Multi-Phase Trajectory Optimization Methods with Applications to Hypersonic Vehicles

Abstract

Numerical solutions of multi-phase optimal control problems are considered, where a phase is defined as a subinterval in which the right-hand si des 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 weH 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 coHocation 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 vehic\e. Both methods are embedded into an advanced user interface wh ich aHows a user to edit most of the necessary input in a simple way. This utility is described briefly