Extremum Seeking Control for Multivariable Maps under Actuator Saturation

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.