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

  • 摘要: 应用微分博弈理论研究了噪声依赖于状态 xt)、 控制 ut)和干扰 vt)的Itô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 ut)视为博弈的一方,随机性干扰 vt)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.

     

    Abstract: A game approach to Hrobust control for Markov jump linear systems with ( x , u , v )-dependent noise described by an Itô-type equation is presented. By viewing the control variable u (t) and stochastic disturbance v (t) of the system as one player and the other player respectively, the H robust control problem is transformed into a two-person zero-sum differential 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.

     

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