  We present a data-driven model predictive control scheme for
chance-constrained Markovian switching systems with unknown switching
probabilities. Using samples of the underlying Markov chain, ambiguity sets of
transition probabilities are estimated which include the true conditional
probability distributions with high probability. These sets are updated online
and used to formulate a time-varying, risk-averse optimal control problem. We
prove recursive feasibility of the resulting MPC scheme and show that the
original chance constraints remain satisfied at every time step. Furthermore,
we show that under sufficient decrease of the confidence levels, the resulting
MPC scheme renders the closed-loop system mean-square stable with respect to
the true-but-unknown distributions, while remaining less conservative than a
fully robust approach.
