Structure‐preserving local optimal control of mechanical systems

Fla?kamp Kathrin; Murphey Todd D.

摘要

Summary >While system dynamics are usually derived in continuous time, respective model‐based optimal control problems can only be solved numerically, ie, as discrete‐time approximations. Thus, the performance of control methods depends on the choice of numerical integration scheme. In this paper, we present a first‐order discretization of linear quadratic optimal control problems for mechanical systems that is structure preserving and hence preferable to standard methods. Our approach is based on symplectic integration schemes and thereby inherits structure from the original continuous‐time problem. Starting from a symplectic discretization of the system dynamics, modified discrete‐time Riccati equations are derived, which preserve the Hamiltonian structure of optimal control problems in addition to the mechanical structure of the control system. The method is extended to optimal tracking problems for nonlinear mechanical systems and evaluated in several numerical examples. Compared to standard discretization, it improves the approximation quality by orders of magnitude. This enables low‐bandwidth control and sensing in real‐time autonomous control applications. </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 =“OCA2479-ABS-ABS-0001”> <标题类型=“main”>摘要</ title> 虽然系统动态通常在连续时间导出，但是只能在数值上进行各种模型的最优控制问题，即作为离散时间近似。因此，控制方法的性能取决于数字积分方案的选择。在本文中，我们提出了一种机械系统的线性二次最佳控制问题的一阶离散化，该机械系统是结构保留的，因此优选标准方法。我们的方法基于辛集成方案，从而从原始连续时间问题继承结构。从系统动态的辛离散化开始，推导出修改的离散时间Riccati方程，除了控制系统的机械结构之外，还保留了最佳控制问题的Hamiltonian结构。该方法扩展到非线性机械系统的最佳跟踪问题，并在几个数值示例中进行评估。与标准离散化相比，它通过级别提高了近似质量。这使得能够在实时自主控制应用中进行低带宽控制和感应。</ 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2期</span><b style="margin: 0 2px;">|</b><span>共20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=Fla?kamp Kathrin&option=202" target="_blank" rel="nofollow">Fla?kamp Kathrin;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Murphey Todd D.&option=202" target="_blank" rel="nofollow">Murphey Todd D.;</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>Optimization and Optimal Control Center for Industrial MathematicsUniversity of BremenBremen Germany;</p> <p>Neuroscience and Robotics LaboratoryNorthwestern UniversityEvanston Illinois;</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=discrete Riccati equations&option=203" rel="nofollow">discrete Riccati equations;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=linear quadratic control&option=203" rel="nofollow">linear quadratic control;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=optimal control&option=203" rel="nofollow">optimal control;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=symplectic integration&option=203" rel="nofollow">symplectic integration;</a> </p> <div class="translation"> 机译：离散的Riccati方程;线性二次控制;最优控制;辛融合; 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