随机动力系统最优控制准则研究  

Analysis of optimal control criteria for stochastic dynamic systems

作　　者：李杰[1] 彭勇波[1,2] 陈建兵[1] 

机构地区：[1]同济大学土木工程防灾国家重点实验室,上海200092 [2]同济大学上海防灾救灾研究所,上海200092

出　　处：《地震工程与工程振动》2010年第1期112-117,共6页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金创新研究群体科学基金项目(50621062);国家自然科学基金项目(10872148);863计划(2008AA05Z413)联合资助项目

摘　　要：根据线性二次最优控制理论,给出了系统随机最优控制的控制律一般形式。从目标控制量的物理意义出发,提出了基于系统概率密度演化分析的最优控制准则,建立了递阶层次的演化过程控制准则类。以线性单自由度体系随机地震反应最优控制为例,分析了各控制准则类的权矩阵参数优化结果,并根据最优控制律进行了系统随机最优控制研究。结果表明,本文提出的系统随机最优控制的控制律确定方法可以对系统性态进行有效的控制。The general form of system stochastic optimal control policy is proposed in this classical optimal control theory of linear quadratic regulator （LQR）. The control criteria of paper according to the system stochastic optimal control involving the probabihty density evolution analysis are presented in reference to the physical senses of control objectives developed. The o , and three classes of control criteria ptimal hinging on evolution processes with hierarchical levels are control of stochastic seismic response of a linear single-degree-of-freedom system is investi- gated for illustrative purpose. Optimal weighting matrices related to the classes of control criteria are addressed, by which the stochastic optimal control is carried out. The numerical results reveal that the control effect relies on the physical meanings of control criteria, of which the exceedance probability criterion of the class of comprehensive control criteria is more elegant and more economic than other criteria. It is noted, meanwhile, that the proposed methodology designing control policies of system stochastic optimal control can govern the system performance efficiently.

关 键 词：随机最优控制 概率密度演化 最优控制准则 超越概率 权矩阵优化 

分 类 号：O232[理学—运筹学与控制论] TB114.2[理学—数学]