{"id":76481,"date":"2026-02-22T15:26:04","date_gmt":"2026-02-22T07:26:04","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/76481.html"},"modified":"2026-02-22T15:26:04","modified_gmt":"2026-02-22T07:26:04","slug":"mpc%e6%a8%a1%e5%9e%8b%e9%a2%84%e6%b5%8b%e6%8e%a7%e5%88%b6%ef%bc%9a%e6%95%b0%e5%ad%a6%e6%8e%a8%e5%af%bc%e4%b8%8eoctave%e5%ae%9e%e7%8e%b0","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/76481.html","title":{"rendered":"MPC\u6a21\u578b\u9884\u6d4b\u63a7\u5236\uff1a\u6570\u5b66\u63a8\u5bfc\u4e0eoctave\u5b9e\u73b0"},"content":{"rendered":"<p>\u00a0\u58f0\u660e&#xff1a;\u672c\u5b66\u4e60\u7b14\u8bb0\u4f7f\u7528\u57fa\u4e8eTeXmacs\u7684\u4e13\u4e1a\u7f16\u8f91\u5de5\u5177\u548coctave\u73af\u5883\u5b9e\u73b0&#xff0c;\u7406\u8bba\u63a8\u5bfc\u975e\u539f\u521b&#xff0c;\u53ea\u662f\u7b14\u8bb0\u548c\u79fb\u690d&#xff01;\u5185\u5bb9\u5b8c\u5168\u662f\u524d\u51e0\u5e74\u5b66\u4e60B\u7ad9\u5927\u795eDR_CAN\u7684\u76f8\u5173\u89c6\u9891\u8bfe\u7a0b\u505a\u7684\u7b14\u8bb0\u6574\u7406&#xff0c;\u6211\u53ea\u662f\u5c06\u5b66\u4e60\u8fc7\u7a0b\u4f7f\u7528\u683c\u5f0f\u5316\u7f16\u8f91\u5de5\u5177\u505a\u4e86\u7b14\u8bb0&#xff0c;\u5e76\u5c06\u6e90\u4ee3\u7801\u8fdb\u884c\u6574\u7406\u6ce8\u91ca\u79fb\u690d\u5230\u4e86octave&#xff08;\u8bed\u6cd5\u548cmatlab\u57fa\u672c\u901a\u7528&#xff09;\u8c03\u8bd5\u8fd0\u884c&#xff0c;\u5e76\u5bfb\u627e\u4e86\u7f51\u4e0a\u5176\u5b83\u6587\u7ae0\u6709\u6c34\u5370\u7684\u56fe\u7247\u8865\u5145\u7406\u89e3&#xff0c;\u5982\u679c\u76f8\u5173\u4f5c\u8005\u8ba4\u4e3a\u4fb5\u6743&#xff0c;\u6211\u7acb\u9a6c\u5220\u9664\u3002<\/p>\n<p>\u56e0\u4e3a\u7f51\u7ad9\u65e0\u6cd5\u5b9e\u73b0\u4e13\u4e1a\u7f16\u8f91\u5de5\u5177\u5448\u73b0\u6548\u679c&#xff0c;\u90e8\u5206\u5185\u5bb9\u4e0d\u5f97\u4e0d\u4f7f\u7528\u622a\u56fe&#xff0c;\u4e0d\u7136\u683c\u5f0f\u4f1a\u4e71\u3002<\/p>\n<p>\u539f\u89c6\u9891\u94fe\u63a5&#xff1a;https:\/\/space.bilibili.com\/230105574<\/p>\n<p>MPC&#xff08;Model Predictive Control&#xff09;\u6a21\u578b\u9884\u6d4b\u63a7\u5236<\/p>\n<p>\u80cc\u666f\u77e5\u8bc6&#xff1a;\u72b6\u6001\u7a7a\u95f4\u65b9\u7a0b&#xff08;State Space&#xff09;, \u53cd\u9988\u63a7\u5236\u5668\u8bbe\u8ba1&#xff08;Feedback Control&#xff09;\u3001\u89c2\u6d4b\u5668<\/p>\n<h2>\u5b9a\u4e49\u00a01.\u00a0\u6700\u4f18\u63a7\u5236&#xff08;Optimal Control&#xff09;<\/h2>\n<p>\u7814\u7a76\u52a8\u673a&#xff08;Motivation&#xff09;&#xff1a;\u5728\u7ea6\u675f\u6761\u4ef6&#xff08;\u7269\u7406\u9650\u5236&#xff0c;\u5982\u65b9\u5411\u76d8\u8f6c\u52a8\u6781\u9650&#xff09;\u4e0b\u8fbe\u5230\u6700\u4f18&#xff08;\u7efc\u5408\u6700\u4f18\u5206\u6790&#xff0c;\u601d\u8fa8Critical Thinking&#xff09;\u7684\u7cfb\u7edf\u8868\u73b0Get the best performace within certain limitation&#xff0c;<\/p>\n<p>\u6570\u5b66\u6a21\u578b&#xff08;Mathmatical Model&#xff09;&#xff1a;<\/p>\n<p>1.