8fdb\u524d\u8ff0\u65b9\u6cd5\uff0c\u4f7f\u4e4b\u66f4\u9002\u5408\u771f\u5b9e\u7cfb\u7edf\u3002<\/span><\/section>\n
4.1 \u7f51\u7edc\u590d\u6742\u6027\u4f1a\u589e\u52a0\u591a\u5c11\uff1f<\/strong><\/span><\/section>\n
\u8fd1\u5e74\u6765\uff0c\u589e\u52a0\u7f51\u7edc\u590d\u6742\u6027\u4e00\u76f4\u662f\u7269\u7406\u5b66\u7814\u7a76\u7684\u7126\u70b9\u3002\u201c\u7f51\u7edc\u201d\u5728\u5f62\u5f0f\u4e0a\u7531\u5143\u7d20\u4e4b\u95f4\u7684\u6210\u5bf9\u4ea4\u4e92\u7684\u96c6\u5408\u7ec4\u6210\uff0c\u4f46\u662f\u771f\u5b9e\u7f51\u7edc\u4e2d\u7ecf\u5e38\u53ef\u4ee5\u627e\u5230\u8d85\u8d8a\u4e8c\u5143\u7684\u9ad8\u9636\u4ea4\u4e92\u4f5c\u7528\u3002\u4f8b\u5982\uff0c\u5728\u5316\u5b66\u53cd\u5e94\u7f51\u7edc\u4e2d\uff0c\u53cd\u5e94\u8fdb\u884c\u53ef\u80fd\u9700\u8981\u4e09\u79cd\u8bd5\u5242\uff1b\u5728\u5171\u540c\u4f5c\u8005\u7f51\u7edc\u4e2d\uff0c\u5e38\u6709\u591a\u4e2a\u4f5c\u8005\u3002\u6709\u4eba\u7528\u8d85\u56fe<\/span>\uff08hypergraphs\uff09<\/span>\u548c\u5355\u7eaf\u590d\u5f62<\/span>\uff08simplicial complexes\uff09<\/span>\u6765\u89e3\u51b3\u8fd9\u4e2a\u6311\u6218[130\uff0c131]\u3002\u8be5\u90e8\u5206\u524d\u6cbf\u8fdb\u5c55\u5305\u62ec\u5b9a\u4e49\u7edf\u8ba1\u7cfb\u7efc[132\uff0c133]\u3001\u5206\u6790\u53ef\u63a5\u53d7\u7684\u540c\u6b65\u6a21\u5f0f\u3001\u5b8c\u5168\u540c\u6b65[134 -136]\u548c\u96c6\u7fa4\u540c\u6b65[137\uff0c138]\u7684\u7a33\u5b9a\u6027\u4ee5\u53ca\u53ef\u63a7\u6027[139]\uff0c\u4f46\u76ee\u524d\u7279\u5b9a\u95ee\u9898\u7684\u63a7\u5236<\/span>\uff08ad hoc control\uff09<\/span>\u7b56\u7565\u5c1a\u672a\u5b8c\u5168\u5f00\u53d1\u3002<\/span><\/section>\n
\u540c\u6837\uff0c\u63d0\u4f9b\u7f51\u7edc\u52a8\u529b\u5b66\u7684\u77ac\u65f6\u63cf\u8ff0[140-141]\u7684\u6d3b\u52a8\u9a71\u52a8\u65f6\u5e8f\u7f51\u7edc<\/strong><\/span>\uff08activity-driven temporal networks\uff09<\/span>\u7684\u8303\u5f0f\u4e5f\u5bcc\u6709\u6210\u6548\u3002\u5728\u8fd9\u79cd\u65b9\u6cd5\u4e2d\uff0c\u6bcf\u4e2a\u8282\u70b9\u7684\u6d3b\u52a8\u6f5c\u529b<\/span>\uff08activity potential\uff09<\/span>\u662f\u6839\u636e\u8be5\u8282\u70b9\u76f8\u5bf9\u6d3b\u52a8\u7a0b\u5ea6\u6765\u786e\u5b9a\u7684\uff0c\u76f8\u5bf9\u6d3b\u52a8\u7a0b\u5ea6\u53ef\u4ee5\u4ece\u7ed9\u5b9a\u65f6\u95f4\u7a97\u7684\u65f6\u5e8f\u7f51\u7edc\u6570\u636e\u96c6\u4e2d\u6d4b\u51fa\uff0c\u6d3b\u52a8\u7535\u4f4d\u5206\u5e03\u51fd\u6570\u53ef\u4ee5\u8868\u5f81\u7cfb\u7edf\u7ea7\u52a8\u529b\u5b66\u3002<\/span><\/section>\n
\u771f\u5b9e\u4e16\u754c\u7cfb\u7edf\u901a\u5e38\u662f\u591a\u5c42\u7f51\u7edc<\/strong><\/span>\uff08multilayered networks\uff09<\/span>\u5f62\u5f0f\u7684\u3002\u4f8b\u5982\uff0c\u6bcf\u4e2a\u4eba\u6709\u8bb8\u591a\u79cd\u793e\u4f1a\u8eab\u4efd\uff0c\u5173\u952e\u57fa\u7840\u8bbe\u65bd\u7f51\u7edc\u901a\u5e38\u5177\u6709\u7269\u7406\u5206\u5c42\u6216\u903b\u8f91\u5206\u5c42\u7ed3\u6784\u3002\u8fd9\u4e00\u6982\u5ff5\u662f\u591a\u5c42\u7f51\u7edc\u7ed3\u6784\u63a7\u5236<\/span>\uff08structural control of multiplex networks\uff09<\/span>[142\u3001143]\u3001\u4f7f\u7528\u56fe\u8bba\u6355\u6349\u5206\u5c42\u5173\u952e\u57fa\u7840\u67b6\u6784[144\u3001145]\u548c\u4f7f\u7528\u591a\u91cd\u63a7\u5236\u7b56\u7565[146]\u7684\u57fa\u7840\u3002<\/span><\/section>\n
4.2 \u4eba\u4eec\u80fd\u63a7\u5236\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u6a21\u578b\u5417\uff1f<\/strong><\/span><\/section>\n
\u7edf\u8ba1\u7269\u7406\u5b66\u65b9\u6cd5\u503e\u5411\u4e8e\u5173\u6ce8\u5e73\u8861\u7cfb\u7edf\uff0c\u4f46\u5bf9\u4e8e\u7ec6\u81f4\u5e73\u8861<\/span>\uff08detailed balance\uff0c\u4e25\u683c\u70ed\u52a8\u5e73\u8861\uff09<\/span>\u7684\u7cfb\u7edf\u4ecd\u5b58\u5728\u6da8\u843d\u8017\u6563\u5173\u7cfb<\/span>\uff08fluctuation\u2013dissipation relations\uff09<\/span>\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u4f7f\u7528\u53cc\u91cf\u5b50\u70b9\u6a21\u578b<\/span>\uff08double quantum dot