{"id":419,"date":"2014-07-21T07:25:25","date_gmt":"2014-07-20T23:25:25","guid":{"rendered":"http:\/\/blog.stlover.org\/?p=419"},"modified":"2014-07-21T08:40:50","modified_gmt":"2014-07-21T00:40:50","slug":"%e6%8e%a7%e5%88%b6%e5%9f%ba%e7%a1%80%ef%bc%8c%e4%bb%8e%e7%ba%bf%e6%80%a7%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%88%b0%e6%97%a0%e4%ba%ba%e6%9c%ba","status":"publish","type":"post","link":"http:\/\/blog.xuhao1.me\/?p=419","title":{"rendered":"\u63a7\u5236\u57fa\u7840\uff0c\u4ece\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u5230\u65e0\u4eba\u673a"},"content":{"rendered":"<p>\u6700\u8fd1\u770b\u4e86\u4e0d\u5c11\u94b1\u8001\u7684\u63a7\u5236\u8bba\uff0c\u4e5f\u5728coursera\u770b\u4e86\u4e00\u4e2a\u504f\u5e94\u7528\u5411\u7684\u63a7\u5236\u8bfe\u7a0b\uff0c\u662f\u65f6\u5019\u5199\u70b9\u9879\u76ee\u4e86\u3002<\/p>\n<p><!--more--><\/p>\n<p>\u9996\u5148\u5148\u7701\u7565\u7406\u8bba\u5316\u7684\u4e1c\u897f\u7684\u8bc1\u660e\uff08\u6691\u5047\u6392\u671f\u6bd4\u8f83\u7d27\uff0c\u8fd8\u8981\u770b\u91cf\u5b50\u529b\u5b66\uff0c\u5199\u6709\u9650\u5143\uff0c\u4ee5\u540e\u540c\u6837\u4f1a\u53d1\u91cf\u5b50\u529b\u5b66\uff0c\u6709\u9650\u5143\u7b49\u9ad8\u7aef\u70b9\u7684\u73a9\u610f\u7684\u7b14\u8bb0\uff0c\u5c11\u5199\u70b9\u4e09\u5e74\u4e00\u6362\u4ee3\u7684API\uff0c\u8bba\u559c\u6b22\u4e00\u4e2aGPA\u4e0a4\u7684\u540c\u5b66\u5bf9\u5b66\u4e60\u79ef\u6781\u6027\u7684\u8c03\u52a8\uff09\uff0c\u8bf7\u53c2\u7167Coursera\u548c\u300a\u5de5\u7a0b\u63a7\u5236\u8bba\u300b\u3002\u535a\u4e3b\u5728\u8fd9\u91cc\u5c31\u7528Mathematica\u6765\u8fdb\u884c\u4e00\u4e9b\u63a7\u5236\u57fa\u7840\u7684\u63a8\u6f14\u3002\u672c\u6587\u76ee\u6807\uff1a\u4f7f\u7528MMA\u8fdb\u884c\u4e00\u4e2a\u56db\u8f74\u98de\u884c\u5668\u7684\u63a7\u5236\u7cfb\u7edf\u8bbe\u8ba1\uff0c\u5e76\u7528Arduino\u642d\u8f7d\uff0c\u5347\u7a7a\uff0c\u6d4b\u8bd5\u3002<\/p>\n<p>\uff1d\uff1d\uff1d\u672c\u6587\u7684\u9884\u8bbe\u57fa\u7840\u662f\u7ebf\u6027\u4ee3\u6570\u6570\u7406\u65b9\u7a0b\u548c\u7406\u8bba\u529b\u5b66\u4e0e\u4e00\u5b9a\u7684\u8ba1\u7b97\u673a\u57fa\u7840\uff0c\u5982\u679c\u7f3a\u5c11\u8fd9\u90e8\u5206\u5efa\u8bae\u53bbCoursera\u4e0a\u770b\u300a\u79fb\u52a8\u673a\u5668\u4eba\u7684\u63a7\u5236\u300b\u6216\u8005\u94b1\u8001\u7684\u300a\u5de5\u7a0b\u63a7\u5236\u8bba\u300b\uff0c\u90a3\u91cc\u9762\u8865\u4e86\u70b9\u8fd9\u65b9\u9762\u7684\u57fa\u7840\uff0c\u4f46\u662f\u535a\u4e3b\u89c9\u5f97\u8fc7\u4e8e\u5197\u6742\uff0c\u5728\u8fd9\u91cc\u7684\u7b14\u8bb0\u76f4\u63a5\u7701\u53bb\u3002<\/p>\n<h2>\u6982\u8bba LTI Model<\/h2>\n<p>\u9996\u5148\u5148\u660e\u786e\u6211\u4eec\u8981\u63a7\u5236\u7684\u5bf9\u8c61\uff0c\u662f\u4e00\u4e2a\u7531\u5411\u91cf$$!