\u5355\u8f93\u5165\u5355\u8f93\u51faSISO&#xff08;Single Input Single Output&#xff09;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"1394\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072555-699aaf83ce8e7.png\" width=\"3548\" \/><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"24\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072557-699aaf85e901a.png\" width=\"484\" \/>&#xff0c;\u5f15\u7533\u5b66\u4e60\u6cdb\u51fd\u5206\u6790\u7684\u5185\u79ef\u7a7a\u95f4<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"34\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072558-699aaf8621dd4.png\" width=\"466\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"410\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072558-699aaf8657af5.png\" width=\"2588\" \/><\/p>\n<p>siso\u7684\u72b6\u6001\u7a7a\u95f4\u65b9\u7a0b\u7c7b\u4f3c\u4e8emimo&#xff0c;\u53ea\u662f\u8f93\u5165\u8f93\u51fa\u662f1\u00d71\u7684\u6807\u91cf&#xff0c;\u4f46\u72b6\u6001\u5411\u91cf\u7684\u7ef4\u5ea6 n \u53ef\u4ee5\u5927\u4e8e1&#xff0c;\u56e0\u4e3a\u7cfb\u7edf\u5185\u90e8\u53ef\u80fd\u5305\u542b\u591a\u4e2a\u76f8\u4e92\u5173\u8054\u7684\u72b6\u6001\u53d8\u91cf\u3002<\/p>\n<p>2.\u591a\u8f93\u5165\u591a\u8f93\u51faMIMO&#xff08;Multiple Input Multiple Output&#xff09;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"27\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072559-699aaf874ad64.png\" width=\"213\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"106\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072559-699aaf8760e53.png\" width=\"265\" \/><\/p>\n<table border=\"1\" cellspacing=\"0\">\n<tbody>\n<tr>\n<td>\u7b26\u53f7<\/td>\n<td>\u540d\u79f0<\/td>\n<td>\u7ef4\u5ea6<\/td>\n<td>\u4f5c\u7528<\/td>\n<\/tr>\n<tr>\n<td>A<\/td>\n<td>\u7cfb\u7edf\u77e9\u9635\u3001\u72b6\u6001\u77e9\u9635\u3001\u52a8\u6001\u77e9\u9635<\/td>\n<td>n\u00d7n<\/td>\n<td>\u63cf\u8ff0\u7cfb\u7edf\u72b6\u6001\u53d8\u91cf\u4e4b\u95f4\u5173\u7cfb<\/td>\n<\/tr>\n<tr>\n<td>B<\/td>\n<td>\u8f93\u5165\u77e9\u9635\u3001\u63a7\u5236\u77e9\u9635<\/td>\n<td>n\u00d7p<\/td>\n<td>\u5916\u90e8\u7cfb\u7edf\u5982\u4f55\u5f71\u54cd\u7cfb\u7edf\u72b6\u6001<\/td>\n<\/tr>\n<tr>\n<td>C<\/td>\n<td>\u8f93\u51fa\u77e9\u9635\u3001\u89c2\u6d4b\u77e9\u9635<\/td>\n<td>m\u00d7n<\/td>\n<td>\u7cfb\u7edf\u72b6\u6001\u5982\u4f55\u5f71\u54cd\u8f93\u51fa<\/td>\n<\/tr>\n<tr>\n<td>D<\/td>\n<td>\u76f4\u63a5\u4f20\u9012\u77e9\u9635<\/td>\n<td>m\u00d7p<\/td>\n<td>\u8868\u793a\u8f93\u5165\u5982\u4f55\u76f4\u63a5\u4f5c\u7528\u4e8e\u8f93\u51fa&#xff0c;\u53ef\u80fd\u4e3a0<\/td>\n<\/tr>\n<tr>\n<td>X<\/td>\n<td>\u7cfb\u7edf\u72b6\u6001\u5411\u91cf<\/td>\n<td>n\u00d71<\/td>\n<td>\u5305\u542b\u4e86\u8db3\u4ee5\u5b8c\u5168\u8868\u5f81\u7cfb\u7edf\u8fd0\u52a8\u72b6\u6001\u7684\u6700\u5c0f\u4e2a\u6570\u53d8\u91cf<\/td>\n<\/tr>\n<tr>\n<td>Y<\/td>\n<td>\u7cfb\u7edf\u8f93\u51fa\u5411\u91cf<\/td>\n<td>m\u00d71<\/td>\n<td>\u7cfb\u7edf\u5728t\u65f6\u523b\u8f93\u51fa<\/td>\n<\/tr>\n<tr>\n<td>u<\/td>\n<td>\u8f93\u5165\u5411\u91cf<\/td>\n<td>p\u00d71<\/td>\n<td>\u4f5c\u7528\u4e8e\u7cfb\u7edf\u4e0a\u7684\u5916\u90e8\u8f93\u5165\u6216\u63a7\u5236\u4fe1\u53f7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>A&#xff1a;\u7cfb\u7edf\u77e9\u9635\u3001\u72b6\u6001\u77e9\u9635&#xff0c;\u