Extremum Seeking Control for Multivariable Maps under Actuator Saturation
Enzo Ferreira Tomaz Silva, Pedro Henrique Silva Coutinho, Tiago Roux Oliveira, Miroslav Krstić
TL;DR
This work tackles gradient-based extremum seeking for multi-input maps with actuator saturation. It employs a polytopic embedding of the unknown Hessian $H$ and an averaging framework to derive an LMI-based condition that guarantees exponential stability of the average error dynamics, followed by convergence to the unknown optimum via Lyapunov theory. A constructive design procedure is provided to compute stabilizing gains $K$ under Hessian uncertainty using LMIs, including a non-diagonal gain option that offers design flexibility beyond common diagonal gains. Numerical results demonstrate that the LMI-designed gain stabilizes the system under saturation, outperforming a diagonal-gain baseline. The approach advances real-time, model-free optimization in the presence of input constraints and extends ES theory to multivariable, constrained settings with practical relevance to saturated actuators.
Abstract
This paper deals with the gradient-based extremum seeking control for multivariable maps under actuator saturation. By exploiting a polytopic embedding of the unknown Hessian, we derive a LMI-based synthesis condition to ensure that the origin of the average closed-loop error system is exponentially stable. Then, the convergence of the extremum seeking control system under actuator saturation to the unknown optimal point is proved by employing Lyapunov stability and averaging theories. Numerical simulations illustrate the efficacy of the proposed approach.