Optimal command control of flight paths of aerospace system hypersonic first stage in conditions of atmospheric disturbances

The paper deals with disturbed motion of the hypersonic first stage of an aerospace system in accelerated climb. Disturbances are deviations of atmospheric density from the values of a standard model. A multistep control process is accepted. The command angle-of-attack schedule is specified at each step of control using the method of Pontryagins maximum principle. The nominal control program is applied at the first step. We present the results of modeling disturbed motion with command control of the angle of attack for maximum rarified and maximum dense atmosphere. The angle-of-attack constraint is violated for rarified and dense atmosphere at the end of the accelerated flight segment when a boundary value problem is solved. If command control obtained as a result of solving the boundary value problem is maintained the target terminal speed and altitude conditions are fulfilled. The finite value of the flight path inclination angle for rarefied atmosphere is 10% lower than the target one, while for dense atmosphere it is 12% higher.