Multivariable Extremum Seeking Control for Dynamic Maps through Sliding Modes and Periodic Switching Function

TL;DR

This paper introduces a multivariable extremum seeking control method using sliding modes and periodic switching, ensuring global convergence for nonlinear dynamic systems with arbitrary relative degrees.

Contribution

It proposes a novel extremum seeking controller combining sliding modes and cyclic search, with time-scaling to handle systems of arbitrary relative degree.

Findings

System rapidly converges to optimal parameters in simulations.

Guarantees global convergence to a neighborhood of the optimum.

Effective for nonlinear multivariable dynamic systems.

Abstract

This paper presents the design of an extremum seeking controller based on sliding modes and cyclic search for real-time optimization of non-linear multivariable dynamic systems. These systems have arbitrary relative degree, compensated by the technique of time-scaling. The resulting approach guarantees global convergence of the system output to a small neighborhood of the optimum point. To corroborate with the theoretical results, numerical simulations are presented considering a system with two inputs and one output, which rapidly converges to the optimal parameters of the objective function.