Optimal synthesis for an intermediate vehicle model with state constraints

The problem of optimal thrust programming for an intermediate vehicle model is considered. The motion occurs in a vertical plane under a uniform gravitational field, quadratic resistance friction, and thrust force. The control variables are the angle of attack and the thrust force. Phase constraints are imposed on the trajectory inclination angle. It is assumed that the total fuel consumption for thrust control is negligible compared to the vehicle mass, the fuel mass variation does not affect the center of mass dynamics, and a change of the lifting force does not affect the drag force. The region in the space of initial variables for which the problem is solvable is determined, and an optimal synthesis is constructed. It is established that within this domain, the thrust can be maximum, intermediate, or zero. The number and sequence of trajectory arcs with corresponding thrust values and the number of exits to state constrains are determined.