Performance Optimization of a Maneuvering Re-entry Vehicle Using a Legendre Pseudospectral Method

The problem of performance optimization of a maneuvering re-entry vehicle is studied. The objective is to determine an optimal steering law for a high lift-to-drag ratio vehicle. An optimization criteria is derived that attempts to maximize the control margin of the vehicle in order to account for unmodeled perturbations during actual flight. The optimization problem is formulated as an optimal control problem. The optimal control problem is transcribed to a nonlinear programming via a Legendre pseudospectral method and is solved using a sparse nonlinear optimization algorithm. The key features of the optimal trajectory are described and the quality of the trajectory obtained from the Legendre pseudospectral method is discussed. Finally, a motivation is given for using the pseudospectral method as a guidance law.