无限时域离散时间随机系统的H_2/H_∞探究

Infinite Horizon Stochastic Mixed H_2/H_∞ Control for Stochastic Systems

该文用H2/H∞混合控制法通过系统的精确能观性和精确能检性来求出无限时区离散时间随机系统的线性二次型随机微分对策问题的解,并且给出了无限时域随机微分对策问题的最优策略[1](纳什均衡点)以及最优消耗函数值,解决此类问题的关键在于寻求四个耦合的方程组的解,同时给出了一种解决此类耦合方程组的递归方法。

In this paper,infinite-time linear quadratic（LQ） differential games for discrete-time stochastic s- ystems are discussed via the exact observability and exact detectability with mixed HJH,, control method. By means of them,the optimal strategies（Nash equilibrium strategies） and the optimal cost values for infinite horizon stochastic differential games are obtain-ed.lt indicates that the infinite horizon LQ stochastic dif- ferential games are associated with four coupled matrix-valued equations.Furthermore,an iterative algo- rithm is proposed to solve the four coupled equations.