Adaptive model predictive control of uncertain constrained systems

This paper studies adaptive model predictive control (AMPC) of systems with time-varying and state-dependent uncertainties. We propose an estimation and prediction architecture within the min-max MPC framework. An adaptive estimator is presented to estimate the set-valued measure of the uncertainty using piecewise constant adaptive law. We show that this measure can be arbitrarily accurate if the sampling period in adaptation is small enough. Based on this measure, a prediction scheme is provided that predicts the time-varying feasible set of the uncertainty over the prediction horizon. The results indicate that the proposed approach can efficiently reduce the size of the feasible set for the uncertainty in min-max MPC setting, and therefore improve the control performance. Simulations verify the theoretical results.