A para-model agent for dynamical systems

Consider a dynamical system $u \mapsto x, \dot{x} = f_{nl}(x,u)$ where $f_{nl}$ 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 "extremum-seeking" procedure. Multiple applications are presented and the robustness of the proposed method is studied in simulation.