Multiparameter extremum seeking with output delays

In this paper, we generalize the previous results of multivariable extremum seeking by assuming output delays not considered before in the control system. The phase compensation of the dither signals and the inclusion of an averaging-based predictor in the closed-loop feedback allow to obtain exponential convergence results to a small neighborhood of the optimal point, even in the presence of delays. The stability analysis is carried out using backstepping transformation and averaging in infinite dimensions. The proposed approach also removes the dependence of the convergence rate on the unknown Hessian of the nonlinear map to be optimized, being user-assignable as in Newton-based extremum seeking results. The control performance is evaluated by numerical simulations.