model\uff09<\/span>[147]\u4e0a\u7684\u53cd\u9988\u63a7\u5236\u65b9\u6848\u5c06\u70ed\u91cf\u8f6c\u6362\u4e3a\u529f\uff0c\u8fd9\u4e00\u53d1\u73b0\u6b63\u63a8\u52a8\u5173\u4e8e\u53cd\u9988\u63a7\u5236\u548c\u6da8\u843d<\/span>\u7684\u8fdb\u4e00\u6b65\u7814\u7a76[148]\u3002\u540c\u6837\uff0c\u6709\u51e0\u4e2a\u7ecf\u5178\u7684\u9a71\u52a8\u8fdc\u79bb\u5e73\u8861\u7cfb\u7edf\u7684\u6a21\u578b\uff0c\u5982\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027[42]<\/span>\uff08\u5728\u201c\u7edf\u8ba1\u7269\u7406\u65b9\u6cd5\u201d\u4e00\u8282\u6709\u53d9\u8ff0\uff09<\/span>\u3001Kardar-Parisi-Zhang<\/span>\uff08KPZ\uff09<\/span>\u65b9\u7a0b[149]\u548c\u4e0d\u5bf9\u79f0\u7b80\u5355\u6392\u65a5\u8fc7\u7a0b<\/span>\uff08ASEP\uff09<\/span>\u6a21\u578b[150]\u3002\u5c3d\u7ba1\u8fd9\u4e9b\u6a21\u578b\u4f34\u968f\u7740\u8bb8\u591a\u666e\u904d\u73b0\u8c61<\/span>\uff08\u7531\u4e00\u822c\u5c5e\u6027\u652f\u914d\uff0c\u4e00\u822c\u5c5e\u6027\u72ec\u7acb\u4e8e\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u7ec6\u8282\u7684\u57fa\u672c\u5bf9\u79f0\u6027\uff09<\/span>\uff0c\u4f46\u6211\u4eec\u4ecd\u53ef\u4ee5\u7528\u53cd\u9988\u6765\u5f71\u54cd\u548c\u63a7\u5236\u884c\u4e3a\u3002<\/span><\/section>\n
4.3 \u7ed3\u6784\u63a7\u5236\u6846\u67b6\u8f83\u7ebf\u6027\u6a21\u578b\u597d\u591a\u5c11\uff1f<\/strong><\/span><\/section>\n
\u7ed3\u6784\u63a7\u5236\u7684\u7ecf\u5178\u6846\u67b6\u4e2d\u6709\u4e00\u4e2a\u57fa\u672c\u9650\u5236\uff1a\u57fa\u4e8e\u7ebf\u6027\u975e\u65f6\u53d8\u52a8\u529b\u5b66\u3002<\/span><\/section>\n
<\/section>\n
\u5176\u4e2dA,B\u4e2d\u7684\u5143\u7d20\u90fd\u662f\u96f6\u6216\u72ec\u7acb\u7684\u81ea\u7531\u53c2\u6570\u3002\u8fd9\u4e2a\u6846\u67b6\u57fa\u4e8e\u7ebf\u6027\u7cfb\u7edf\u7684\u7ed3\u6784\u53ef\u63a7\u6027\u7684\u6982\u5ff5\u3002\u5982\u679c\u6211\u4eec\u8bf4\u7cfb\u7edf\uff08A,B\uff09\u662f\u7ed3\u6784\u53ef\u63a7<\/strong>\u7684\uff0c\u90a3\u5c31\u662f\u8bf4\uff0c\u53ef\u4ee5\u5728A,B\u4e2d\u8bbe\u7f6e\u7279\u5b9a\u975e\u96f6\u5143\u7d20\uff0c\u4f7f\u5f97\u7cfb\u7edf\u53ef\u63a7\u3002\u8fd9\u9700\u8981\u6ee1\u8db3\u5361\u592b\u66fc\u53ef\u63a7\u6027\u5224\u636e<\/span>\uff08Kalman\u2019s criterion of controllability\uff09<\/span>\uff1a<\/span><\/section>\n
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\u6700\u8fd1\uff0c\u6709\u5b66\u8005\u5728\u7ed3\u6784\u63a7\u5236\u6846\u67b6\u7684\u57fa\u7840\u4e0a\u63d0\u51fa\u4e86\u975e\u7ebf\u6027\u7cfb\u7edf\u7ed3\u6784\u53ef\u8fbe\u6027<\/strong>\uff08structural accessibility\uff09<\/span>\u7684\u6982\u5ff5[151-152]\uff0c\u5e76\u5c06\u5176\u9002\u7528\u4e8e\u4e00\u822c\u975e\u7ebf\u6027\u7cfb\u7edf\uff1a<\/span><\/section>\n
<\/section>\n
\u52a8\u529b\u5b66\u5047\u8bbe\u7684\u6761\u4ef6\u4e0d\u4e25\uff0c\u8981\u6c42f(x(t))\u548cg(x(t))\u662f\u4e9a\u7eaf\u51fd\u6570<\/span>\uff08meromorphic functions\uff09<\/span>\u3002\u4e9a\u7eaf\u51fd\u6570\u4e00\u8bcd\u6e90\u4e8e\u5e0c\u814a\u8bed<\/span> (meros<\/em>)<\/span>\uff0c\u5b9a\u4e49\u4e3a\u4e24\u4e2a\u6574\u51fd\u6570\u4e4b\u6bd4\uff0c\u53ea\u6709\u6709\u9650\u9636\u3001\u5b64\u7acb\u7684\u6781\u70b9\u548c\u96f6\u70b9\uff0c\u65e0\u975e\u5fc5\u8981\u5947\u70b9\u3002\u7ed3\u6784\u53ef\u8fbe\u6027\u7684\u6982\u5ff5\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u7ebf\u6027\u7cfb\u7edf\u4e2d\u7ed3\u6784\u53ef\u63a7\u6027\u7684\u975e\u7ebf\u6027\u63a8\u5e7f\u3002\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c\u7ed3\u6784\u53ef\u8fbe\u6027\u548c\u7ed3\u6784\u53ef\u63a7\u6027\u51e0\u4e4e\u6709\u76f8\u540c\u7684\u56fe\u8bba\u6761\u4ef6\u3002\u4e8c\u8005\u5173\u952e\u533a\u522b\u662f\uff0c\u201c\u81ea\u5faa\u73af\u201d<\/span>\uff08\u5bf9\u5e94\u5185\u7980\u8282\u70b9\u52a8\u529b\u5b66\uff09<\/span>\u662f\u7ed3\u6784\u53ef\u63a7\u6027\u7684\u56fe\u8bba\u5145\u5206\u6761\u4ef6\uff0c\u800c\u975e\u7ed3\u6784\u53ef\u8fbe\u6027\u7684\u5145\u5206\u6761\u4ef6\u3002\u8fd9\u79cd\u7ed3\u6784\u53ef\u8fbe\u6027\u6846\u67b6\u53ef\u4ee5\u4ece\u5e95\u5c42\u7f51\u7edc\u7ed3\u6784\u4e2d\u8bc6\u522b\u9a71\u52a8\u8282\u70b9[151]\uff0c\u5e76\u5df2\u5728\u751f\u6001\u548c\u751f\u5316\u7cfb\u7edf\u4e2d\u5f97\u5230\u4e86\u5e94\u7528\u3002<\/span><\/section>\n
4.4 \u5982\u4f55\u5904\u7406\u5927\u578b\u590d\u6742\u7684\u591a\u667a\u80fd\u4f53\u7cfb\u7edf\uff1f<\/strong><\/span><\/section>\n
