基于博弈论方法的线性马尔可夫跳变系统H_∞控制

H_∞ Control Based on Game Theory Approach for Markov Jump Linear Systems

应用微分博弈理论研究了噪声依赖于状态x(t)、控制u(t)和干扰v(t)的Ito型线性马尔可夫跳变系统H∞鲁棒控制设计问题.首先将系统的控制变量u(t)视为博弈的一方,随机性干扰v(t)视为博弈的另一方,从而把H∞鲁棒控制问题转化为一个二人零和微分博弈问题,然后通过分析此微分博弈问题得到了H∞鲁棒控制存在的条件等价于相应的矩阵Riccati代数方程存在解,同时给出了H∞鲁棒控制策略的显式表达式,最后给出数值算例验证了其可行性.

A game approach to H∞robust control for Markov jump linear systems with （x, u, v）-dependent noise described by an It6-type equation is presented. By viewing the control variable u（t） and stochastic disturbance v（t） of the system as oneplayer and the other player respectively, the H∞ robust control problem is transformed into a two-person zero-sum diflbrential game model. Moreover, by solving this differential game, it is proved that the existence condition of the H∞ robust control strategy is equivalent to the solvability of the associated Riccati equation, and the explicit formula of the H~ robust control strategy is obtained. Finally, a numeric example is given to prove its feasibility.