基于鲁棒分析的一类随机系统的保性能控制

Guaranteed Cost Control of a Class of Linear Stochastic Systems on the Basis of Robust Analysis

在不确定线性系统保性能控制研究的基础上,对成本控制矩阵不确定随机二次控制问题进行了研究,给出了一类线性随机系统及相应系数不确定线性随机系统保性能控制的定义,并利用伊藤公式和LM I(线性矩阵不等式)方法,在其满足均方稳定的条件下,得到了相应线性随机系统的保性能控制律的存在条件,即若线性随机系统均方稳定,则其相应的保性能控制律存在.最后将最优保成本控制律的设计转化为一个凸优化问题,即求解一个线性矩阵不等式问题.

This paper discusses the guaranteed cost control of a class of linear stochastic systems on the research of uncertain linear systems. The authors give the definition of this linear stochastic systems＇guaranteed cost control, by using Ito formula and linear matrix inequality, combined its square-stability, under the supposition of the square stability of this kind of linear stochastic system, gets the accordingly guaranteed cost control condition. The conclusion is, if the linear stochastic system is square-stability, then its guaranteed cost control exists. Finally, the problem of designing a optimal guaranteed cost control can be turned into a convex optimal problem.