{"id":315,"date":"2024-12-09T20:55:38","date_gmt":"2024-12-09T12:55:38","guid":{"rendered":"http:\/\/106.12.148.75\/?p=315"},"modified":"2024-12-14T15:12:04","modified_gmt":"2024-12-14T07:12:04","slug":"%e3%80%90acados%e3%80%91%e4%b8%8d%e5%90%8c%e7%a7%af%e5%88%86%e5%99%a8%e7%9a%84%e5%8c%ba%e5%88%ab-2","status":"publish","type":"post","link":"https:\/\/jamilblog.top\/?p=315","title":{"rendered":"\u3010Acados\u3011\u4e0d\u540c\u79ef\u5206\u5668\u7684\u533a\u522b"},"content":{"rendered":"\n<p>\u8fd9\u4e9b\u4e0d\u540c\u7684<strong>\u79ef\u5206\u5668\u7c7b\u578b\uff08Integrator type\uff09<\/strong>\uff0c\u901a\u5e38\u662f\u6307\u6570\u503c\u6c42\u89e3\u5668\u5728\u6c42\u89e3\u5e38\u5fae\u5206\u65b9\u7a0b\uff08ODE\uff09\u6216\u5dee\u5206\u65b9\u7a0b\u65f6\u4f7f\u7528\u7684\u7b97\u6cd5\u3002\u4e0d\u540c\u7c7b\u578b\u7684\u79ef\u5206\u5668\u5bf9\u4e8e\u7cfb\u7edf\u7684\u7a33\u5b9a\u6027\u3001\u7cbe\u5ea6\u3001\u8ba1\u7b97\u6548\u7387\u6709\u4e0d\u540c\u7684\u8868\u73b0\uff0c\u5c24\u5176\u662f\u5728\u63a7\u5236\u7cfb\u7edf\u3001\u4f18\u5316\u3001\u7269\u7406\u5efa\u6a21\u7b49\u9886\u57df\u3002\u4ee5\u4e0b\u662f\u8fd9\u4e9b\u79ef\u5206\u5668\u7c7b\u578b\u7684\u7b80\u4ecb\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. <strong>ERK (Explicit Runge-Kutta)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u63cf\u8ff0<\/strong>\uff1a\u663e\u5f0fRunge-Kutta\u65b9\u6cd5\uff08Explicit Runge-Kutta\uff09\u662f\u4e00\u79cd\u5e38\u7528\u7684\u79ef\u5206\u65b9\u6cd5\uff0c\u5c5e\u4e8e\u663e\u5f0f\u6570\u503c\u65b9\u6cd5\u3002\u5b83\u901a\u8fc7\u9010\u6b65\u8ba1\u7b97\u72b6\u6001\u7684\u53d8\u5316\u6765\u63a8\u8fdb\u7cfb\u7edf\u7684\u89e3\u3002<\/li>\n\n\n\n<li><strong>\u4f18\u70b9<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u901a\u5e38\u8ba1\u7b97\u6bd4\u8f83\u7b80\u5355\u548c\u9ad8\u6548\uff0c\u7279\u522b\u9002\u5408\u5904\u7406\u975e\u521a\u6027\u7cfb\u7edf\u3002<\/li>\n\n\n\n<li>\u5bf9\u4e8e\u4e00\u4e9b\u7b80\u5355\u7684\u52a8\u529b\u5b66\u6a21\u578b\uff0c\u6548\u679c\u975e\u5e38\u597d\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u7f3a\u70b9<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5728\u5904\u7406\u521a\u6027\u7cfb\u7edf\u65f6\u53ef\u80fd\u4e0d\u7a33\u5b9a\uff0c\u56e0\u4e3a\u5b83\u9700\u8981\u5f88\u5c0f\u7684\u65f6\u95f4\u6b65\u957f\u6765\u4fdd\u8bc1\u6570\u503c\u7a33\u5b9a\u6027\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>\u9002\u7528\u573a\u666f<\/strong>\uff1a\u9002\u5408\u5904\u7406\u975e\u521a\u6027\u3001\u53d8\u5316\u4e0d\u5267\u70c8\u7684\u7cfb\u7edf\uff0c\u5e38\u7528\u4e8e\u8f83\u4e3a\u7b80\u5355\u7684\u52a8\u529b\u5b66\u95ee\u9898\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. <strong>IRK (Implicit Runge-Kutta)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u63cf\u8ff0<\/strong>\uff1a\u9690\u5f0fRunge-Kutta\u65b9\u6cd5\uff08Implicit