Chance-Constrained Covariance Steering for Discrete-Time Markov Jump Linear Systems
In this paper, we solve the chance-constrained covariance steering problem for discrete-time Markov Jump Linear Systems (MJLS) using a convex optimization framework. We derive the analytical expressions for the mean and covariance trajectories of time-varying discrete-time MJLS and show that they cannot be separated even without chance constraints, unlike the single-mode dynamics case. To solve the covariance steering problem, we propose a two-step convex optimization framework, which optimizes the mean and covariance subproblems sequentially. Further, we incorporate chance constraints and propose an iterative optimization framework to solve the chance-constrained covariance steering problem. Both problems are originally nonconvex, and we derive convex relaxations which are proved to be lossless at optimality using the Karush-Kuhn-Tucker (KKT) conditions. Numerical simulations demonstrate the proposed method by achieving target covariances while respecting chance constraints under additive noise, bias, and Markovian jump dynamics.