离散时间时变Markov跳变系统的线性二次最优控制
Linear Quadratic Optimal Control for Discrete Time Time-Varying Markov Jump Systems
摘要: 研究了离散时间时变Markov跳变系统在有限时域上的最优控制问题。证明了任何离散时间时变Markov跳变系统的最优控制问题都可以通过广义代数Riccati方程的解来确定；也证明了最优控制问题的可达性是广义代数Riccati方程解的存在性的充分条件；最后通过数值举例来验证结果的正确性。
Abstract: The optimal control of discrete-time time-varying Markov jump systems in infinite horizon is stud-ied. It is proved that the optimal control problem of any discrete time time-varying Markov jump system can be determined by the solution of generalized algebraic Riccati equation. It is also proved that the attainablility of the optimal control problem is a sufficient condition for the existence of so-lutions of generalized algebraic Riccati equations. Finally, numerical examples are given to verify the correctness of the results.
文章引用：赵红霞, 何鑫, 贾亚琪, 张春梅. 离散时间时变Markov跳变系统的线性二次最优控制[J]. 应用数学进展, 2023, 12(5): 2569-2581. https://doi.org/10.12677/AAM.2023.125258

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