This paper develops a robust Linear Quadratic Regulator (LQR) approach applicable to nonhomogeneous Markov jump linear systems with uncertain transition probability distributions. The stochastic control problem is investigated under two equivalent formulations, using (i) minimax optimization theory, and (ii) a total variation distance metric as a tool for codifying the level of uncertainty of the jump process. By following a dynamic programming approach, a robust optimal controller is derived, which in addition to minimizing the quadratic cost, it also restricts the influence of uncertainty. A solution procedure for the LQR problem is also proposed, and an illustrative example is presented. Numerical results indicate the applicability and effectiveness of the proposed approach.

中文翻译：

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具有未知转移概率的跳跃 LQR 系统


本文开发了一种鲁棒的线性二次调节器（LQR）方法，适用于具有不确定转移概率分布的非齐次马尔可夫跳跃线性系统。在两个等效公式下研究随机控制问题，使用（i）极小极大优化理论，以及（ii）总变差距离度量作为编码跳跃过程不确定性水平的工具。通过遵循动态规划方法，导出了鲁棒的最优控制器，除了最小化二次成本外，还限制了不确定性的影响。还提出了 LQR 问题的求解过程，并给出了一个说明性示例。数值结果表明了所提出方法的适用性和有效性。