Adaptive model predictive control for a class of constrained linear systems with parametric uncertainties

Abstract This paper investigates adaptive model predictive control (MPC) for a class of constrained linear systems with unknown model parameters. We firstly propose an online strategy for the estimation of unknown parameters and uncertainty sets based on the recursive least square technique. Then the estimated unknown parameters and uncertainty sets are employed in the construction of homothetic prediction tubes for robust constraint satisfaction. By deriving non-increasing properties on the proposed estimation routine, the resulting tube-based adaptive MPC scheme is recursively feasible under recursive model updates, while providing the less conservative performance compared with the robust tube MPC method. Furthermore, we theoretically show that the perturbed closed-loop system is asymptotically stable under standard assumptions. Finally, numerical simulations and comparisons are given to illustrate the efficacy of the proposed method.