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

TL;DR

This paper introduces a self-triggered adaptive model predictive control method for constrained nonlinear systems with uncertainties, reducing conservatism and improving efficiency through a zonotope-based estimator and a min-max optimization scheme.

Contribution

It develops a novel self-triggered adaptive MPC algorithm that incorporates a zonotope-based uncertainty estimator and a min-max formulation to reduce conservatism and optimize triggering intervals.

Findings

Guarantees recursive feasibility of the control scheme.

Achieves less conservative performance compared to existing robust MPC methods.

Demonstrates effectiveness through numerical examples and comparisons.

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 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.