63cf\u8ff0\u7cfb\u7edf\u72b6\u6001\u53d8\u91cf\u4e4b\u95f4\u5173\u7cfb<\/p>\n<p>B&#xff1a;\u8f93\u5165\u77e9\u9635\u3001\u63a7\u5236\u77e9\u9635&#xff0c;\u5916\u90e8\u7cfb\u7edf\u5982\u4f55\u5f71\u54cd\u7cfb\u7edf\u72b6\u6001<\/p>\n<p>C&#xff1a;\u8f93\u51fa\u77e9\u9635\u3001\u89c2\u6d4b\u77e9\u9635&#xff0c;\u7cfb\u7edf\u72b6\u6001\u5982\u4f55\u5f71\u54cd\u8f93\u51fa<\/p>\n<p>D&#xff1a;\u76f4\u63a5\u4f20\u9012\u77e9\u9635&#xff0c;\u8868\u793a\u8f93\u5165\u5982\u4f55\u76f4\u63a5\u4f5c\u7528\u4e8e\u8f93\u51fa&#xff0c;\u53ef\u80fd\u4e3a0<\/p>\n<p>X&#xff1a;\u7cfb\u7edf\u72b6\u6001\u5411\u91cf&#xff0c;\u5305\u542b\u4e86\u8db3\u4ee5\u5b8c\u5168\u8868\u5f81\u7cfb\u7edf\u8fd0\u52a8\u72b6\u6001\u7684\u6700\u5c0f\u4e2a\u6570\u53d8\u91cf<\/p>\n<p>Y&#xff1a;\u7cfb\u7edf\u8f93\u51fa\u5411\u91cf&#xff0c;\u7cfb\u7edf\u5728t\u65f6\u523b\u8f93\u51fa<\/p>\n<p>u&#xff1a;\u8f93\u5165\u77e9\u9635<\/p>\n<p>\u4ee3\u4ef7\u51fd\u6570(Q\u3001R\u662f\u8c03\u8282\u6743\u91cd\u7cfb\u6570\u7684\u5bf9\u89d2\u77e9\u9635)&#xff1a;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"192\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072559-699aaf8779bf0.png\" width=\"973\" \/><\/p>\n<p>\u4ee5\u4e8c\u7ef4\u7cfb\u7edf\u4e3a\u4f8b&#xff1a;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"1169\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072559-699aaf879d123.png\" width=\"2140\" \/><\/p>\n<p>q1\u3001q2\u3001r1\u3001r2&#xff1a;\u6700\u4f18\u5316\u7cfb\u7edf\u7684\u6743\u91cd\u7cfb\u6570<\/p>\n<h2>\u5b9a\u4e49\u00a02.\u00a0MPC\u57fa\u672c\u6982\u5ff5&#xff08;concept&#xff09;<\/h2>\n<p>\u901a\u8fc7\u6a21\u578b\u6765\u9884\u6d4b\u7cfb\u7edf\u5728\u67d0\u4e00\u672a\u6765\u65f6\u95f4\u6bb5\u5185\u7684\u8868\u73b0\u6765\u8fdb\u884c\u4f18\u5316\u63a7\u5236&#xff0c;\u56e0\u4e3a\u591a\u7528\u4e8e\u6570\u4f4d\u63a7\u5236&#xff0c;\u6240\u4ee5\u91c7\u7528\u79bb\u6563\u578b\u72b6\u6001\u7a7a\u95f4\u8868\u8fbe<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"279\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072600-699aaf88e51a4.png\" width=\"931\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"75\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072601-699aaf891b8f7.png\" width=\"3454\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"187\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072601-699aaf8948ded.png\" width=\"829\" \/><\/p>\n<p>\u4ee3\u4ef7\u51fd\u6570(\u79bb\u6563\u578b\u7528\u52a0\u548c&#xff0c;Q\u3001R\u3001F\u662f\u8c03\u8282\u6743\u91cd\u7cfb\u6570\u7684\u5bf9\u89d2\u77e9\u9635&#xff0c;F\u77e9\u9635\u6d89\u53ca\u6c42\u89e3\u674e\u4e9a\u666e\u8bfa\u592b\u51fd\u6570&#xff0c;\u4e3a\u4e86\u4fdd\u8bc1\u7cfb\u7edf\u7a33\u5b9a\u6027&#xff0c;\u5f85\u6269\u5c55\u5b66\u4e60)&#xff1a;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"247\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072601-699aaf89614e3.png\" width=\"1936\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"22\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072601-699aaf89988ba.png\" width=\"35\" \/>&#xff1a;\u9884\u6d4b\u533a\u95f4\u6700\u7ec8N\u65f6\u523b\u8bef\u5dee\u4ee3\u4ef7\u51fd\u6570&#xff0c;\u8fc7\u7a0b\u6700\u4f18&#043;\u7ec8\u503c\u6700\u4f18<\/p>\n<p>\u8fd8\u9700\u8981\u8003\u8651\u7cfb\u7edf\u7ea6\u675f&#xff08;Constrains&#xff09;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"512\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072601-699aaf89a3e7c.png\" width=\"852\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"644\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072601-699aaf89dbc9f.png\" width=\"951\" \/><\/p>\n<p>\u5de5\u4f5c\u6b65\u9aa4\u52063\u6b65&#xff1a;<\/p>\n<p>step 1&#xff1a;\u5728k\u65f6\u523b&#xff0c;\u4f30\u8ba1&#xff08;\u6709\u4e9b\u65e0\u6cd5\u76f4\u63a5\u6d4b\u91cf&#xff0c;\u8bbe\u8ba1\u89c2\u6d4b\u5668&#xff09;\/\u6d4b\u91cf\u8bfb\u53d6\u5f53\u524d\u7cfb\u7edf\u72b6\u6001<\/p>\n<p>step 2&#xff1a;\u5728k\u65f6\u523b&#xff0c;\u57fa\u4e8e<img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"17\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072602-699aaf8a21239.png\" width=\"27\" \/>,<img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"16\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072602-699aaf8a2c5e2.png\" width=\"130\" \/>\u6765\u8fdb\u884c\u6700\u4f18\u5316\u63a7\u5236&#xff08;\u4e8c\u6b21\u89c4\u5212&#xff09;<\/p>\n<p>step 3&#xff1a;\u6eda\u52a8\u4f18\u5316&#xff08;Horizon Control&#xff09;&#xff0c;\u5728k\u65f6\u523b\u53ea\u53d6<img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"18\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072602-699aaf8a3c164.png\" width=\"30\" \/>&#xff0c;\u5bf9\u6297\u6270\u52a8\u548c\u5b9e\u9645\u73af\u5883\u8bef\u5dee&#xff0c;\u770bN\u6b65\u8d701\u6b65&#xff0c;\u540e\u7eed\u53d6\u70b9\u8d8a\u591a\u53ea\u4e3a\u4fdd\u8bc1k\u65f6\u523b\u503c\u8d8a\u4f18&#xff0c;\u6bcf\u4e00\u6b65\u90fd\u8981\u8fdb\u884c\u6700\u4f18\u5316\u6c42\u89e3&#xff0c;\u6240\u4ee5\u5bf9\u786c\u4ef6\u6027\u80fd\u8981\u6c42\u9ad8<\/p>\n<h2>\u5b9a\u4e49\u00a03.\u00a0\u4e8c\u6b21\u89c4\u5212&#xff08;Quadratic Programing&#xff09;<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"178\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072602-699aaf8a46e89.png\" width=\"2328\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"763\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222072602-699aaf8a7eb2b.png\" width=\"1831\" \/><\/p>\n<p>\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u6cd5&#xff08;Weighted Least Squares, WLS&#xff09;\u662f\u4e00\u79cd\u6570\u5b66\u4f18\u5316\u6280\u672f&#xff0c;\u5b83\u5728\u666e\u901a\u6700\u5c0f\u4e8c\u4e58\u6cd5&#xff08;Least