Runge-Kutta\uff09\u662f\u663e\u5f0f\u65b9\u6cd5\u7684\u5bf9\u7acb\u9762\uff0c\u79ef\u5206\u6b65\u9aa4\u4e2d\u6d89\u53ca\u5230\u6c42\u89e3\u9690\u5f0f\u65b9\u7a0b\u3002\u5b83\u901a\u8fc7\u8fed\u4ee3\u6c42\u89e3\u6765\u63a8\u8fdb\u72b6\u6001\u7684\u53d8\u5316\u3002<\/li>\n\n\n\n<li><strong>\u4f18\u70b9<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u4e8e\u521a\u6027\u7cfb\u7edf\uff08\u5373\u7cfb\u7edf\u7684\u53d8\u5316\u975e\u5e38\u5267\u70c8\u6216\u53d8\u5316\u901f\u5ea6\u4e0d\u5747\u5300\uff09\uff0cIRK\u65b9\u6cd5\u975e\u5e38\u6709\u6548\uff0c\u80fd\u591f\u5728\u66f4\u5927\u7684\u65f6\u95f4\u6b65\u957f\u4e0b\u4fdd\u6301\u7a33\u5b9a\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u7f3a\u70b9<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u8ba1\u7b97\u76f8\u5bf9\u590d\u6742\uff0c\u56e0\u4e3a\u5b83\u9700\u8981\u89e3\u51b3\u975e\u7ebf\u6027\u65b9\u7a0b\u6216\u8fed\u4ee3\u8fc7\u7a0b\uff0c\u901a\u5e38\u8ba1\u7b97\u91cf\u8f83\u5927\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>\u9002\u7528\u573a\u666f<\/strong>\uff1a\u5f53\u7cfb\u7edf\u5305\u542b\u521a\u6027\u90e8\u5206\u6216\u7cfb\u7edf\u7684\u52a8\u6001\u53d8\u5316\u8f83\u4e3a\u590d\u6742\u65f6\uff0cIRK\u65b9\u6cd5\u66f4\u4e3a\u7a33\u5b9a\u548c\u9ad8\u6548\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. <strong>GNSF (Generalized Neural-Symbolic Framework)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u63cf\u8ff0<\/strong>\uff1aGNSF\u65b9\u6cd5\u4e3b\u8981\u7528\u4e8e\u5904\u7406\u7b26\u53f7\u63a8\u7406\u548c\u795e\u7ecf\u7f51\u7edc\u7684\u7ed3\u5408\u6846\u67b6\uff0c\u5728\u6c42\u89e3\u4f18\u5316\u95ee\u9898\u65f6\u80fd\u591f\u7075\u6d3b\u5904\u7406\u8fde\u7eed\u548c\u79bb\u6563\u52a8\u6001\u3002\u5b83\u901a\u5e38\u7528\u4e8e\u590d\u6742\u7cfb\u7edf\u7684\u5efa\u6a21\u548c\u6c42\u89e3\u3002<\/li>\n\n\n\n<li><strong>\u4f18\u70b9<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u53ef\u4ee5\u7075\u6d3b\u5730\u5904\u7406\u591a\u79cd\u7c7b\u578b\u7684\u52a8\u6001\u7cfb\u7edf\uff0c\u5c24\u5176\u662f\u7ed3\u5408\u4e86\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u7684\u4f18\u5316\u95ee\u9898\u3002<\/li>\n\n\n\n<li>\u5728\u63a7\u5236\u548c\u7269\u7406\u5efa\u6a21\u4e2d\u53ef\u80fd\u66f4\u9002\u5408\u4e00\u4e9b\u590d\u6742\u7684\u6df7\u5408\u52a8\u529b\u7cfb\u7edf\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u7f3a\u70b9<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u8ba1\u7b97\u4e0a\u53ef\u80fd\u975e\u5e38\u590d\u6742\uff0c\u4e14\u5bf9\u95ee\u9898\u7684\u8bbe\u5b9a\u8981\u6c42\u8f83\u9ad8\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>\u9002\u7528\u573a\u666f<\/strong>\uff1a\u9002\u7528\u4e8e\u7ed3\u5408\u795e\u7ecf\u7f51\u7edc\u548c\u7b26\u53f7\u63a8\u7406\u7684\u65b9\u6cd5\uff0c\u7279\u522b\u662f\u5904\u7406\u9ad8\u5ea6\u975e\u7ebf\u6027\u6216\u590d\u6742\u7684\u7cfb\u7edf\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. <strong>DISCRETE (Discrete)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u63cf\u8ff0<\/strong>\uff1a\u79bb\u6563\u79ef\u5206\u65b9\u6cd5\u901a\u5e38\u7528\u4e8e\u79bb\u6563\u4e8b\u4ef6\u7684\u7cfb\u7edf\u6a21\u62df\uff0c\u9002\u5408\u6a21\u62df\u90a3\u4e9b\u5728\u79bb\u6563\u65f6\u95f4\u70b9\u4e0a\u66f4\u65b0\u72b6\u6001\u7684\u7cfb\u7edf\u3002\u8fd9\u79cd\u65b9\u6cd5\u5728\u6bcf\u4e2a\u65f6\u95f4\u6b65\u90fd\u4f1a\u76f4\u63a5\u8ba1\u7b97\u7cfb\u7edf\u72b6\u6001\uff0c\u800c\u4e0d\u662f\u8fde\u7eed\u5730\u63a8\u8fdb\u3002<\/li>\n\n\n\n<li><strong>\u4f18\u70b9<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u8ba1\u7b97\u7b80\u5355\u4e14\u6548\u7387\u8f83\u9ad8\uff0c\u9002\u7528\u4e8e\u6570\u5b57\u5316\u63a7\u5236\u7cfb\u7edf\u6216\u79bb\u6563\u63a7\u5236\u7cfb\u7edf\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u7f3a\u70b9<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u53ef\u80fd\u4e0d\u9002\u5408\u9700\u8981\u8fde\u7eed\u6c42\u89e3\u7684\u7cfb\u7edf\uff0c\u7279\u522b\u662f\u52a8\u6001\u53d8\u5316\u6bd4\u8f83\u8fde\u7eed\u7684\u7cfb\u7edf\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>\u9002\u7528\u573a\u666f<\/strong>\uff1a\u9002\u7528\u4e8e\u79bb\u6563\u63a7\u5236\u548c\u79bb\u6563\u7cfb\u7edf\u7684\u6a21\u62df\uff0c\u4f8b\u5982\u8ba1\u7b97\u673a\u63a7\u5236\u7cfb\u7edf\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5. <strong>LIFTED_IRK (Lifted Implicit Runge-Kutta)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u63cf\u8ff0<\/strong>\uff1aLifted IRK\u65b9\u6cd5\u662fIRK\u65b9\u6cd5\u7684\u6269\u5c55\uff0c\u5b83\u901a\u8fc7\u63d0\u5347\uff08lifting\uff09\u6280\u672f\u5c06\u79bb\u6563\u7684\u52a8\u6001\u7cfb\u7edf\u8f6c\u5316\u4e3a\u66f4\u9ad8\u7ef4\u5ea6\u7684\u7cfb\u7edf\uff0c\u8fdb\u800c\u8fdb\u884c\u6c42\u89e3\u3002\u8fd9\u79cd\u65b9\u6cd5\u7279\u522b\u9002\u5408\u5904\u7406\u591a\u91cd\u65f6\u95f4\u5c3a\u5ea6\u6216\u8005\u6709\u590d\u6742\u7ea6\u675f\u7684\u7cfb\u7edf\u3002<\/li>\n\n\n\n<li><strong>\u4f18\u70b9<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u9002\u7528\u4e8e\u5904\u7406\u9ad8\u5ea6\u7ea6\u675f\u7684\u590d\u6742\u7cfb\u7edf\u6216\u591a\u5c3a\u5ea6\u52a8\u6001\u7cfb\u7edf\u3002<\/li>\n\n\n\n<li>\u63d0\u4f9b\u66f4\u9ad8\u7684\u7cbe\u5ea6\u548c\u7a33\u5b9a\u6027\uff0c\u5c24\u5176\u5728\u7ea6\u675f\u4f18\u5316\u548c\u63a7\u5236\u95ee\u9898\u4e2d\u975e\u5e38\u6709\u6548\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u7f3a\u70b9<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u8ba1\u7b97\u5f00\u9500\u8f83\u5927\uff0c\u8981\u6c42\u8f83\u9ad8\u7684\u6570\u503c\u7a33\u5b9a\u6027\u548c\u8ba1\u7b97\u80fd\u529b\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