Robust model predictive control with discrete-time integral sliding surface

In this paper, a method of robust model predictive control for constrained linear discrete-time systems with bounded disturbances is presented. The approach is based on modifying the concept of discrete-time integral sliding mode control into an optimal constrained control problem. By introducing an additional sliding mode control term into the state feedback law, the closed-loop system can be maintained within a quasi-sliding band throughout the entire response. To avoid violating the original constraints, we need to tighten the constraints beforehand based on the knowledge of the quasisliding band and the switching signal in the sliding mode control. As the result, the tightened optimal control problem determines the discrete-time integral sliding surface and the associated sliding mode control term rejects the additional disturbance. The theoretical analysis and a numerical example illustrate the validity of the proposed method. A key feature of this method is its constraint tightening approach, which eliminates the complexity of iterative computation for the robust invariant set.