Multi-Phase Trajectory Optimization Methods with Applications to Hypersonic Vehicles

Numerical solutions of multi-phase optimal control problems are considered, where a phase is defined as a subinterval in which the right-hand sides of the differential equations are continuous. At the phase boundaries, the state, control, and design vectors may have jumps; in addition, the dimension of these vectors as well as the dimension of the right-hand sides may change. Two direct methods for solving such problems are presented : a multiple-shooting approach and a collocation method. Both methods avoid the adjoint differential equations. By these transcriptions, the optimal control problem is converted into a nonlinear programming problem (NLP), which is solved using standard sequential quadratic programming (SQP) algorithms. The methods are applied to determine optimal ascent and reentry trajectories of a two-stage-to-orbit vehicle. Both methods are embedded into an advanced user interface which allows a user to edit most of the necessary input in a simple way. This utility is described briefly.