Optimal feedback switching laws for autonomous hybrid automata

We define a new class of hybrid systems called autonomous hybrid automata that can be seen as a generalization of the class of switched systems we have considered in previous works. In this new model there are two types of edges: a controllable edge represents a mode switch that can be triggered by the controller; an autonomous edge represents a mode switch that is triggered by the continuous state of the system as it reaches a given threshold. We show how to solve an infinite time horizon quadratic optimization problem with a numerically viable procedure for such a class of hybrid automata; the optimal control law is a state-feedback.