Dynamic Event-Triggered Control of Discrete-Time Nonlinear Systems based on Difference-Algebraic Representations

TL;DR

This paper develops a dynamic event-triggered control approach for discrete-time nonlinear systems with difference-algebraic representations, incorporating system nonlinearities and asynchronous sampling to ensure stability and optimize event frequency.

Contribution

It introduces a less conservative co-design method for gain-scheduled control and dynamic triggering, accounting for nonlinearities and asynchronous terms.

Findings

Derived a co-design condition ensuring asymptotic stability.

Formulated an optimization to reduce event frequency and enlarge the attraction region.

Validated the approach with a numerical example.

Abstract

This paper addresses the dynamic event-triggered control for a class of discrete-time nonlinear systems described by a difference-algebraic representation (DAR), using a gain-scheduled controller. An outstanding aspect of the proposed method is the incorporation of information about the system's nonlinearities into the control law and the trigger function. The proposed event-triggered mechanism also incorporates information on the asynchronous terms induced by the event-based sampling. All these ingredients enable the derivation of a less conservative co-design condition for the simultaneous design of the gain-scheduled control law and the dynamic triggering mechanism to ensure the asymptotic stability of the closed-loop system. An estimate of the region of attraction of the origin of the closed-loop system is obtained to guarantee the closed-loop system's operation within the domain of validity of the DAR. Then, an optimization problem is formulated to reduce the number of events and enlarge the estimated region of attraction. Finally, the effectiveness of the proposed condition is illustrated by a numerical example.