The maximum principle for the optimal control of some linear switching controlled ordinary differential equations

In this paper, we analyze the problem of switching controls for control systems endowed with different actuators. The goal is to control the system by switching from an actuator to the other so that, in each instant of time, only one actuator is active. We first address a finite-dimensional model and show that, under suitable rank conditions, the controllability for the switching controls system without the controls constraint. Then, we studies a time optimal control problem (P) for the switching controlled systems. With the aid of Ekeland´s variational principle, we obtain the Pontryagain maximum principle for this problem.