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

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 set-membership parameter estimator is developed, which is also compatible with the aperiodic sampling resulted from the self-triggering 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 time-varying 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.