Event-Triggered Newton Extremum Seeking for Multivariable Optimization

TL;DR

This paper introduces an event-triggered control method for multivariable Newton extremum seeking that reduces actuation updates while ensuring fast convergence through a dynamic Hessian inverse estimator.

Contribution

It develops a novel event-triggered Newton extremum seeking approach with a Riccati-based Hessian inverse estimator, improving efficiency and convergence speed over traditional methods.

Findings

Reduces control updates compared to continuous methods.

Achieves exponential convergence to a neighborhood of the extremum.

Demonstrates improved performance in numerical simulations.

Abstract

This paper presents a static event-triggered control strategy for multivariable Newton-based extremum seeking. The proposed method integrates event-triggered actuation into the Newton-based optimization framework to reduce control updates while maintaining rapid convergence to the extremum. Unlike traditional gradient-based extremum seeking, where the convergence rate depends on the unknown Hessian of the cost function, the proposed approach employs a dynamic estimator of the Hessian inverse, formulated as a Riccati equation, enabling user-assignable convergence rates. The event-triggering mechanism is designed to minimize unnecessary actuation updates while preserving stability and performance. Using averaging theory, we establish local stability results and exponential convergence to a neighborhood of the unknown extremum point. Additionally, numerical simulations illustrate the benefits of the proposed approach over gradient-based and continuously actuated Newton-based extremum seeking, showing improved convergence rates and reduced control update frequency, leading to more efficient implementation in real-time optimization scenarios.