Extremum seeking control of a class of constrained nonlinear systems

TL;DR

This paper introduces a novel extremum seeking control method for constrained nonlinear systems, enabling optimization without explicit performance function knowledge, handling output constraints, and accommodating internal dynamics.

Contribution

It proposes a new numerical optimization-based ESC approach that explicitly manages output constraints and internal dynamics without requiring stability.

Findings

Effective in handling output constraints

Optimizes performance functions dependent on internal states

Demonstrated success through extensive numerical simulations

Abstract

This paper studies the extremum seeking control (ESC) problem for a class of constrained nonlinear systems. Specifically, we focus on a family of constraints allowing to reformulate the original nonlinear system in the so-called input-output normal form. To steer the system to optimize a performance function without knowing its explicit form, we propose a novel numerical optimization-based extremum seeking control (NOESC) design consisting of a constrained numerical optimization method and an inversion based feedforward controller. In particular, a projected gradient descent algorithm is exploited to produce the state sequence to optimize the performance function, whereas a suitable boundary value problem accommodates the finite-time state transition between each two consecutive points of the state sequence. Compared to available NOESC methods, the proposed approach i) can explicitly deal with output constraints; ii) the performance function can consider a direct dependence on the states of the internal dynamics; iii) the internal dynamics do not have to be necessarily stable. The effectiveness of the proposed ESC scheme is shown through extensive numerical simulations.