Robust Adaptive Model Predictive Control: Performance and Parameter Estimation

For systems with uncertain linear models, bounded additive disturbances and state and control constraints, a robust model predictive control algorithm incorporating online model adaptation is proposed. Sets of model parameters are identified online and employed in a robust tube MPC strategy with a nominal cost. The algorithm is shown to be recursively feasible and input-to-state stable. Computational tractability is ensured by using polytopic sets of fixed complexity to bound parameter sets and predicted states. Convex conditions for persistence of excitation are derived and are related to probabilistic rates of convergence and asymptotic bounds on parameter set estimates. We discuss how to balance conflicting requirements on control signals for achieving good tracking performance and parameter set estimate accuracy. Conditions for convergence of the estimated parameter set are discussed for the case of fixed complexity parameter set estimates, inexact disturbance bounds and noisy measurements.