A unified model-free controller for switching minimum phase, non-minimum phase and time-delay systems

Consider a dynamical system u 7→ x, ẋ = fnl(x, u) where fnl is a nonlinear (convex or nonconvex) function, or a combination of nonlinear functions that can eventually switch. We present, in this preliminary work, a generalization of the standard model-free control, that can either control the dynamical system, given an output reference trajectory, or optimize the dynamical system as a derivative-free optimization based ”extremumseeking” procedure. Multiple applications are presented and the robustness of the proposed method is studied in simulation.