离散奇异随机Markov跳变系统Stackelberg博弈及其应用

The Stackelberg games for discrete-time stochastic singular markov jump systems and its application

应用配方法探讨一类离散奇异随机Markov跳变系统的Stackelberg博弈问题。分别得到有限时间和无限时间情形下,离散奇异随机Markov跳变系统Stackelberg策略的存在条件等价于相应的代数Riccati方程组存在解,并给出了Stackelberg均衡策略的显式表达及最优性能泛函值。最后借鉴前人研究,将所得结果应用于离散奇异随机Markov跳变系统的H_(2)/H_(∞)控制问题,得到离散奇异随机Markov跳变系统的H_(2)/H_(∞)控制策略存在条件及其显式表达。

The linear quadratic Stackelberg games for discrete-time stochastic singular Markov jump systems in finite time and infinite time were studied respectively in this paper.By using the square completion technique,the existence conditions of the Stackelberg strategies for the discrete-time stochastic singular Markov jump system were equivalent to the solvability of the associated algebraic Riccati equations in the finite time case and infinite time case respectively.The explicit expressions of the Stackelberg equilibrium strategies and the optimal functional value were also obtained.Finally,the results were applied to the H_(2)/H_(∞) control problem of discrete-time stochastic singular Markov jump systems,and the existence and explicit expression of the corresponding H_(2)/H_(∞) control strategy were obtained.