\u53e6\u4e00\u4e2a\u7d27\u8feb\u7684\u4f17\u6240\u5468\u77e5\u7684\u63a7\u5236\u96be\u9898\u662f\uff0c\u5982\u4f55\u89e3\u51b3\u590d\u6742\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u7684\u8282\u70b9\u6570\u76ee\u9650\u5236\uff1f\u6216\u8005\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u8ba9\u7cfb\u7edf\u51fa\u73b0\u6d8c\u73b0\u884c\u4e3a\u65f6\u8282\u70b9\u6570\u76ee\u4ecd\u4fdd\u6301\u4e0d\u53d8\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u95ee\u9898\u5c31\u53d8\u6210\u4e86\uff1a\u627e\u5230\u4e00\u4e2a\u5bf9\u76ee\u6807\u53ef\u89c2\u6d4b\u91cf<\/span>\uff08\u6211\u4eec\u5e0c\u671b\u63a7\u5236\u7684\uff09<\/span>\u7684\u5b8f\u89c2\u63cf\u8ff0\u3002\u8fd9\u6837\u505a\u9700\u8981\u76ee\u6807\u53d8\u91cf\u5728\u5b8f\u89c2\u5c3a\u5ea6<\/strong>\u548c\u88ab\u63a7\u5fae\u89c2\u4e2a\u4f53\u5c42\u9762\u7684\u95ed\u5faa\u73af<\/strong>\u3002\u5bf9\u4e8e\u6781\u5176\u590d\u6742\u548c\u5927\u578b\u7684\u7f51\u7edc\uff0c\u5373\u4f7f\u662f\u7ebf\u6027\u65f6\u53d8\u7684\u7cfb\u7edf\uff0c\u90fd\u5f88\u96be\u5b9e\u73b0\u9664\u4e86\u8bc6\u522b\u9a71\u52a8\u8282\u70b9\u4e4b\u5916\u7684\u4efb\u4f55\u63a7\u5236\u76ee\u6807\u3002<\/span><\/section>\n
\u8fde\u7eed\u5316<\/span>\uff08continuification or continuation\uff09<\/span>\u65b9\u6cd5[153\uff0c154]\u5c06\u7531\u5927\u91cf\u5e38\u5fae\u5206\u65b9\u7a0b\u63cf\u8ff0\u7684\u5fae\u89c2\u95ee\u9898\uff0c<\/strong>\u8f6c\u5316\u4e3a\u63cf\u8ff0\u5b8f\u89c2\u6c34\u5e73\u4e0a\u76ee\u6807\u53ef\u89c2\u6d4b\u91cf\u7684\u504f\u5fae\u5206\u65b9\u7a0b<\/strong><\/span>\uff08PDE\uff09\uff08\u8fde\u7eed\u5316\u9636\u6bb5\uff09<\/span>\u3002\u7136\u540e\uff0c\u4f7f\u7528\u63a7\u5236\u504f\u5fae\u5206\u65b9\u7a0b[155\u3001156]\u7684\u6280\u672f\u6765\u8bbe\u8ba1\u5b8f\u89c2\u63a7\u5236\u52a8\u4f5c\uff0c\u5e76\u4e14\u6700\u7ec8\u5c06\u6240\u5f97\u7684\u63a7\u5236\u5f8b\u79bb\u6563\u5316\uff0c\u4f7f\u5f97\u5176\u53ef\u4ee5\u88ab\u90e8\u7f72\u56de\u5230\u5fae\u89c2\u4e2a\u4f53\u7ea7\u522b[157]\u3002\u5728\u8fd9\u79cd\u65b9\u6cd5\u4e2d\uff0c\u6311\u6218\u5c31\u8f6c\u53d8\u6210\u4e86\u5bfb\u627e\u8fde\u7eed\u5316\u76ee\u6807\u95ee\u9898\u7136\u540e\u79bb\u6563\u5316<\/strong>\u7684\u65b9\u6cd5\uff0c\u5728\u5fae\u89c2\u6c34\u5e73\u4e0a\u8fdb\u884c\u5206\u5e03\u5f0f\u63a7\u5236\u7b56\u7565\u3002\u7136\u800c\u4e3b\u8981\u969c\u788d\u662f\u5f53\u4ecePDE\u5f97\u5230\u7684\u63a7\u5236\u5f8b\u88ab\u79bb\u6563\u5316\u65f6\uff0c\u5927\u591a\u6570\u5fae\u89c2\u4e2a\u4f53\u901a\u5e38\u4f1a\u53d7\u5230\u63a7\u5236\u8f93\u5165\u7684\u5f71\u54cd\uff0c\u8fd9\u4e0e\u7275\u5236\u63a7\u5236\u7684\u601d\u60f3<\/span>\uff08\u63a7\u5236\u5c11\u7684\u8282\u70b9\u5b9e\u73b0\u76ee\u6807\uff09<\/span>\u76f8\u53cd\u3002<\/span><\/section>\n
\u53e6\u4e00\u4e2a\u6846\u67b6\u662f\u57fa\u4e8e\u7ebf\u6027\u7cfb\u7edf\u7684\u5927\u89c4\u6a21\u7f51\u7edc\u7684\u56fe\u5b50\u63a7\u5236<\/strong><\/span>\uff08graphon control\uff09<\/span>[158]\u3002\u56fe\u5b50<\/span>\uff08graphon\uff09<\/span>\u662f\u6536\u655b\u56fe\u5e8f\u5217\u7684\u6781\u9650\uff0c\u5f62\u6210\u4e86\u4e00\u79cd\u81ea\u7136\u7684\u975e\u53c2\u6570\u65b9\u6cd5\u6765\u5efa\u6a21\u548c\u4f30\u8ba1\u8d85\u5927\u578b\u7f51\u7edc[159]\u3002\u7531\u4e8e\u5176\u4e0e\u7edf\u8ba1\u7269\u7406\u3001\u6781\u503c\u7ec4\u5408\u5b66\u548c\u7f51\u7edc\u4e0a\u7684\u975e\u53c2\u6570\u7edf\u8ba1\u5206\u6790\u7684\u8054\u7cfb\u88ab\u5e7f\u6cdb\u8ba8\u8bba[160 -162]\uff0c\u56fe\u5b50\u7406\u8bba<\/span>\uff08Graphon theory\uff09<\/span>\u5df2\u7ecf\u6210\u4e3a\u56fe\u8bba\u7684\u4e00\u4e2a\u5b50\u9886\u57df\u3002<\/span><\/section>\n
\u57fa\u4e8e\u56fe\u5b50\u7684\u63a7\u5236\u590d\u6742\u5927\u578b\u7f51\u7edc\u7cfb\u7edf\u7684\u7b56\u7565\u7531\u4e09\u4e2a\u6b65\u9aa4\u7ec4\u6210\uff1a<\/span><\/section>\n
\u4e00\u3001\u5f53\u8282\u70b9\u6570\u8d8b\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c\u9996\u5148\u786e\u5b9a\u6709\u9650\u7f51\u7edc\u7cfb\u7edf\u5e8f\u5217S\u7684\u56fe\u5b50\u6781\u9650\u3002<\/span><\/section>\n
\u4e8c\u3001\u5728\u6b64\u7ea6\u675f\u4e0b\u89e3\u51b3\u76f8\u5e94\u7684\u63a7\u5236\u95ee\u9898\u3002<\/span><\/section>\n
\u4e09\u3001\u901a\u8fc7\u903c\u8fd1\u6781\u9650\u7cfb\u7edf\u7684\u63a7\u5236\u5f8b\uff0c\u751f\u6210\u6cbf\u7740\u6709\u9650\u7f51\u7edc\u7cfb\u7edf\u7684\u5e8f\u5217S\u7684\u4efb\u4f55\u7cfb\u7edf\u7684\u63a7\u5236\u5f8b\u3002<\/span><\/section>\n
\u8be5\u7b56\u7565\u5df2\u88ab\u7528\u4e8e\u5927\u89c4\u6a21\u590d\u6742\u7f51\u7edc\u7684\u72b6\u6001\u63a7\u5236\u95ee\u9898\u548c\u7ebf\u6027\u4e8c\u6b21\u578b\u8c03\u8282\u5668\u95ee\u9898\u3002<\/span><\/section>\n
