Robust Model Predictive Control Algorithms for Nonlinear Systems: an Input-to-State Stability Approach

Abstract

This paper presents and compares two robust MPC controllers for constrained nonlinear systems based on the minimization of a nominal performance index. Under suitable modifications of the constraints of the Finite Horizon Optimization Control Problems (FHOCP), the derived controllers ensure that the closed loop system is Input-to-State Stable (ISS) with a robust invariant region, with relation to additive uncertainty/disturbance. Assuming smoothness of the model function and of the ingredients of the FHOCP, the effect of each admissible disturbance in the predictions is considered and taken into account by the inclusion in the problem formulation of tighter state and terminal constraints. A simulation example shows the potentiality of both the algorithms and highlights their complementary aspects.