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| 线性Markov 切换系统的随机Nash 微分博弈及混合H2/H∞ 控制 | |
| 引用本文： | 朱怀念,张成科,王明亮.线性Markov 切换系统的随机Nash 微分博弈及混合H2/H∞ 控制[J].控制与决策,2013,28(8):1157-1164. |
| 作者姓名： | 朱怀念 张成科 王明亮 |
| 作者单位： | 1. 广东工业大学 管理学院,广州,510520 2. 广东工业大学 经济与贸易学院,广州,510520 |
| 基金项目： | 国家自然科学基金项目(71171061)；广东省自然科学基金项目 |
| 摘 要： | 研究线性Markov切换系统的随机Nash微分博弈问题。首先借助线性Markov切换系统随机最优控制的相关结果，得到了有限时域和无线时域Nash均衡解的存在条件等价于其相应微分(代数) Riccati方程存在解，并给出了最优解的显式形式；然后应用相应的微分博弈结果分析线性Markov切换系统的混合H2/H∞控制问题；最后通过数值算例验证了所提出方法的可行性。 |
| 关 键 词： | 线性Markov切换系统 微分博弈 混合H2/H∞控制 |
| 收稿时间： | 2012/4/16 0:00:00 |
| 修稿时间： | 2012/10/19 0:00:00 |
Linear quadratic stochastic Nash differential games and mixed H2/H∞ control for Markov jump linear systems |
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| ZHU Huai-nian,ZHANG Cheng-ke,WANG Ming-liang.Linear quadratic stochastic Nash differential games and mixed H2/H∞ control for Markov jump linear systems[J].Control and Decision,2013,28(8):1157-1164. | |
| Authors: | ZHU Huai-nian ZHANG Cheng-ke WANG Ming-liang |
| Abstract: | Linear quadratic stochastic Nash differential games for Markov jump linear systems are studied. By utilizing some results of stochastic optimal control for Markov jump linear systems, the existence condition of finite horizon stochastic Nash games is equivalent to the solvability of the associated differential Riccati equations, and that of infinite horizon stochastic Nash games is equivalent to the solvability of the associated algebraic Riccati equations. Moreover, explicit expressions of the optimal strategies are constructed. The results are applied to the mixed H2/H∞ control problem for Markov jump linear systems. Finally, a numeric example is given to show the feasibility of the proposed method. |
| Keywords: | Markov jump linear systems differential games mixed H2/H∞control |
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