\u56fe\u5b50\u535a\u5f08<\/span>\uff08graphon games\uff09<\/span>\u7684\u6982\u5ff5\u6e90\u4e8e\u7f51\u7edc\u535a\u5f08\u548c\u5e72\u9884\u7684\u7edf\u8ba1\u6846\u67b6\u3002\u6b64\u6846\u67b6\u662f\u7528\u56fe\u5b50\u7406\u8bba\u7814\u7a76\u5927\u578b\u7f51\u7edc\u5e72\u9884\u7684\u53e6\u4e00\u5178\u4f8b\u3002\u4f46\u5982\u4f55\u5229\u7528\u56fe\u5b50\u7406\u8bba\u6765\u63a7\u5236\u5177\u6709\u4e00\u822c\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7684\u4efb\u610f\u5927\u7f51\u7edc\u4ecd\u6709\u5f85\u89e3\u51b3\u3002<\/span><\/section>\n
\u968f\u7740\u7814\u7a76\u6e10\u6e10\u5f00\u59cb\u9762\u5411\u66f4\u5927\u89c4\u6a21\u7684\u7f51\u7edc\uff0c\u901a\u8fc7\u63a7\u5236\u548c\u89c2\u5bdf\u4ecb\u89c2\u5c3a\u5ea6\u6765\u63a7\u5236\u76ee\u6807\u590d\u6742\u7f51\u7edc\u7684\u95ee\u9898\u53d8\u5f97\u6108\u53d1\u91cd\u8981\uff0c\u8fd9\u6837\u7684\u4ecb\u89c2\u5c3a\u5ea6\u53ef\u4ee5\u662f\u7fa4\u4f53\u6216\u8282\u70b9\u6216\u8fde\u8fb9\u7684\u96c6\u7fa4\u6c34\u5e73\u3002\u8fd9\u4e2a\u65b9\u5411\u6709\u5f85\u8fdb\u4e00\u6b65\u7814\u7a76\uff0c\u5e76\u4e14\u9700\u8981\u4ece\u63a7\u5236\u7684\u89c2\u70b9\u6765\u5b9a\u4e49\u9002\u5f53\u7684\u4ecb\u89c2\u5c42\u6b21\u3002<\/span><\/section>\n
4.5 \u6211\u4eec\u80fd\u7528\u6570\u636e\u91cd\u6784\u8fd0\u52a8\u65b9\u7a0b\u5417\uff1f<\/strong><\/span><\/section>\n
\u9664\u4e86\u6210\u719f\u7684\u7cfb\u7edf\u8bc6\u522b<\/span>\uff08system identification\uff09<\/span>\u65b9\u6cd5\u4e4b\u5916\uff0c\u8fd8\u6709\u5176\u4ed6\u7684\u65b9\u6cd5\u53ef\u4ee5\u91cd\u5efa\u6709\u6548\u7684\u8fd0\u52a8\u65b9\u7a0b<\/strong>\u3002<\/span><\/section>\n
Koopman\u7b97\u5b50\u65b9\u6cd5\u5c31\u662f\u5176\u4e2d\u4e00\u79cd\u3002\u5b83\u662f\u5bf9\u53ef\u89c2\u6d4b\u5411\u91cf\u7a7a\u95f4\u7684\u7ebf\u6027\u53d8\u6362<\/strong>\uff0c\u7528\u8457\u540d\u7684Koopman\u7b97\u5b50\u7684\u7279\u5f81\u51fd\u6570\u5c06\u5176\u8868\u793a\u4e3a\u7ebf\u6027\u5c55\u5f00\u5f0f\uff0c\u4ee5\u5b9e\u73b0\u4ece\u65e0\u9650\u7ef4\u7684\u89c2\u6d4b\u7a7a\u95f4\u5230\u7ebf\u6027\u7684\u6f14\u5316\u3002\u4e0d\u7a33\u5b9a\u6027\u4e0e\u5177\u6709\u6b63\u672c\u5f81\u503c\u7684\u6a21\u5f0f\u6709\u5173\uff0c\u751a\u81f3\u53ef\u4ee5\u901a\u8fc7\u76f8\u5173\u8054\u7684\u672c\u5f81\u5411\u91cf\u4e2d\u7684\u76f8\u5bf9\u632f\u5e45\u6765\u8bc6\u522b\u5404\u4e2a\u8282\u70b9\u5728\u4e0d\u7a33\u5b9a\u6027\u4e2d\u7684\u4f5c\u7528\u3002Koopman\u7b97\u5b50\u7528\u4e8e\u52a8\u529b\u7cfb\u7edf\u5206\u6790\u7684\u80fd\u529b\u5df2\u7ecf\u6bcb\u5eb8\u7f6e\u7591[164\uff0c165]\uff0c\u5e76\u4e14\u4e5f\u53ef\u4ee5\u5e94\u7528\u4e8e\u975e\u7ebf\u6027\u6d41[166]\u4e2d\uff0c\u4f8b\u5982\u8fd1\u671f\u5728\u5e94\u7528\u6700\u4f18\u63a7\u5236\u5668[167\uff0c168]\u548c\u53cd\u9988\u63a7\u5236[169 -171]\u7684\u65b9\u6cd5\u4e2d\u6548\u679c\u663e\u8457\u3002\u53c2\u8003\u6587\u732e[172]\u662f\u4e00\u672c\u5b9e\u7528\u7684\u5165\u95e8\u4e66\uff0c\u53c2\u8003\u6587\u732e[173\uff0c174]\u4ecb\u7ecd\u4e86\u6700\u8fd1\u7684\u4e24\u4e2a\u7efc\u5408\u5e94\u7528\u3002<\/span><\/section>\n
\u53e6\u4e00\u79cd\u4e0d\u540c\u7684\u6570\u636e\u9a71\u52a8\u65b9\u6cd5\u4f9d\u8d56\u4e8e\u8fd9\u6837\u7684\u5047\u8bbe\u2014\u2014\u5c3d\u7ba1\u6570\u636e\u662f\u9ad8\u7ef4\u7684\uff0c\u4f46\u52a8\u529b\u5b66\u4e3b\u8981\u53ea\u53d7\u51e0\u4e2a\u4e3b\u8981\u53d8\u91cf\u7684\u5f71\u54cd\uff0c\u4f7f\u5f97\u65b9\u7a0b\u5728\u53ef\u80fd\u7684\u51fd\u6570\u7a7a\u95f4\u4e2d\u662f\u7a00\u758f\u7684<\/strong>\u3002\u7a00\u758f\u6027\u4fc3\u8fdb\u6280\u672f\u548c\u673a\u5668\u5b66\u4e60\u53ef\u4ee5\u5728\u6709\u566a\u58f0\u7684\u6d4b\u91cf\u6570\u636e\u4e0a\u7ec4\u5408\u4f7f\u7528\u4ee5\u8bc6\u522b\u63a7\u5236\u65b9\u7a0b\uff0c\u8fd9\u662f\u4e00\u79cd\u88ab\u79f0\u4e3a\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7684\u7a00\u758f\u8bc6\u522b<\/span>\uff08sparse identification of nonlinear dynamics\uff0cSINDY\uff09<\/span>[175]\u7684\u6280\u672f\u3002SINDY\u5df2\u88ab\u6269\u5c55\u5230\u5305\u62ec\u9a71\u52a8\u7684\u5f71\u54cd\uff0c\u5e76\u4e14\u80fd\u663e\u793a\u5982\u4f55\u57fa\u4e8e\u6709\u9650\u7684\u566a\u58f0\u6570\u636e\u589e\u5f3a\u6a21\u578b\u9884\u6d4b\u63a7\u5236\u7684\u6027\u80fd[176]\u3002<\/span><\/section>\n