Squares, LS&#xff09;\u7684\u57fa\u7840\u4e0a\u5f15\u5165\u4e86\u6743\u91cd&#xff0c;\u4ee5\u8c03\u6574\u4e0d\u540c\u6837\u672c\u8bef\u5dee\u5bf9\u635f\u5931\u51fd\u6570\u7684\u8d21\u732e\u7387\u3002\u8fd9\u79cd\u65b9\u6cd5\u5728\u6570\u636e\u5b58\u5728\u5f02\u65b9\u5dee\u6027&#xff08;\u5373\u8bef\u5dee\u9879\u7684\u65b9\u5dee\u4e0d\u540c&#xff09;\u65f6\u7279\u522b\u6709\u7528&#xff0c;\u53ef\u4ee5\u901a\u8fc7\u52a0\u6743\u4f7f\u5f97\u6a21\u578b\u66f4\u52a0\u51c6\u786e\u5730\u53cd\u6620\u6570\u636e\u7684\u5b9e\u9645\u7279\u6027\u3002<\/p>\n<p>\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u6cd5\u4e3b\u8981\u9002\u7528\u4e8e\u7ebf\u6027\u6a21\u578b\u6216\u53ef\u4ee5\u8f6c\u5316\u4e3a\u7ebf\u6027\u6a21\u578b\u7684\u975e\u7ebf\u6027\u6a21\u578b\u3002\u5bf9\u4e8e\u67d0\u4e9b\u590d\u6742\u7684\u975e\u7ebf\u6027\u6a21\u578b&#xff0c;\u53ef\u80fd\u9700\u8981\u91c7\u7528\u5176\u4ed6\u4f18\u5316\u65b9\u6cd5\u3002<\/p>\n<p>\u5bf9\u4e8eMPC&#xff0c;\u9700\u8981\u628a\u6a21\u578b\u8f6c\u5316\u6210\u4e00\u822c\u5f62\u5f0f&#xff0c;\u7136\u540e\u4f7f\u7528\u5de5\u5177\u6c42\u89e3\u3002<\/p>\n<p>\u6700\u5c0f\u4e8c\u4e58\u6c42\u89e3\u5de5\u5177&#xff1a;matlab&#xff0c;python<\/p>\n<\/p>\n<h2>\u63a8\u8bba\u00a04.\u00a0MPC\u8f6c\u4e8c\u6b21\u89c4\u5212\u6c42\u89e3\u63a8\u5bfc<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"851\" src=\"2026-02-2230sxdcmdh25.png\" width=\"3288\" \/><\/p>\n<p>N&#xff1a;\u9884\u6d4b\u533a\u95f4&#xff08;Predictive Horizon&#xff09;<\/p>\n<p>\u4e3a\u4e86\u7b80\u5316\u63a8\u5bfc&#xff0c;\u5047\u8bbe\u8f93\u51faY&#061;X&#xff0c;\u53c2\u8003R&#061;0&#xff0c;E&#061;Y-R&#061;X-0&#061;X<\/p>\n<p>\u4ee3\u4ef7\u51fd\u6570(\u79bb\u6563\u578b\u7528\u52a0\u548c&#xff0c;Q\u3001R\u3001F\u662f\u8c03\u8282\u6743\u91cd\u7cfb\u6570\u7684\u5bf9\u89d2\u77e9\u9635&#xff0c;\u9010\u9879\u5bf9\u5e94x\u548cu\u7684\u5411\u91cf\u4e2d\u6bcf\u4e00\u9879\u6743\u91cd\u7cfb\u6570)&#xff1a;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"246\" src=\"2026-02-22faotf3t3car.png\" width=\"3740\" \/><\/p>\n<p>\u524d\u534a\u90e8\u5206\u662f\u8bef\u5dee\u52a0\u6743\u548c&#xff0c;\u540e\u534a\u90e8\u5206\u662f\u8f93\u5165\u52a0\u6743\u548c<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"31\" src=\"2026-02-220kaet3pnpq3.png\" width=\"191\" \/>\u5728\u9884\u6d4b\u533a\u95f4\u7ec8\u7aef\u7684\u8bef\u5dee<\/p>\n<p>\u73b0\u5728\u6709x\u548cu\u4e24\u4e2a\u53d8\u91cf&#xff0c;\u4f46\u662f\u4e8c\u6b21\u578b\u6c42\u89e3\u53ea\u6709\u4e00\u4e2a\u53d8\u91cf&#xff0c;\u63a7\u5236\u5668\u9700\u8981\u7684\u662f\u63a7\u5236\u91cfu&#xff0c;\u9700\u8981\u628ax\u8f6c\u5316\u6210u<\/p>\n<p>\u6839\u636e\u72b6\u6001\u7a7a\u95f4\u65b9\u7a0b&#xff1a;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"729\" src=\"2026-02-22ijnml3bdnyr.png\" width=\"5384\" \/><\/p>\n<p>\u6574\u7406\u53ef\u5f97&#xff08;\u4e0b\u9762\u76840\u63070\u77e9\u9635&#xff09;&#xff1a;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"527\" src=\"2026-02-22vzfnd55qziy.png\" width=\"2791\" \/><\/p>\n<p>\u5176\u4e2d<img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"18\" src=\"2026-02-22eyfxrpzmctv.png\" width=\"128\" \/><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"18\" src=\"2026-02-224j3e5gz0jwo.png\" width=\"105\" \/>&#xff0c;\u4e5f\u662f\u4e00\u4e2a\u591a\u72b6\u6001\u5411\u91cf<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"3741\" src=\"2026-02-22enfj3q3vgta.png\" width=\"4808\" \/><\/p>\n<p>Tips&#xff1a;<\/p>\n<p>\u77e9\u9635\u7684\u8f6c\u7f6e\u5206\u914d\u5f8b\u53ef\u4ee5\u8868\u8ff0\u4e3a&#xff1a;<\/p>\n<p>&#xff08;A&#043;B&#xff09;\u7684\u8f6c\u7f6e\u7b49\u4e8eA\u7684\u8f6c\u7f6e\u4e0eB\u7684\u8f6c\u7f6e\u7684\u548c&#xff0c;\u5373&#xff1a;(A &#043; B)^T &#061; A^T &#043; B^T<\/p>\n<p>\u77e9\u9635\u7684\u8f6c\u7f6e\u7684\u8f6c\u7f6e\u7b49\u4e8e\u539f\u77e9\u9635&#xff0c;\u5373&#xff1a;(AT)T &#061; A\u3002<\/p>\n<p>\u77e9\u9635\u4e0e\u5176\u8f6c\u7f6e\u7684\u4e58\u79ef\u662f\u4e00\u4e2a\u5bf9\u79f0\u77e9\u9635&#xff0c;\u5373&#xff1a;A^T * A \u7684\u7ed3\u679c\u662f\u4e00\u4e2a\u5bf9\u79f0\u77e9\u9635&#xff08;\u5f53A\u4e3a\u65b9\u9635\u65f6&#xff09;\u3002<\/p>\n<p>\u77e9\u9635\u4e58\u79ef\u7684\u8f6c\u7f6e\u6ee1\u8db3(AB)^T &#061; B^T * A^T&#xff0c;\u8fd9\u4e2a\u6027\u8d28\u5728\u5904\u7406\u77e9\u9635\u4e58\u6cd5\u65f6\u975e\u5e38\u6709\u7528\u3002<\/p>\n<p>(ABC)^T &#061;C^T * B^T * A^T<\/p>\n<h2>\u4f8b\u00a05.\u00a0\u5355\u8f93\u5165\u4e8c\u9636\u7cfb\u7edf<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"1928\" src=\"2026-02-22q0koukndhul.png\" width=\"3326\" \/><\/p>\n<p>\u5047\u8bbeN&#061;3<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"2192\" src=\"2026-02-22svombf3bher.png\" width=\"1656\" \/><\/p>\n<\/p>\n<p>%% \u6e05\u5c4f<br \/>\nclear all; %\u91ca\u653e\u5185\u5b58&#xff0c;\u4e0d\u53d7\u4e4b\u524d\u5b9a\u4e49\u7684\u53d8\u91cf\u6216\u51fd\u6570\u5f71\u54cd<br \/>\nclose all; %\u5173\u95ed\u5f53\u524d\u6253\u5f00\u7684\u6240\u6709\u56fe\u5f62\u7a97\u53e3<br \/>\nclc; %\u6e05\u7406\u547d\u4ee4\u7a97\u53e3&#xff0c;\u4ee5\u4fbf\u67e5\u770b\u6700\u65b0\u7684\u547d\u4ee4\u8f93\u51fa\u6216\u7ed3\u679c<br \/>\n%% \u52a0\u8f7d optim package,\u82e5\u4f7f\u7528matlab&#xff0c;\u5219\u6ce8\u91ca\u6389\u6b64\u884c<br \/>\npkg load optim; <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"1448\" src=\"2026-02-22zews3z3cpch.png\" width=\"3953\" \/><\/p>\n<p>function [E , H]&#061;MPC_Matrices(A,B,Q,R,F,N)<\/p>\n<p>    n&#061;size(A,1);   % A \u662f n \u00d7 n \u77e9\u9635, \u5f97\u5230\u884c\u6570 n<br \/>\n    disp(n);<\/p>\n<p>    p&#061;size(B,2);   % B \u662f n \u00d7 p \u77e9\u9635, \u5f97\u5230\u5217\u6570 p<br \/>\n    disp(p);<\/p>\n<p>    % \u5b9a\u4e49M \u548c C<br \/>\n    M&#061;[eye(n);zeros(N*n,n)]; % \u521d\u59cb\u5316 M \u77e9\u9635. M \u77e9\u9635\u662f (N&#043;1)n \u00d7 n\u7684&#xff0c;<br \/>\n                             % \u4e0a\u9762\u662f n \u00d7 n \u4e2a &#034;I&#034;\u5355\u4f4d\u77e9\u9635<br \/>\n                             % \u4e0b\u9762\u662f N*n \u00d7 n \u7684\u96f6\u77e9\u9635&#xff0c;\u4e0a\u4e0b\u884c\u5806\u53e0<br \/>\n    disp(M);<\/p>\n<p>    C&#061;zeros((N&#043;1)*n,N*p); % \u521d\u59cb\u5316 C \u77e9\u9635, \u8fd9\u4e00\u6b65\u4ee4\u5b83\u6709 (N&#043;1)n x NP \u4e2a 0<br \/>\n    disp(C);<\/p>\n<p>    % \u66f4\u65b0M\u548cC<br \/>\n    tmp&#061;eye(n);  %\u5b9a\u4e49\u4e00\u4e2an x n \u7684 I \u5355\u4f4d\u77e9\u9635<br \/>\n    disp(tmp);<\/p>\n<p>    for i&#061;1:N % \u5faa\u73af&#xff0c;i \u4ece 1\u5230 N<\/p>\n<p>        rows &#061;i*n&#043;(1:n); %\u5b9a\u4e49\u5f53\u524d\u884c\u6570&#xff0c;\u4ecei x n\u5f00\u59cb&#xff0c;\u5171n\u884c<\/p>\n<p>        C(rows,:)&#061;[tmp*B,C(rows-n, 1:end-p)]; %\u5c06c\u77e9\u9635\u586b\u6ee1<\/p>\n<p>        tmp&#061; A*tmp; %\u6bcf\u4e00\u6b21\u5c06tmp\u5de6\u4e58\u4e00\u6b21A<\/p>\n<p>        M(rows,:)&#061;tmp; %\u5c06M\u77e9\u9635\u5199\u6ee1<\/p>\n<p>    end<br \/>\n    disp(M);<br \/>\n    disp(C);<\/p>\n<p>    % \u5b9a\u4e49Q_bar\u548cR_bar<br \/>\n    % \u514b\u7f57\u5185\u514b\u79ef\u662f\u5f20\u91cf\u79ef\u7684\u7279\u6b8a\u5f62\u5f0f&#xff0c;<br \/>\n    % \u5982\u679cA\u662fm\u00d7n\u7684\u77e9\u9635&#xff0c;\u800cB\u662fp\u00d7q\u7684\u77e9\u9635&#xff0c;\u514b\u7f57\u5185\u514b\u79ef\u5219\u662fmp\u00d7nq\u7684\u5206\u5757\u77e9\u9635<br \/>\n    Q_bar &#061; kron(eye(N),Q);<br \/>\n    disp(Q_bar);<\/p>\n<p>    % \u521b\u5efa\u5206\u5757\u5bf9\u89d2\u77e9\u9635&#xff0c;\u5373\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7531\u591a\u4e2a\u5b50\u77e9\u9635\u7ec4\u6210&#xff0c;\u800c\u5176\u4f59\u4f4d\u7f6e\u90fd\u662f\u96f6\u7684\u77e9\u9635<br \/>\n    Q_bar &#061; blkdiag(Q_bar,F);<br \/>\n    disp(Q_bar);<\/p>\n<p>    R_bar &#061; kron(eye(N),R);<br \/>\n    disp(R_bar);<\/p>\n<p>    % \u8ba1\u7b97G, E, H<br \/>\n    % G: n x n<br \/>\n    G&#061;M&#039;*Q_bar*M;<br \/>\n    disp(G);<\/p>\n<p>    % E: NP x n<br \/>\n    E&#061;C&#039;*Q_bar*M;<br \/>\n    disp(E);<\/p>\n<p>    % NP x NP<br \/>\n    H&#061;C&#039;*Q_bar*C&#043;R_bar;<br \/>\n    disp(H);<\/p>\n<p>end<\/p>\n<p>quadprog<\/p>\n<p>\u4e8c\u6b21\u89c4\u5212&#xff0c;quadprog\u00a0\u4ec5\u9002\u7528\u4e8e\u57fa\u4e8e\u6c42\u89e3\u5668\u7684\u65b9\u6cd5\u3002<\/p>\n<p>x\u00a0&#061; quadprog(H,f)\u00a0\u8fd4\u56de\u4f7f\u00a01\/2*x&#039;*H*x &#043; f&#039;*x\u00a0\u6700\u5c0f\u7684\u5411\u91cf\u00a0x\u3002\u8981\u4f7f\u95ee\u9898\u5177\u6709\u6709\u9650\u6700\u5c0f\u503c&#xff0c;\u8f93\u5165\u00a0H\u00a0\u5fc5\u987b\u4e3a\u6b63\u5b9a\u77e9\u9635\u3002\u5982\u679c\u00a0H\u00a0\u662f\u6b63\u5b9a\u77e9\u9635&#xff0c;\u5219\u89e3\u00a0x &#061; H\\\\(-f)\u3002<\/p>\n<p>function u_k&#061; Prediction(x_k,E,H,N,p)<\/p>\n<p>    U_k &#061; zeros(N*p,1); % NP x 1<\/p>\n<p>    U_k &#061; quadprog(H,E*x_k); %\u6c42\u89e3\u4e8c\u6b21\u89c4\u5212\u95ee\u9898<\/p>\n<p>    u_k &#061; U_k(1:p,1); % \u53d6\u7b2c\u4e00\u4e2a\u7ed3\u679c<\/p>\n<p>end <\/p>\n<p>\u5047\u8bbe&#xff1a;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"1268\" src=\"2026-02-22vgadikfbcrc.png\" width=\"2460\" \/><\/p>\n<p>%% \u7b2c\u4e00\u6b65&#xff0c;\u5b9a\u4e49\u72b6\u6001\u7a7a\u95f4\u77e9\u9635<br \/>\n%% \u5b9a\u4e49\u72b6\u6001\u77e9\u9635 A, n x n \u77e9\u9635<br \/>\nA &#061; [1 0.1; -1 2];<br \/>\nn&#061; size (A,1); %\u83b7\u53d6\u77e9\u9635A\u7684\u7b2c\u4e00\u7ef4\u7684\u5927\u5c0f&#xff0c;\u5373\u77e9\u9635A\u7684\u884c\u6570<br \/>\ndisp(A);<br \/>\ndisp(n);<\/p>\n<p>%% \u5b9a\u4e49\u8f93\u5165\u77e9\u9635 B, n x p \u77e9\u9635<br \/>\nB &#061; [ 0.2 1; 0.5 2];<br \/>\np &#061; size(B,2); %\u83b7\u53d6\u77e9\u9635B\u7684\u7b2c\u4e8c\u7ef4\u7684\u5927\u5c0f&#xff0c;\u5373\u77e9\u9635B\u7684\u5217\u6570<br \/>\ndisp(B);<br \/>\ndisp(p);<\/p>\n<p>%% \u5b9a\u4e49Q\u77e9\u9635&#xff0c;n x n \u77e9\u9635&#xff0c;x1\u548cx2\u7684\u6743\u91cd<br \/>\nQ&#061;[100 0;0 1];<br \/>\ndisp(Q);<\/p>\n<p>%% \u5b9a\u4e49F\u77e9\u9635&#xff0c;n x n \u77e9\u9635&#xff0c;\u7ec8\u9879x1\u548cx2\u7684\u6743\u91cd<br \/>\nF&#061;[100 0;0 1];<br \/>\ndisp(F);<\/p>\n<p>%% \u5b9a\u4e49R\u77e9\u9635&#xff0c;p x p \u77e9\u9635&#xff0c;u1\u548cu2\u7684\u6d88\u8017\u6743\u91cd<br \/>\nR&#061;[1 0 ;0 .1];<br \/>\ndisp(R);<\/p>\n<p>%% \u5b9a\u4e49step\u6570\u91cfk&#xff0c;\u9884\u6d4b100\u6b21<br \/>\nk_steps&#061;100;<br \/>\n%% \u5b9a\u4e49\u77e9\u9635 X_K&#xff0c; n x k \u77e9 \u9635<br \/>\nX_K &#061; zeros(n,k_steps); % \u521b\u5efa\u4e00\u4e2an * k_steps\u7684\u5168\u96f6\u77e9\u9635<br \/>\ndisp(X_K);<br \/>\n%% \u6bcf\u4e00\u5217\u90fd\u662f\u67d0\u4e00\u65f6\u523b\u7684\u7cfb\u7edf\u72b6\u6001<\/p>\n<p>%% \u521d\u59cb\u72b6\u6001\u53d8\u91cf\u503c&#xff0c; n x 1 \u5411\u91cf<br \/>\nX_K(:,1) &#061;[20;-20]; % \u5bf9\u6240\u6709\u884c\u7684\u7b2c1\u5217\u8d4b\u503c\u5411\u91cf<br \/>\ndisp(X_K);<\/p>\n<p>%% \u5b9a\u4e49\u8f93\u5165\u77e9\u9635 U_K&#xff0c; p x k \u77e9\u9635<br \/>\nU_K&#061;zeros(p,k_steps); % \u521b\u5efa\u4e00\u4e2ap * k_steps\u7684\u5168\u96f6\u77e9\u9635<br \/>\ndisp(U_K);<br \/>\n%% \u5b9a\u4e49\u9884\u6d4b\u533a\u95f4K<br \/>\nN&#061;5;<\/p>\n<p>%% Call MPC_Matrices \u51fd\u6570 \u6c42\u5f97 E,H\u77e9\u9635<br \/>\n[E,H]&#061;MPC_Matrices(A,B,Q,R,F,N);<br \/>\ndisp([E,H]);<\/p>\n<p>%% \u8ba1\u7b97\u6bcf\u4e00\u6b65\u7684\u72b6\u6001\u53d8\u91cf\u7684\u503c&#xff0c;\u628a100\u6b21\u7684\u8f93\u5165\u8f93\u51fa\u8bb0\u4e0b\u6765\u51c6\u5907\u7ed8\u56fe<\/p>\n<p>for k &#061; 1 : k_steps<\/p>\n<p>  %% \u6c42\u5f97U_K(:,k),\u5f97\u5230\u6bcf\u4e2a\u9884\u6d4b\u7684\u7b2c\u4e00\u4e2a\u8f93\u5165&#xff0c;\u5199\u5230k\u5217<\/p>\n<p>  U_K(:,k) &#061; Prediction(X_K(:,k),E,H,N,p);<\/p>\n<p>  %% \u6839\u636e\u72b6\u6001\u65b9\u7a0b\u8ba1\u7b97\u7b2ck&#043;1\u6b65\u65f6\u72b6\u6001\u53d8\u91cf\u7684\u503c<\/p>\n<p>  X_K(:,k&#043;1)&#061;(A*X_K(:,k)&#043;B*U_K(:,k));<\/p>\n<p>end<br \/>\ndisp(U_K);<\/p>\n<p>disp(X_K);<\/p>\n<p>%% \u7ed8\u5236\u72b6\u6001\u53d8\u91cf\u548c\u8f93\u5165\u7684\u53d8\u5316<br \/>\nfigure;<br \/>\n%subplot (2, 1, 1);<br \/>\nhold on; %\u542f\u7528\u4fdd\u6301\u5f53\u524d\u56fe\u5f62\u72b6\u6001&#xff0c;\u5141\u8bb8\u5728\u540c\u4e00\u5750\u6807\u7cfb\u4e0a\u7ed8\u5236\u65b0\u7684\u56fe\u5f62\u3002<\/p>\n<p>for i &#061;1 :size (X_K,1)<\/p>\n<p>  plot (X_K(i,:));<\/p>\n<p>end<\/p>\n<p>legend(&#034;x1&#034;,&#034;x2&#034;) %\u6dfb\u52a0\u56fe\u4f8b&#xff0c;\u4ee5\u4fbf\u533a\u5206\u56fe\u5f62\u4e2d\u7684\u4e0d\u540c\u6570\u636e\u7cfb\u5217<br \/>\ntitle(&#039;system state&#039;);<br \/>\nxlabel(&#039;k&#039;);<br \/>\nylabel(&#039;X_K&#039;);<br \/>\ndrawnow; % \u5f3a\u5236\u66f4\u65b0\u56fe\u5f62<\/p>\n<p>hold off; 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