A semidefinite programming approach for polynomial switched optimal control problems

Davoudi Ramtin; Hosseini Seyed Mohammad

摘要

Summary >This paper considers solving optimal control of switched systems with polynomial data globally, where the number of switches and the switching signal are not preassigned. The problem is transformed into an embedded polynomial form in which a continuous variable controls the switching policy. Then, using occupation measures, the embedded optimal control problem is formulated as an infinite‐dimensional linear programming (LP) over the space of measures. A polynomial sum‐of‐squares strengthening corresponding to conic dual of the measure LP problem provides an approximating optimal feedback control for both classical control and the switching signal. Furthermore, the optimal switching signal is calculated without mode projection. Finally, three simulation experiments are included to confirm the theoretical results in the paper. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“main”XML：Lang =“en”XML：ID =“OCA2500-ABS-0001”> <标题类型=“main”>摘要</ title> >本文考虑了全球多项式数据的开关系统的最佳控制，其中开关的数量和开关信号不会预先评估。问题被转换为嵌入多项式形式，其中连续变量控制切换策略。然后，使用占用措施，嵌入式最优控制问题被制定为措施空间的无限维线性编程（LP）。对应于测量LP问题的锥形双量的强化电力的多项式平方和为经典控制和开关信号提供近似最佳反馈控制。此外，无需模式投影计算最佳切换信号。最后，包括三个模拟实验，以确认纸张中的理论结果。</ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-27675/'>《Optimal Control Applications and Methods》</a> <b style="margin: 0 2px;">|</b><span>2019年第4期</span><b style="margin: 0 2px;">|</b><span>共21页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Davoudi Ramtin&option=202" target="_blank" rel="nofollow">Davoudi Ramtin;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Hosseini Seyed Mohammad&option=202" target="_blank" rel="nofollow">Hosseini Seyed Mohammad;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department of Applied Mathematics Faculty of Mathematical SciencesTarbiat Modares UniversityTehran Iran;</p> <p>Department of Applied Mathematics Faculty of Mathematical SciencesTarbiat Modares UniversityTehran Iran;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/1147.html" title="应用数学">应用数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=embedding transformation&option=203" rel="nofollow">embedding transformation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=feedback control&option=203" rel="nofollow">feedback control;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=moments&option=203" rel="nofollow">moments;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=sum‐of‐squares&option=203" rel="nofollow">sum‐of‐squares;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=switched systems&option=203" rel="nofollow">switched systems;</a> </p> <div class="translation"> 机译：嵌入转化;反馈控制;矩;平方和平方和切换系统; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704024160864.html">A semidefinite programming approach for polynomial switched optimal control problems</a> <b>[J]</b> . <span> <a 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According to the method, an application program is stored in nonvolatile memory of a first computer as a plurality of individual and independent machine executable code modules. in response to a request from a second computer transmitted over a network connection, the first computer retrieves a selected module from said machine-executable code modules and only that selected code module from memory and transmits the code module selected by network connection to the second computer.</a> <b>[P]</b> . <span> 外国专利：  BR9811593A </span> <span> . 2002-01-22</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> 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