\u6211\u4eec\u5e38\u7528\u964d\u7ef4\u6280\u672f\u5c06\u9ad8\u7ef4\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u6620\u5c04\u5230\u4f4e\u7ef4\u5b50\u7a7a\u95f4\uff0c\u7136\u540e\u7528\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7684\u7a00\u758f\u8bc6\u522b<\/span>\uff08SINDY\uff09<\/span>\u6765\u786e\u5b9a\u5931\u53bb\u7684\u52a8\u529b\u5b66\u4fe1\u606f\u3002<\/span><\/section>\n
\u5982\u679c\u6240\u5f97\u5230\u7684\u76f8\u7a7a\u95f4\u7531\u51e0\u4e2a\u56fa\u5b9a\u70b9\u7ec4\u6210\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8c03\u8282\u7cfb\u7edf\uff0c\u8bf1\u5bfc\u671f\u671b\u7684\u4e0d\u7a33\u5b9a\u6027\u548c\u5438\u5f15\u5b50\uff0c\u4ece\u800c\u5b9e\u73b0\u9ad8\u7ef4\u3001\u975e\u7ebf\u6027\u3001\u7f51\u7edc\u7cfb\u7edf\u7684\u524d\u9988\u63a7\u5236[177]\u3002<\/span><\/section>\n


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4.6 \u5982\u4f55\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u548c\u6570\u636e\u9a71\u52a8\u7684\u63a7\u5236\u65b9\u6cd5\u6765\u5f81\u670d\u590d\u6742\u6027\uff1f<\/strong>
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5. \u7814\u7a76\u6307\u5357<\/strong><\/strong><\/strong><\/p>\n<\/section>\n

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\u8981\u60f3\u63a8\u8fdb\u524d\u6cbf\u548c\u89e3\u51b3\u5b9e\u9645\u95ee\u9898\uff0c\u5c31\u9700\u8981\u63a8\u8fdb\u591a\u5b66\u79d1\u548c\u4ea4\u53c9\u5b66\u79d1\u7684\u7814\u7a76\u3002\u4e0d\u4ec5\u8981\u5f81\u670d\u590d\u6742\u6027\uff0c\u8fd8\u8981\u987a\u52bf\u5229\u7528\u5b83\uff0c\u6765\u5b9e\u73b0\u66f4\u597d\u7684\u63a7\u5236\u6027\u80fd\u3001\u6765\u89e3\u51b3\u66f4\u590d\u6742\u7684\u95ee\u9898\u3002\u7814\u7a76\u76ee\u6807\u5e94\u8be5\u662f\u53cc\u91cd\u7684\uff1a<\/span><\/section>\n
\u7b2c\u4e00\uff0c\u8981\u5f25\u8865\u5b66\u79d1\u4e4b\u95f4\u5dee\u8ddd\uff0c\u5c06\u5e73\u5747\u573a\u65b9\u6cd5\u7b49\u6280\u672f\u7684\u4f7f\u7528\u6269\u5c55\u5230\u590d\u6742\u7f51\u7edc\u7684\u63a7\u5236<\/strong>\u4e2d\u53bb<\/strong>[182]<\/span>\u3002\u540c\u65f6\uff0c\u8981\u8003\u8651\u5230\u73b0\u5b9e\u7684\u7ea6\u675f\u6761\u4ef6\u548c\u5b9e\u73b0\u53cd\u9988\u7b56\u7565\u7684\u9700\u8981\uff0c\u4ee5\u4fdd\u8bc1\u7814\u7a76\u95ee\u9898\u6240\u9700\u7684\u7a33\u5b9a\u6027\u3001\u76ee\u6807\u6027\u80fd\u548c\u9c81\u68d2\u6027\u3002<\/span><\/section>\n
\u7b2c\u4e8c\uff0c\u786e\u5b9a\u4e00\u7ec4\u8303\u4f8b\u95ee\u9898\u6216\u6807\u51c6\u6848\u4f8b\u7528\u4e8e\u9a8c\u8bc1\u548c\u5bf9\u6bd4\u63a7\u5236\u590d\u6742\u7cfb\u7edf\u7684\u4e0d\u540c\u65b9\u6cd5<\/strong>\u3002\u8fd9\u6837\u505a\u975e\u5e38\u91cd\u8981\uff0c\u56e0\u4e3a\u5728\u8bb8\u591a\u4e0d\u540c\u9886\u57df\u4e2d\u51fa\u73b0\u7684\u5e94\u7528\u7a0b\u5e8f\u548c\u5728\u7279\u5b9a\u9886\u57df\u4e2d\u5f00\u53d1\u7684\u6280\u672f\u53ef\u4ee5\u88ab\u62bd\u8c61\u4ee5\u89e3\u51b3\u66f4\u4e00\u822c\u7684\u95ee\u9898\u3002\u4f8b\u5982\u5206\u6790\u975e\u7ebf\u6027\u632f\u8361\u5668<\/span>\uff08\u5982\u795e\u7ecf\u5143\uff09<\/span>\u7684\u52a8\u529b\u5b66\u76f8\u4f4d\u54cd\u5e94\u66f2\u7ebf\u6280\u672f\uff0c\u6700\u8fd1\u5c31\u6709\u4eba\u5229\u7528\u5b83\u6765\u5b9e\u73b0\u66f4\u666e\u904d\u7c7b\u522b\u7684\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u63a7\u5236<\/span>\uff08\u89c1\u53c2\u8003\u6587\u732e[183]\u548c\u5176\u4e2d\u7684\u53c2\u8003\u6587\u732e\uff09<\/span>\u3002<\/span><\/section>\n
\u4e3a\u4e86\u63a8\u52a8\u8fd9\u4e00\u9886\u57df\u7684\u53d1\u5c55\u5e76\u4fc3\u8fdb\u8de8\u5b66\u79d1\u7684\u5408\u4f5c\uff0c\u6211\u4eec\u9700\u8981\u96c6\u4f53\u5171\u540c\u52aa\u529b\u3002\u4e3a\u89e3\u51b3\u63a7\u5236\u590d\u6742\u7cfb\u7edf\u7684\u57fa\u672c\u95ee\u9898\uff0c\u7b2c\u4e00\u4e2a\u547c\u5401\u5c31\u662f\uff1a\u53d1\u8d77\u4e00\u7cfb\u5217\u9488\u5bf9\u6807\u51c6\u65b9\u6cd5\u7684\u6311\u6218\uff01<\/strong>\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u9886\u57df\uff0c\u4e3e\u884c\u6311\u6218\u8d5b\u5df2\u7ecf\u6210\u4e3a\u4e00\u79cd\u4f20\u7edf\u3002\u76ee\u524d\u5df2\u7ecf\u6709\u4e00\u7cfb\u5217\u6210\u529f\u7684\u6311\u6218\u8d5b\uff0c\u5982\u5fae\u8f6f\u60f3\u8c61\u676f\u3001\u8c37\u6b4c\u4eba\u5de5\u667a\u80fd\u6311\u6218\u8d5b\u3001ImageNet\u6311\u6218\u8d5b\u548cNetflix\u5956\u7b49\u7b49\u3002\u53ef\u4ee5\u8bf4\uff0c\u8fd9\u4e9b\u6311\u6218<\/span>\uff08\u5982ImageNet\u6311\u6218\uff09<\/span>\u4fc3\u8fdb\u4e86\u5f53\u4eca\u7684\u4eba\u5de5\u667a\u80fd\u7684\u7e41\u8363\u3002\u540c\u6837\u5730\uff0c\u5728\u7cfb\u7edf\u751f\u7269\u5b66\u548c\u533b\u5b66\u9886\u57df\uff0c\u4e5f\u6709\u4e00\u4e2a\u5f88\u597d\u7684\u6311\u6218\u8d5b\u699c\u6837\uff0c\u5373\u68a6\u60f3\u6311\u6218\u8d5b<\/span>\uff08DREAM