Adaptive model predictive control with one free control move for uncertain discrete-time linear systems with bounded disturbance

This paper proposes an adaptive model predictive control (MPC) with one free control move for uncertain discrete-time linear systems with additive bounded disturbance. With the set-based parameter estimation strategy, the estimated parameters and uncertainty set are simultaneously updated to adapt the true system model online. Then the parameter uncertainty set is used by the modified MPC with one free control move to enhance the control performance. By utilizing the quadratic boundedness (QB) condition, the robust min–max MPC optimization formulation with the infinite horizon is converted into the form of a series of standard linear matrix inequalities (LMIs). Furthermore, the recursive feasibility and robust stability of the proposed method are rigorously proven, respectively. In addition, a numerical simulation example is considered to verify the validity of the designed algorithm.