Control of Markov Jump Linear Systems with Uncertain Lumpable Cluster Observations

Abstract

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.