Self-Triggered Adaptive Model Predictive Control of Constrained Nonlinear Systems: A Min-Max Approach

Abstract

In this paper, a self-triggered adaptive model predictive control (MPC) algorithm is proposed for constrained discrete-time nonlinear systems subject to parametric uncertainties and additive disturbances. To bound the parametric uncertainties with reduced overestimation, a zonotope-based setmembership parameter estimator is developed, which is also compatible with the aperiodic sampling resulted from the selftriggering mechanism. The estimation of uncertainties is employed to reformulate the optimization problem in a min-max MPC scheme to reduce the conservatism. By designing a timevarying penalty in the cost function, the estimation of uncertainties is implicitly considered in the self-triggering scheduler, therefore making the triggering interval further optimized. The resulting self-triggered adaptive MPC algorithm guarantees the recursive feasibility, while providing less conservative performance compared with the self-triggered robust MPC method. Furthermore, we theoretically show that the closed-loop system is input-to-state practical stable (ISpS) at triggering time instants. A numerical example and comparison study are performed to demonstrate the efficacy of the proposed method.