Algorithm for Switching-Time Optimization in Hybrid Dynamical Systems

We consider the problem of minimizing a cost functional defined on the state trajectory of a switched-mode dynamical system with respect to the switching times. Following the derivation, in recent years, of various results concerning the gradient of the cost functional, we present a suitable algorithm, based on gradient projection, for computing local minima. Utilizing the problem´s special structure, we prove a convenient formula for the direction of descent, and apply the Armijo procedure for computing the step size. A potential extension to the optimal mode-insertion problem is discussed, and numerical examples are provided