Structure-Exploiting Distributionally Robust Control of Non-Homogeneous Markov Jump Linear Systems

Abstract

The contribution of this letter is the mean-square stabilization of discrete-time Markov jump linear systems with mixed known, unknown, and time-varying transition probabilities. To handle uncertainties in the transition probabilities, we develop a control strategy utilizing mode-dependent static state feedback controllers and introduce data-based ambiguity sets that, extending existing literature, account for known, unknown and time-varying probabilities. These ambiguity sets are constructed using estimated transition matrices and probabilistic bounds derived from the Dvoretzky-Kiefer-Wolfowitz inequality. We validate the effectiveness of our method with numerical simulations on a control system subject to deadline overruns, demonstrating the improvements of incorporating partial knowledge of the transition probabilities.