Event-Triggered Newton-Based Extremum Seeking Control
Victor Hugo Pereira Rodrigues, Tiago Roux Oliveira, Miroslav Krstic, Paulo Tabuada
TL;DR
The paper addresses efficient extremum seeking for unknown scalar static maps by decoupling convergence rate from the (unknown) Hessian via a Newton-based, event-triggered framework. It introduces SET-NewtonES, which employs a Riccati equation filter to estimate the inverse Hessian and uses time-triggered updates to reduce communication and computation. Stability is established through Lyapunov analysis and averaging theory for discontinuous systems, yielding local exponential practical stability with controllable residuals that shrink with stronger averaging (larger $ u$) and smaller probing amplitude $a$. Numerical results show faster convergence and fewer actuator updates compared to gradient-based ETC, highlighting practical benefits for bandwidth-constrained control of unknown nonlinear plants.
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.