On Event Triggered Tracking for Nonlinear Systems

TL;DR

This paper develops an event-based control algorithm for nonlinear system trajectory tracking, ensuring bounded tracking error and non-accumulation of control updates, with adjustable bounds depending on input smoothness.

Contribution

It introduces an event-triggered control scheme that guarantees bounded tracking error for nonlinear systems, extending existing methods to handle piecewise continuous inputs.

Findings

Guarantees uniform ultimate boundedness of tracking error.

Ensures non-accumulation of control update times.

Achieves arbitrarily small bounds when input derivatives are bounded.

Abstract

In this paper we study an event based control algorithm for trajectory tracking in nonlinear systems. The desired trajectory is modelled as the solution of a reference system with an exogenous input and it is assumed that the desired trajectory and the exogenous input to the reference system are uniformly bounded. Given a continuous-time control law that guarantees global uniform asymptotic tracking of the desired trajectory, our algorithm provides an event based controller that not only guarantees uniform ultimate boundedness of the tracking error, but also ensures non-accumulation of inter-execution times. In the case that the derivative of the exogenous input to the reference system is also uniformly bounded, an arbitrarily small ultimate bound can be designed. If the exogenous input to the reference system is piecewise continuous and not differentiable everywhere then the achievable ultimate bound is constrained and the result is local, though with a known region of attraction. The main ideas in the paper are illustrated through simulations of trajectory tracking by a nonlinear system.