Optimal control of switching times in switched dynamical systems

This paper considers an optimal control problem for switched dynamical systems, where the objective is to minimize a cost functional defined on the state, and where the control variable consists of the switching times. The gradient of the cost functional is derived on an especially simple form, which lends itself to be directly used in gradient-descent algorithms. This special structure of the gradient furthermore allows for the number of switching points to become part of the control variable, instead of being a given constant. Numerical examples testify to the viability of the proposed approach.