\\vec x=(x_1,x_2,x_3..)$$\u63cf\u8ff0\u7684\u72b6\u6001\u7a7a\u95f4\u7684\u4e00\u70b9\u3002\u6211\u4eec\u53d6\u4e00\u4e9b\u7269\u7406\u91cf\uff0c\u7ec4\u6210$$\\vec x$$\u4f7f\u5f97$$\\vec x$$\u8db3\u4ee5\u5b8c\u5168\u63cf\u8ff0\u8fd9\u4e2a\u7cfb\u7edf\u3002<\/p>\n<p>\u6bd4\u5982\u5bf9\u4e8e\u4e00\u4e2a\u8d28\u70b9\u7684\u4e00\u7ef4\u8fd0\u52a8\uff0c\u8bbe\u5176\u5750\u6807\u4e3aq\uff0c\u901f\u5ea6\u4e3a$$\\dot q$$,\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u7528$$!\\vec x=(x1,x2)=(q,\\dot q)$$\u6765\u63cf\u8ff0\u8fd9\u4e2a\u7cfb\u7edf\u3002<\/p>\n<p>OK\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u6709\u7ebf\u6027\u5e38\u5fae\u5206\u65b9\u7a0b\u63a7\u5236\u7684\u8fd0\u52a8\uff0c\u6211\u4eec\u53ef\u4ee5\u603b\u7ed3\u51fa\u6765\u5982\u4e0b\u5f0f\u5b50\uff08\u6dd1\u82ac\u5b66\u7684\u591a\u7684\u559c\u6b22\u770b\u8bc1\u660e\u7684\u8bf7\u53c2\u7167\u5de5\u7a0b\u63a7\u5236\u8bba\u7b2c22\u9875\u4ee5\u540e\u7684\u5341\u9875\uff09<\/p>\n<p>$$!\\dot{\\vec x}=A \\vec x$$<\/p>\n<p>\u8fd9\u4e2a\u5fae\u5206\u65b9\u7a0b\u63a7\u5236\u4e86\u7cfb\u7edf\u7684\u8fd0\u52a8\uff0c\u6bd4\u5982\u56de\u5230\u4e00\u7ef4\u8d28\u70b9\uff0c\u4e00\u4e2a\u81ea\u7531\u7684\u4e00\u7ef4\u8d28\u70b9\u6709<\/p>\n<p>$$!\\dot{\\vec x} = \\begin{bmatrix} 0 &amp; 1\\\\0 &amp; 0\\end{bmatrix} \\vec x$$<br \/>\n\u5176\u4e2d<\/p>\n<p>$$!\\vec x=\\begin{bmatrix} q \\\\ \\dot q \\end{bmatrix}$$<\/p>\n<p>(MathJax\u6253\u77e9\u9635\u771f\u9ebb\u70e6)<\/p>\n<p>\u90a3\u4e48\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u4e00\u4e2a\u72b6\u6001\u7a7a\u95f4\u7684\u8fd0\u884c\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u521d\u59cb\u6761\u4ef6$$\\vec x_0$$\u5c31\u53ef\u4ee5\u8f7b\u677e\u5f97\u5230\u6574\u4e2a\u7cfb\u7edf\u7684\u8f68\u8ff9\u3002<\/p>\n<h2>\u7a33\u5b9a\u6027\u4e0e\u80fd\u63a7\u6027<\/h2>\n<p>\u6839\u636e\u4e00\u5927\u5806\u7684\u8bc1\u660e\uff0c\u5bf9\u4e8e\u8fd9\u79cd\u7ebf\u6027\u7cfb\u7edf\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a\u7b80\u5355\u7684\u7ed3\u8bba\uff0c\u5982\u679c\u8fd9\u4e2a\u77e9\u9635A\u7684\u6bcf\u4e2a\u7279\u5f81\u6839 $$\\lambda$$\u6709$$Re (\\lambda)&lt;0$$\uff0c\u5219\u662f\u6e10\u8fdb\u7a33\u5b9a\uff1b\u5982\u679c$$Re (\\lambda)&lt;=0$$\uff1b\u5219\u4e34\u754c\u7a33\u5b9a\uff0c\u5982\u679c$$Re (\\lambda)&gt;0$$\u5219\u53d1\u6563\u3002<\/p>\n<p>\u4e14\u53d1\u6563\u7684\u65b9\u5411\u548c\u6b64\u7279\u5f81\u503c\u5bf9\u5e94\u7684\u7279\u5f81\u5411\u91cf\u6709\u4e00\u5b9a\u5173\u7cfb\uff08\u53ef\u4ee5\u8ba4\u4e3a\u662f\u671d\u5411\uff09<\/p>\n<p>\u5177\u4f53\u5173\u4e8e\u7a33\u5b9a\u6027\u7684\u5b9a\u4e49\u8bf7\u53c2\u89c1wiki\u767e\u79d1\u00a0<a href=\"\u674e\u96c5\u666e\u8bfa\u592b\u7a33\u5b9a\u6027\">\u674e\u96c5\u666e\u8bfa\u592b\u7a33\u5b9a\u6027<\/a><\/p>\n<p>\u8fd9\u65f6\u5019\u6211\u4eec\u5982\u679c\u60f3\u63a7\u5236\u8fd9\u4e2a\u7cfb\u7edf\uff0c\u5c31\u9700\u8981\u7ed9\u7cfb\u7edf\u52a0\u5165\u4e00\u4e9b\u5e72\u6270\u3002\u6211\u4eec\u8bbe\u8fd9\u4e2a\u5e72\u6270\u4e3a\u4e00\u4e2a\u5411\u91cf $$\\vec u$$\uff0c\u8fd9\u65f6\u5019\u6211\u4eec\u53ef\u4ee5\u5c06\u7cfb\u7edf\u7684\u8fd0\u52a8\u65b9\u7a0b\u91cd\u65b0\u5199\u4f5c<\/p>\n<p>$$!\\dot{\\vec x}=A \\vec x+B \\vec u$$<\/p>\n<p>\u6bd4\u5982\u5728\u4e0a\u9762\u7684\u90a3\u4e2a\u8d28\u70b9\u7684\u95ee\u9898\uff0cu\u53ef\u4ee5\u662f\u6a21\u62df\u4e00\u4e2a\u7cfb\u6570\u4e3ak\u7684\u5f39\u7c27\u7684\u8f93\u51fa\uff0c\u90a3\u4e48\u5e76\u4e14\u6709w\u7684\u963b\u5c3c<\/p>\n<p>$$B=\\begin{bmatrix}0 &amp; 0\\\\-k&amp; -w\\end{bmatrix}$$<\/p>\n<p>\u8fd9\u65f6\u5019\u6211\u4eec\u53ef\u4ee5\u91cd\u65b0\u770b\u4e0b\uff0c$$\\vec x$$\u7684\u7cfb\u6570\u6210\u4e3a\u4e86A+B<\/p>\n<p>\u6211\u4eec\u65e0\u59a8\u770b\u4e0b\uff0c\u5bf9\u4e8e\u5355\u72ec\u8d28\u70b9\u7684\u8fd0\u52a8\uff0cA\u7684\u7279\u5f81\u503c\u4e3a(0,0)\u8fd9\u4e5f\u5c31\u662f\u610f\u5473\u7740A\u53ea\u6709\u57280\u521d\u59cb\u6761\u4ef6\u4e0b\u7a33\u5b9a<\/p>\n<p>$$A=\\begin{bmatrix}0 &amp; 1\\\\-k&amp; -w\\end{bmatrix}$$<\/p>\n<p>\u800c\u52a0\u5165\u5f39\u7c27\u540e\u5176\u7279\u5f81\u503c\u6210\u4e3a<\/p>\n<p>$$!\\lambda = \\frac{1}{2} ( -w \\pm \\sqrt{ 4-k^2 + w^2} ) $$<\/p>\n<p>\u53ea\u6709\u5728w&gt;0\u65f6,$$Re(\\lambda)&lt;0 $$\u662f\u6e10\u8fdb\u7a33\u5b9a\uff0c\u5373\u6536\u655b\u5230\u539f\u70b9\uff0c\u82e5w=0,$$Re(\\lambda)=0 $$\uff0c\u5728\u975e0\u8d77\u59cb\u70b9\u4f1a\u9677\u5165\u65e0\u5c3d\u7684\u8fd0\u52a8\uff0cw&gt;0\u5219$$Re(\\lambda)&gt;0 $$\u53d1\u6563\u3002<\/p>\n<p>\u53e6\u4e00\u4e2a\u9700\u8981\u8ba8\u8bba\u7684\u95ee\u9898\u662f\u7cfb\u7edf\u7684<a