切换系统线性二次最优控制:动态规划方法  

Linear quadratic optimal control of switching systems:dynamic programming approach

作　　者：吕东方[1] 毕永利[1] 丛屾[1] LYU Dong-Fang;BI Yong-Li;CONG Shen(School of Mechanical ＆ Electrical Engineering, Heilongjiang University, Harbin 150080, China)

机构地区：[1]黑龙江大学机电工程学院,哈尔滨150080

出　　处：《黑龙江大学工程学报》2017年第4期68-74,共7页Journal of Engineering of Heilongjiang University

基　　金：国家自然科学基金资助项目(61573131);黑龙江省自然科学基金资助项目(F201429;LC201428)

摘　　要：考虑切换系统线性二次最优控制问题,对于时变子系统,研究由状态反馈控制与切换控制组成的最优反馈控制对的存在性。利用动态规划的原理和方法,论证了同时构造最优状态反馈控制与切换控制的可行性,并且通过一组微分Riccati边值问题的解给出了最优控制对的设计方案。对于一维切换系统,证明了最优控制对存在性的结论。提出了便于实现的反馈控制与切换控制分层独立设计的次优化方法。The linear quadratic optimal control of switched systems is investigated. For the time-varying subsystems, the problem is to find the optimal control pair consisting of the state-feedback control and the switching control. Based on the dynamic programming approach, the optimal switching control and optimal state-feedback control are constructed simultaneously by solving a set of differential Riccati equations with boundary conditions. For the one-dimensional case, it is shown the existence of optimal control pair. Meanwhile a flexible suboptimal control sketch is presented, for which the switching control and state-feedback control are constructed separately.

关 键 词：切换系统 时变系统 线性二次最优控制 动态规划 微分Riccati方程 

分 类 号：TP271[自动化与计算机技术—检测技术与自动化装置]