challenges\uff09<\/span>\u3002\u8be5\u6bd4\u8d5b\u63d0\u4f9b\u9ad8\u8d28\u91cf\u7684\u751f\u7269\u533b\u5b66\u6807\u51c6\u6570\u636e\u96c6\uff0c\u9080\u8bf7\u53c2\u4e0e\u8005\u9488\u5bf9\u6307\u5b9a\u95ee\u9898\u63d0\u51fa\u89e3\u51b3\u65b9\u6848\uff0c\u4fc3\u8fdb\u4ea4\u6d41\u5e76\u5728\u6b64\u8fc7\u7a0b\u4e2d\u5efa\u7acb\u5408\u4f5c\u56e2\u4f53\u3002\u7f51\u7edc\u63a7\u5236\u9886\u57df\u7684\u7814\u7a76\u4eba\u5458\u4e5f\u53ef\u4ee5\u4ece\u5176\u4ed6\u9886\u57df\u73b0\u6709\u7684\u6311\u6218\u5e73\u53f0\u4e2d\u5b66\u4e60\uff0c\u4ee5\u8fdb\u4e00\u6b65\u63a8\u8fdb\u9886\u57df\u524d\u6cbf\uff0c\u8ba9\u201c\u7fa4\u4f17\u7684\u667a\u6167\u201d\u53d1\u6325\u5bf9\u51fa\u6700\u5927\u7684\u79d1\u5b66\u6548\u76ca\u3002<\/span><\/section>\n
\u7531\u4e8e\u63a7\u5236\u590d\u6742\u7cfb\u7edf\u5177\u6709\u591a\u5b66\u79d1\u6027\u8d28\uff0c\u6311\u6218\u4e0d\u5fc5\u96c6\u4e2d\u5728\u7eaf\u7406\u8bba\u95ee\u9898\u4e0a\uff0c\u4e5f\u53ef\u4ee5\u662f\u5e94\u7528\u751a\u81f3\u662f\u8f6c\u5316\u3002<\/strong>\u4f8b\u5982\uff0c\u6709\u4eba\u8bd5\u56fe\u5bf9\u5b9a\u5411\u4eba\u7c7b\u86cb\u767d\u8d28\u76f8\u4e92\u4f5c\u7528\u7f51\u7edc\u8fdb\u884c\u7ed3\u6784\u53ef\u63a7\u6027\u5206\u6790\uff0c\u4ee5\u9274\u5b9a\u75be\u75c5\u57fa\u56e0\u548c\u836f\u7269\u9776\u70b9[184]\uff0c\u867d\u7136\u8fd9\u65b9\u9762\u7684\u7814\u7a76\u8fd8\u6709\u5f85\u8fdb\u4e00\u6b65\u6df1\u5165\u3002\u6b64\u5916\uff0c\u4e3a\u4e86\u8bbe\u8ba1\u66f4\u597d\u5730\u64cd\u7eb5\u4eba\u7c7b\u80a0\u9053\u5fae\u751f\u7269\u7ec4\u7684\u65b9\u6cd5\uff0c\u63a7\u5236\u7406\u8bba\u4e5f\u80fd\u6709\u8bb8\u591a\u6f5c\u5728\u7684\u5e94\u7528<\/span>\uff08\u4eba\u7c7b\u5185\u90e8\u751f\u6001\u7cfb\u7edf\u7531\u6570\u4e07\u4ebf\u5fae\u751f\u7269\u7ec4\u6210\uff0c\u76f8\u4e92\u4f5c\u7528\u65b9\u5f0f\u5f88\u590d\u6742\uff09<\/span>[185]\u3002\u8b6c\u5982\uff0c\u5728\u8be5\u9886\u57df\u4e2d\u4e00\u4e2a\u975e\u5e38\u5b9e\u9645\u7684\u63a7\u5236\u95ee\u9898\u662f\u8bbe\u8ba1\u660e\u786e\u5b9a\u4e49\u7684\u6d3b\u805a\u751f\u4f53\u7ec4<\/span>\uff08consortium of live microorganisms\uff09\uff08\u901a\u5e38\u53eb\u505a\u76ca\u751f\u83cc\u6df7\u5408\u7269\u3001\u7ec6\u83cc\uff0c\u5373\u836f\u7269\u6216\u6d3b\u751f\u7269\u6cbb\u7597\u4ea7\u54c1\uff09<\/span>\u4ee5\u9632\u6b62\u67d0\u4e9b\u75c5\u539f\u4f53\u5bc4\u8eab\uff0c\u4ece\u800c\u9884\u9632\u611f\u67d3[186]\u3002\u6b64\u5916\uff0c\u6807\u51c6\u6d4b\u8bd5\u65b9\u6cd5<\/span>\uff08benchmarking methods\uff09<\/span>\u8fd8\u53ef\u4ee5\u7528\u4e8e\u4fdd\u62a4\u548c\u63a7\u5236\u5fae\u578b\u7535\u7f51<\/span>\uff08microgrids\uff0c\u5373\u5177\u6709\u786e\u5b9a\u7535\u8fb9\u754c\u7684\u672c\u5730\u7535\u7f51\uff0c\u5145\u5f53\u5355\u4e2a\u548c\u53ef\u63a7\u7684\u5b9e\u4f53\uff09<\/span>[187]\u3002<\/span><\/section>\n
\u603b\u4e4b\uff0c\u6211\u4eec\u7684\u6700\u7ec8\u76ee\u6807\u662f\u5c06\u6765\u81ea\u4e0d\u540c\u79d1\u5b66\u6280\u672f\u9886\u57df\u7684\u5de5\u5177\u548c\u6280\u672f\u7ed3\u5408\u8d77\u6765\uff0c\u89e3\u51b3\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u95ed\u5408\u63a7\u5236\u56de\u8def\u7684\u5173\u952e\u95ee\u9898\uff0c\u4ece\u800c\u534f\u8c03\u5927\u89c4\u6a21\u590d\u6742\u7cfb\u7edf\u7684\u96c6\u4f53\u884c\u4e3a\uff0c\u8fd9\u5c06\u4f1a\u5bf9\u5927\u91cf\u4ea4\u53c9\u5b66\u79d1\u7684\u5e94\u7528\u4ea7\u751f\u6781\u5927\u5f71\u54cd\u3002<\/span><\/section>\n

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\u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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    Liu, Y.-Y., Slotine, J.-J. & Barab\u00e1si, A.-L. Controllability of complex networks. Nature 473,<\/section>\n<\/li>\n<\/ol>\n
    167\u2013173 (2011).<\/span><\/section>\n
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      Lin, C.-T. Structural controllability. IEEE Trans. Autom. Control. 19, 201 (1974).<\/section>\n<\/li>\n
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      Liu, Y. Y., Csoka, E., Zhou, H. & Posfai, M. Core percolation on complex networks.<\/section>\n<\/li>\n<\/ol>\n
      Phys. Rev. Lett. 109, 205703 (2012).<\/span><\/section>\n
