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We present a learning model predictive control (MPC) scheme forchance-constrained Markov jump systems with unknown switching probabilities.Using samples of the underlying Markov chain, ambiguity sets of transitionprobabilities are estimated which include the true conditional probabilitydistributions with high probability. These sets are updated online and used toformulate a time-varying, risk-averse optimal control problem. We proverecursive feasibility of the resulting MPC scheme and show that the originalchance constraints remain satisfied at every time step. Furthermore, we showthat under sufficient decrease of the confidence levels, the resulting MPCscheme renders the closed-loop system mean-square stable with respect to thetrue-but-unknown distributions, while remaining less conservative than a fullyrobust approach. Finally, we show that the value function of the learning MPCconverges from above to its nominal counterpart as the sample size grows toinfinity. We illustrate our approach on a numerical example.

A General Framework for Learning-Based Distributionally Robust MPC of Markov Jump Systems