Event-Triggered Newton-Based Extremum Seeking Control

TL;DR

This paper introduces an event-triggered Newton-based extremum seeking control method that improves convergence speed and reduces control signal updates by using a Riccati filter for Hessian estimation, eliminating dependence on unknown Hessian information.

Contribution

It presents a novel event-triggered Newton-based extremum seeking approach with a Riccati filter for Hessian inverse estimation, enhancing convergence and control efficiency over gradient methods.

Findings

Improved convergence speed compared to gradient methods.

Reduced amplitude and frequency of control signal updates.

Guaranteed local exponential practical stability.

Abstract

This paper proposes the incorporation of static event-triggered control in the actuation path of Newton-based extremum seeking and its comparison with the earlier gradient version. As in the continuous methods, the convergence rate of the gradient approach depends on the unknown Hessian of the nonlinear map to be optimized, whereas the proposed event-triggered Newton-based extremum seeking eliminates this dependence, becoming user-assignable. This is achieved by means of a dynamic estimator for the Hessian's inverse, implemented as a Riccati equation filter. Lyapunov stability and averaging theory for discontinuous systems are applied to analyze the closed-loop system. Local exponential practical stability is guaranteed to a small neighborhood of the extremum point of scalar and static maps. Numerical simulations illustrate the advantages of the proposed approach over the previous gradient method, including improved convergence speed, followed by a reduction in the amplitude and updating frequency of the control signals.