href=\"http:\/\/baike.baidu.com\/view\/37816.htm\">\u80fd\u63a7\u6027<\/a><\/p>\n<p>\u5982\u679c\u6211\u4eec\u6709$$!rank[ B,AB, A^2B,&#8230;, A^{n-1} B] = n = dim(A)$$\u5219\u7cfb\u7edf\u80fd\u63a7\uff0c\u5426\u5219\u662f\u4e0d\u884c\u6ef4\u3002\u5bf9\u4e8e\u4e0d\u8db3\u7684\u7cfb\u7edf\uff0c\u8fd9\u610f\u5473\u7740\u6211\u4eec\u65e0\u6cd5\u8fbe\u5230\u73b0\u5728\u786e\u5b9a\u7684\u72b6\u6001\u7a7a\u95f4\u5185\u7684\u6240\u6709\u70b9\uff0c\u8fd9\u6837\u6211\u4eec\u9700\u8981\u5bf9\u4e8e\u72b6\u6001\u7a7a\u95f4\u8fdb\u884c\u7b80\u5316<\/p>\n<h2>\u00a0\u8d1f\u53cd\u9988<\/h2>\n<p>\u90a3\u4e48\u5bf9\u4e8e\u4e00\u4e2a\u7cfb\u7edf\uff0c\u6211\u4eec\u5f15\u5165\u4f20\u611f\u5668\uff0c\u89c2\u6d4b\u5230\u7684\u5750\u6807\u4e3a$$\\vec y$$\uff0c\u5176\u4e2d$$\\vec y=C \\vec x$$\uff0c\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u5f15\u5165<a href=\"http:\/\/zh.wikipedia.org\/wiki\/\u8d1f\u53cd\u9988\">\u8d1f\u53cd\u9988<\/a>\uff08\u5443\u3002\u3002\u8fd9\u4e2a\u73a9\u610f\u80fd\u6709\u5174\u8da3\u8bfb\u8fd9\u4e2ablog\u7684\u4eba\u90fd\u770b\u7684\u5f88\u591a\u4e86\u5427\uff09\u3002\u4f7f\u5f97$$!\\vec u= -k \\vec y$$<\/p>\n<p>\u90a3\u4e48\u6709<\/p>\n<p>$$\\dot {\\vec x}=(A-BKC)x$$<\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u5982\u679c\u60f3\u8981\u7cfb\u7edf\u7a33\u5b9a\u5728\u67d0\u4e00\u4e2a\u72b6\u6001\uff08\u6781\u70b9\uff09\uff0c\u90a3\u4e48\u8bbe\u8ba1k\u4f7f\u5f97<\/p>\n<p>$$Re(\\lambda) &lt; 0 \u00a0, \\forall \\lambda \\in eig(A-BKC)$$\u5373\u53ef\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6700\u8fd1\u770b\u4e86\u4e0d\u5c11\u94b1\u8001\u7684\u63a7\u5236\u8bba\uff0c\u4e5f\u5728coursera\u770b\u4e86\u4e00\u4e2a\u504f\u5e94\u7528\u5411\u7684\u63a7\u5236\u8bfe\u7a0b\uff0c\u662f\u65f6\u5019\u5199\u70b9\u9879\u76ee\u4e86\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/posts\/419"}],"collection":[{"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=419"}],"version-history":[{"count":25,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/posts\/419\/revisions"}],"predecessor-version":[{"id":444,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/posts\/419\/revisions\/444"}],"wp:attachment":[{"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=419"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=419"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}