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        Jia, T. et al. Emergence of bimodality in controlling complex networks. Nat. Commun. 4,<\/section>\n<\/li>\n<\/ol>\n
        2002 (2013).<\/span><\/section>\n
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                                                                                                                                                                                                                                                                                                                                                        \u4e3a\u4e86\u63a2\u8ba8\u56fe\u795e\u7ecf\u7f51\u7edc\u5728\u7b97\u6cd5\u795e\u7ecf\u5316\u6c42\u89e3\u7684\u53d1\u5c55\u4e0e\u73b0\u5b9e\u5e94\u7528\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u56fd\u9632\u79d1\u6280\u5927\u5b66\u7cfb\u7edf\u5de5\u7a0b\u5b66\u9662\u526f\u6559\u6388\u8303\u957f\u4fca\u3001\u4e2d\u56fd\u4eba\u6c11\u5927\u5b66\u9ad8\u74f4\u4eba\u5de5\u667a\u80fd\u5b66\u9662\u52a9\u7406\u6559\u6388\u9ec4\u6587\u70b3\uff0c\u5171\u540c\u53d1\u8d77\u300c\u56fe\u795e\u7ecf\u7f51\u7edc\u4e0e\u7ec4\u5408\u4f18\u5316<\/a>\u300d\u8bfb\u4e66\u4f1a\u3002\u8bfb\u4e66\u4f1a\u5c06\u805a\u7126\u4e8e\u56fe\u795e\u7ecf\u7f51\u7edc\u4e0e\u7b97\u6cd5\u795e\u7ecf\u5316\u6c42\u89e3\u7684\u76f8\u5173\u9886\u57df\uff0c\u5305\u62ec\u795e\u7ecf\u7b97\u6cd5\u63a8\u7406\u3001\u7ec4\u5408\u4f18\u5316\u95ee\u9898\u6c42\u89e3\u3001\u51e0\u4f55\u56fe\u795e\u7ecf\u7f51\u7edc\uff0c\u4ee5\u53ca\u7b97\u6cd5\u795e\u7ecf\u5316\u6c42\u89e3\u5728 AI for Science \u4e2d\u7684\u5e94\u7528\u7b49\u65b9\u9762\u3002\u4ece2023\u5e746\u670814\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u4e09\u665a 19:00-21:00 \u4e3e\u884c\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba18\u5468\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u53c2\u4e0e\uff01<\/span><\/section>\n

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                                                                                                                                                                                                                                                                                                                                                        \u52a0\u901f\u7ecf\u5178\u7b97\u6cd5\u6548\u7387\uff0c\u7a81\u7834\u73b0\u5b9e\u6280\u672f\u74f6\u9888\uff1a\u56fe\u795e\u7ecf\u7f51\u7edc\u4e0e\u7ec4\u5408\u4f18\u5316\u8bfb\u4e66\u4f1a\u542f\u52a8<\/a><\/span><\/section>\n

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                                                                                                                                                                                                                                                                                                                                                        1. <\/strong>Nature Physics \u901f\u9012\uff1a\u590d\u6742\u7f51\u7edc\u52a8\u529b\u5b66\u7684\u6d8c\u73b0\u7a33\u5b9a\u6027<\/a><\/strong><\/span><\/section>\n
                                                                                                                                                                                                                                                                                                                                                        2.<\/strong> Nat.Rev.Phys.\u901f\u9012\uff1a\u7528\u590d\u6742\u8282\u70b9\u63a7\u5236\u590d\u6742\u7f51\u7edc<\/a><\/strong><\/span><\/section>\n
                                                                                                                                                                                                                                                                                                                                                        <\/strong><\/section>\n
                                                                                                                                                                                                                                                                                                                                                        3.<\/strong><\/strong> \u201c\u79d1\u5b66\u63a2\u7d22\u5956\u201d\u5f97\u4e3b\u5415\u7433\u5a9b\uff1a\u63a2\u7d22\u7f51\u7edc\u9ad8\u9636\u7ed3\u6784\uff0c\u7834\u89e3\u590d\u6742\u7cfb\u7edf\u96be\u9898<\/a><\/strong><\/span><\/section>\n
