发表机构
University of São Paulo at São Carlos; University of Illinois Urbana-Champaign（圣保罗大学圣卡洛斯分校; 伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对模式仅知属于不确定簇的马尔可夫跳变线性系统，提出极小极大鲁棒控制，简化为Riccati递归，并证明收敛与稳定。
AI 中文摘要
本文考虑当活动系统模式并非精确已知时，马尔可夫跳变线性系统的控制问题。我们假设真实模式仅已知属于观测到的模式簇，这使得动力学和相关的转移概率均具有不确定性。在此设定下，我们构造了一个极小极大最优控制问题，目标为鲁棒调节。利用正则化最小均方优化结果，我们描述了该问题的解如何简化为Riccati递归，使得控制器仅依赖于模式所属簇的信息。随后，我们建立了递归的收敛性以及所得闭环系统的稳定性。数值算例说明了所提方法的有效性。
英文摘要
In this paper, we consider the control of Markov jump linear systems when the active system mode is not exactly known. We rather assume that this true mode is only known to belong to an observed cluster of modes, making both the dynamics and the associated transition probabilities uncertain. We construct a min-max optimal control problem in this setting, with the objective of robust regulation. Using results in regularized least mean-square optimization, we describe how the solution of this problem can be reduced to a Riccati recursion, such that the controller depends only on knowledge of which cluster the mode lies in. We subsequently establish convergence of the recursion and stability of the resulting closed-loop system. A numerical example illustrates the effectiveness of the proposed methodology.
Comments8 pages, 2 figures
