Extremum Seeking Control with Attenuated Steady-State Oscillations

TL;DR

This paper introduces two novel extremum seeking control schemes that adaptively attenuate steady-state oscillations by reducing excitation signals as the system approaches the extremum, ensuring practical convergence.

Contribution

The paper presents new adaptation laws for excitation amplitudes in ESC schemes that drive oscillations to zero while maintaining convergence to the extremum.

Findings

Achieves practical asymptotic convergence to the extremum.

Attenuates steady-state oscillations as the system stabilizes.

Simulation results validate the effectiveness of the proposed schemes.

Abstract

We propose two perturbation-based extremum seeking control (ESC) schemes for general single input single output nonlinear dynamical systems, having structures similar to that of the classical ESC scheme. We propose novel adaptation laws for the excitation signal amplitudes in each scheme that drive the amplitudes to zero. The rates of decay for both the laws are governed by the gradient measures of the unknown reference-to-output equilibrium map. We show that the proposed ESC schemes achieve practical asymptotic convergence to the extremum with a proper tuning of the parameters in the proposed schemes. As the extremum is reached, and the magnitudes of the gradient measures become small, the excitation signal amplitudes converge to zero. Thus, the proposed schemes ensure that the excitation signal is attenuated as the system output converges to a neighborhood of the extremum and the steady-state oscillations about the extremum, typically observed for the classical ESC schemes, are attenuated. Simulation examples are included to illustrate the effectiveness of the proposed schemes.