Hierarchical-based self-triggered control for linear systems with external disturbances

Abstract

This paper introduces a hierarchical-based robust self-triggered control mechanism for linear systems with disturbances, with the goal of achieving anti-interference and computational resource saving. To address the potential external interference in the system, the $H_{\infty }$ performance index is introduced, and the self-triggered controller is developed based on this index to guarantee the system’s desired anti-interference capabilities. Furthermore, a hierarchical framework is employed to facilitate collaborative optimization of triggering mechanisms and control strategies. Within this framework, the triggering interval values and control input values are computed sequentially using a cyclic iteration approach. By upholding the $H_{\infty }$ performance standard and incorporating a hierarchical optimization framework, the system’s sampling frequency is notably diminished, anti-interference performance is safeguarded, and the convergence speed of the state trajectory is accelerated. The efficacy of the proposed method is validated through two illustrative examples.