Robust self-triggered min–max model predictive control for discrete-time nonlinear systems

Abstract

In this paper, we propose a robust self-triggered model predictive control (MPC) algorithm for constrained discrete-time nonlinear systems subject to parametric uncertainties and disturbances. To fulfill robust constraint satisfaction, we take advantage of the min–max MPC framework to consider the worst case of all possible uncertainty realizations. In this framework, a novel cost function is designed based on which a self-triggered strategy is introduced via optimization. The conditions on ensuring algorithm feasibility and closed-loop stability are developed. In particular, we show that the closed-loop system is input-to-state practical stable (ISpS) in the attraction region at triggering time instants. In addition, we show that the main feasibility and stability conditions reduce to a linear matrix inequality for linear case. Finally, numerical simulations and comparison studies are performed to verify the proposed control strategy.