Learning-Based Distributionally Robust Model Predictive Control of Markovian Switching Systems with Guaranteed Stability and Recursive Feasibility

TL;DR

This paper introduces a data-driven, distributionally robust model predictive control method for Markovian switching systems with unknown transition probabilities, ensuring stability, recursive feasibility, and chance constraint satisfaction.

Contribution

It develops an online adaptive MPC scheme that estimates ambiguity sets of transition probabilities from data, guaranteeing stability and feasibility for systems with unknown Markovian dynamics.

Findings

Recursive feasibility of the proposed MPC scheme is proven.

Chance constraints are satisfied at every time step.

The method achieves less conservativeness than fully robust approaches.

Abstract

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.