Extremum Seeking for Linear Time-Varying Systems with Unknown Control Directions

TL;DR

This paper develops a bounded extremum seeking control method for linear time-varying systems with unknown control directions, uncertainties, and delays, providing stability bounds and delay compensation techniques.

Contribution

It introduces a novel approach using change of variables and Lyapunov functions to handle unknown control directions and delays in time-varying systems.

Findings

Practical exponential stability bounds for system states.

Effective delay compensation strategies.

First analysis of bounded extremum seeking with unknown control directions and delays.

Abstract

We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide practical exponential stability bounds for the states of the closed loop systems that hold for all nonnegative times. For the first time for linear time-varying systems with unknown control directions, we consider bounded extremum seeking controls in the presence of uncertain time-varying input delays with small time-varying delay uncertainties, and we provide reduction model controllers to compensate for the constant part of the delays.