The problem of maximizing the horizontal coordinate of a point mass moving in a vertical plane under the influence of gravity, viscous friction, curve reaction force and thrust is considered. It is assumed that state constraints are imposed on the trajectory inclination angle. The system of equations belongs to a certain type, which allows us to reduce the optimal control problem with constraints on the phase variable to the optimal control problem with control constraints. The sequence and number of inclusions of phase constraints in the optimal trajectory and synthesis of optimal control are determined.
Keywords:
brachistochrone, phase constraints, Pontryagin’s maximum principle, boundary value problem, optimal trajectory
