Elimination of Active Phase Constraints in Optimal Control Problems

The problems of optimal control of continuous systems with phase constraints are considered. It is assumed that the trajectory of the system can be divided into sections, on each of which a set of active phase constraints is fixed. Such trajectories are typical for hybrid systems (HSs) in which the transition from one site to another is considered a switch. Applying the necessary optimality conditions for HSs with intermediate constraints, we obtain a solution to the initial problem with phase constraints.