Investigation of a linear optimal control problem with phase constraints

The paper deals with a linear two-dimensional optimal control problem under phase constraints. The system has the "simple motion" dynamics with circular control constraints, and phase constraints are represented by a rectangular cone. The utility functional is given by an integral of one of these phase coordinates on the unit time interval. par An analytical solution is constructed for the problem considered. It is shown that the optimal trajectory is smooth and consists of two parts: in the beginning the trajectory lies inside the phase constraints, and later it moves along the boundary of the phase constraints.