Analysis of regular and singular solutions to the problem of aircraft optimal thrust control

The paper deals with the problem of optimal thrust control for a given trajectory when flying through dangerous zones with obstacles. The obstacles are represented by the probability function that determines the level of safety of the mission or the probability of aircraft failure. The flight at a constant altitude is considered, along the rectilinear trajectories that correspond to the evolvent of curvilinear trajectories of small curvatures. The problem under consideration is the determination of optimal thrust that ensures the minimum of failure probability for the flight at a given distance with a limit imposed on fuel consumption. A solution to this problem is based on the maximum principle approach. The main difficulty of this problem consists in the existence of singular solutions. The accepted approach enables calculation of singular thrust control and appropriate trajectories in the phase space (velocity and range).