>\u9002\u7528\u573a\u666f<\/strong>\uff1a\u5f53\u7cfb\u7edf\u6d89\u53ca\u591a\u4e2a\u65f6\u95f4\u5c3a\u5ea6\u6216\u590d\u6742\u7ea6\u675f\u65f6\uff0c\u5c24\u5176\u662f\u5728\u591a\u91cd\u52a8\u6001\u7cfb\u7edf\u7684\u4f18\u5316\u4e2d\u3002<\/p>\n\n\n\n<p>1<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u603b\u7ed3\u5bf9\u6bd4\uff1a<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>ERK<\/strong>\uff1a\u9002\u5408\u975e\u521a\u6027\u7cfb\u7edf\uff0c\u8ba1\u7b97\u6548\u7387\u9ad8\uff0c\u9002\u7528\u4e8e\u8f83\u7b80\u5355\u7684\u6a21\u578b\u3002<\/li>\n\n\n\n<li><strong>IRK<\/strong>\uff1a\u9002\u5408\u521a\u6027\u7cfb\u7edf\uff0c\u80fd\u591f\u5904\u7406\u7cfb\u7edf\u4e2d\u7684\u5f3a\u70c8\u52a8\u6001\u53d8\u5316\uff0c\u4f46\u8ba1\u7b97\u590d\u6742\u3002<\/li>\n\n\n\n<li><strong>GNSF<\/strong>\uff1a\u9002\u7528\u4e8e\u7ed3\u5408\u795e\u7ecf\u7f51\u7edc\u4e0e\u7b26\u53f7\u63a8\u7406\u7684\u590d\u6742\u7cfb\u7edf\uff0c\u9002\u5408\u6df7\u5408\u52a8\u529b\u5b66\u5efa\u6a21\u3002<\/li>\n\n\n\n<li><strong>DISCRETE<\/strong>\uff1a\u9002\u5408\u79bb\u6563\u4e8b\u4ef6\u7cfb\u7edf\u6216\u63a7\u5236\u7cfb\u7edf\uff0c\u8ba1\u7b97\u7b80\u5355\u3002<\/li>\n\n\n\n<li><strong>LIFTED_IRK<\/strong>\uff1a\u9002\u5408\u6709\u591a\u91cd\u65f6\u95f4\u5c3a\u5ea6\u6216\u590d\u6742\u7ea6\u675f\u7684\u7cfb\u7edf\uff0c\u7cbe\u5ea6\u9ad8\u4f46\u8ba1\u7b97\u590d\u6742\u3002<\/li>\n\n\n\n<li><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u8fd9\u4e9b\u4e0d\u540c\u7684\u79ef\u5206\u5668\u7c7b\u578b\uff08Integrator type\uff09\uff0c\u901a\u5e38\u662f\u6307\u6570\u503c\u6c42\u89e3\u5668\u5728\u6c42\u89e3\u5e38\u5fae\u5206\u65b9\u7a0b\uff08ODE\uff09\u6216\u5dee\u5206\u65b9\u7a0b\u65f6\u4f7f\u7528\u7684\u7b97\u6cd5\u3002\u4e0d\u540c\u7c7b &#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[6,5],"tags":[],"class_list":["post-315","post","type-post","status-publish","format-standard","hentry","category-solver","category-tools"],"_links":{"self":[{"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/posts\/315","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jamilblog.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=315"}],"version-history":[{"count":2,"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/posts\/315\/revisions"}],"predecessor-version":[{"id":407,"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/posts\/315\/revisions\/407"}],"wp:attachment":[{"href":"https:\/\/jamilblog.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=315"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jamilblog.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=315"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jamilblog.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=315"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}