Constrained extremum seeking stabilization of systems not affine in control

Recently, a form of extremum seeking for control (ESC) was developed for the stabilization of uncertain nonlinear systems. In ESC, the extremum seeker itself directly controls the systems through feedback rather than fine tuning a controller. The ESC results, and other related results, apply only to systems affine in control. However, in most physical systems, the control effort enters the system's dynamics through a nonlinear function, such as an input with deadzone and saturation. In this work, we use our previous results on ESC to develop constrained extremum seeking stabilizing controllers for systems of practical interest that are nonaffine in control. Considering that any odd function can be approximated arbitrarily well by an odd polynomial, we present analytic results for designing controllers for systems in which control enters the system dynamics through an odd polynomial. Furthermore, we study the robustness of the scheme to uncertainty in the odd polynomial degree as well as robustness to even-powered perturbations.