Prescribed Time Dual-Mode Extremum Seeking Control

TL;DR

This paper introduces a dual-mode extremum seeking control method that guarantees real-time optimization within a prescribed time frame for nonlinear systems with unknown dynamics, using a novel timescale transformation.

Contribution

It presents a new control design technique with a timescale transformation that avoids singularities, enabling prescribed-time convergence in extremum seeking control.

Findings

Achieves semi-global practical stability of the optimal equilibrium.

Effectively uses increasing frequency dither signals.

Demonstrated via simulation to validate the approach.

Abstract

We propose a dual mode extremum seeking control design technique that achieves real-time optimization of an unknown measured cost function in a prescribed time. The controller is shown to achieve semi-global practical stability of the optimal equilibrium for the state variables and the input variable for a class of nonlinear dynamical control systems with unknown dynamics. The design technique proposes a timescale transformation that enables the use of dither signals with increasing frequencies. The proposed timescale transformation is designed to avoid the singularity occurring at the prescribed time. A simulation study is performed to demonstrate the effectiveness of the proposed technique.