                                                                                                                                                                                                                                                                                                                                                        4. \u300a\u5f20\u6c5f\u00b7\u590d\u6742\u79d1\u5b66\u524d\u6cbf27\u8bb2\u300b\u5b8c\u6574\u4e0a\u7ebf\uff01<\/strong><\/a><\/strong><\/strong><\/strong><\/section>\n
                                                                                                                                                                                                                                                                                                                                                        <\/strong><\/a><\/strong><\/strong><\/strong><\/section>\n
                                                                                                                                                                                                                                                                                                                                                        5. \u6210\u4e3a\u96c6\u667aVIP\uff0c\u89e3\u9501\u5168\u7ad9\u8bfe\u7a0b\uff0f\u8bfb\u4e66\u4f1a<\/span><\/strong><\/a><\/strong><\/strong><\/strong><\/strong><\/section>\n
                                                                                                                                                                                                                                                                                                                                                        6. <\/strong><\/strong><\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/a><\/strong><\/strong><\/strong><\/span><\/section>\n


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                                                                                                                                                                                                                                                                                                                                                        <\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

                                                                                                                                                                                                                                                                                                                                                        \u5bfc\u8bed \u4ece\u4e92\u8054\u7f51\u3001\u4eba\u7c7b\u793e\u4f1a\u7f51\u7edc\u5230\u751f\u7269\u7f51\u7edc\uff0c\u771f\u5b9e\u4e16\u754c\u7684\u7f51\u7edc\u5e38\u5305\u542b\u6570\u767e\u4e07\u4e2a\u5f02\u8d28\u8282\u70b9\u3002\u8fd9\u4e9b\u590d\u6742\u7f51\u7edc\u4e0d\u4ec5\u8282\u70b9\u4e4b\u95f4\u7684\u8fde\u63a5\u6a21\u5f0f\u590d\u6742\uff0c\u5355\u4e2a\u8282\u70b9\u4e5f\u53ef\u80fd\u5f88\u590d\u6742\u3002\u8981\u5982\u4f55\u63a7\u5236\u5177\u6709\u5982\u6b64\u591a\u590d\u6742\u8282\u70b9\u7684\u590d\u6742\u7f51\u7edc\u5462\uff1f\u4eca\u5e743\u6708\u53d1\u8868\u4e8e Nature Reviews Physics \u7684\u7efc\u8ff0\u6587\u7ae0\u201cControlling complex ne…<\/p>\n","protected":false},"author":0,"featured_media":42518,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/42534"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=42534"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/42534\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/42518"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=42534"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=42534"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=42534"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=42534"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}