Disturbed motion of the hypersonic first stage of an aerospace system in climb

Disturbed motion of the hypersonic first stage of an aerospace system in climb is analyzed. Deviations of atmospheric density from standard values and deviations of aerodynamic force coefficients from reference values are taken as disturbances. Disturbance motion of the hypersonic first stage of a hypersonic vehicle with the optimal angle-of-attack schedule obtained for reference atmosphere and nominal aerodynamic characteristics is modeled. Deviations of terminal conditions of disturbed motion from the target values of velocity, altitude and flight path inclination are determined. The problem of minimum propellant mass consumed in the climb with acceleration to hypersonic velocity is solved for disturbed motion by the method of Pontryagin’s maximum principle. Optimal angle-of-attack schedules, optimal flight paths and finite values of the mass of the hypersonic first stage are determined. Comparative analysis of optimal control programs and flight paths for disturbed and undisturbed motion is made.