Optimal heading change with minimum energy loss for a hypersonic gliding vehicle

A three-state model is presented for analyzing the problem of optimal changes in heading with minimum energy loss for a hypersonic gliding vehicle, A further model order reduction to a single-state model is examined using singular-perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy of the vehicle. A separate boundary-layer analysis is used to account for altitude and flight-path angle dynamics and to obtain lift and bank-angle control solutions. By considering alternative approximations to solve the boundary-layer problem, three guidance laws are obtained, each having a feedback form. The guidance laws are evaluated for a hypothetical vehicle and are compared to an optimal solution obtained using a multiple shooting algorithm.