Adaptive MPC for Uncertain Discrete-Time LTI MIMO Systems with Incremental Input Constraints

Abstract

In this paper, an adaptive model predictive control (MPC) strategy is proposed for controlling a discrete-time linear MIMO system with parametric uncertainties and subjected to actuator constraints. Compared to previous results in literature which either solve the constrained MPC problem for stable uncertain systems or the unconstrained MPC problem for unstable uncertain systems, this result, presents a solution approach for constrained MPC problems for fully uncertain and unstable systems. An adaptive law, designed to update the estimated parameters of the plant, is combined with a constrained MPC for an estimated system. A sufficient condition is imposed on the adaptation gain to account for feasibility of the MPC optimization problem in the presence of the actuator constraint. Stability analysis of the closed loop system with the proposed adaptive MPC strategy has been shown to guarantee the ultimate boundedness of the parameter estimation errors and boundedness as well as asymptotic convergence of the tracking errors to zero.