AN APPROACH TO SWITCHED SYSTEMS OPTIMAL CONTROL BASED ON PARAMETERIZATION OF THE SWITCHING INSTANTS
AN APPROACH TO SWITCHED SYSTEMS OPTIMAL CONTROL BASED ON PARAMETERIZATION OF THE SWITCHING INSTANTS
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一种基于切换时刻参数化的切换系统优化控制方法
DOI：
10.3182/20020721-6-es-1901.00310
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
P. Antsaklis
中科院分区：
文献类型：
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作者：
Xuping Xu;P. Antsaklis
摘要 本文为切换系统最优控制提供了一种可行的通用方法。这种最优控制问题不仅需要求解最优连续输入，还需要求解最优切换序列。许多实际问题仅涉及在给定开关次数和活动子系统序列的情况下的优化。这是作者在之前的论文中提出的两阶段优化方法的第一阶段。为了解决第一阶段的问题，需要知道最优成本相对于切换时刻的导数。在（Xu 和 Antsaklis，2001）中，我们提出了一种解决此类特殊问题的方法，即一般切换线性二次问题。在本文中，（Xu 和 Antsaklis，2001）的思想被扩展到一般的切换系统最优控制问题，并提出了解决这些问题的方法。该方法首先将第一阶段问题转化为由切换时刻参数化的等价问题，然后根据状态、辅态、平稳性方程、边界和连续性条件及其微分形成的两点边值微分代数方程的解来获得导数的值。文中给出了一些例子来说明结果。
Abstract This paper provides a viable general approach to switched systems optimal control. Such optimal control problems require the solutions of not only optimal continuous inputs but also optimal switching sequences. Many practical problems only involve optimization where the number of switchings and the sequence of active subsystems are given. This is stage 1 of the two stage optimization methodology proposed by the authors in previous papers. In order to solve stage 1 problems, the derivatives of the optimal cost with respect to the switching instants need to be known. In (Xu and Antsaklis, 2001), we proposed an approach for solving a special class of such problems, namely, general switched linear quadratic problems. In this paper, the idea of (Xu and Antsaklis, 2001) is extended to general switched systems optimal control problems and an approach is proposed for solving them. The approach first transcribes a stage 1 problem into an equivalent problem parameterized by the switching instants and then the values of the derivatives are obtained based on the solution of a two point boundary value differential algebraic equation formed by the state, costate, stationarity equations, the boundary and continuity conditions and their differentiations. Examples are shown to illustrate the results in the paper.