Discontinuous feedbacks and an application to the rocket car

In this work we consider nonlinear control systems. We review classical results in optimal control theory and more recent results concerning the equivalence of asymptotic controllability and the existence of stabilizing feedbacks. We discuss in some detail patchy vector fields, a class of discontinuous vector fields that has been fruitfully exploited to treat control problems of stabilization, robustness and optimization in the generic nonlinear setting