Nonlinear Optimal Trajectories Using Successive Linearization.

摘要

A method of designing trajectories for maneuvering reentry vehicles is developed in this paper. Optimal control theory using linear perturbation guidance and a quadratic penalty function is employed to design trajectories for these vehicles. The vehicle equations of motion are represented by a five-dimension state vector. The problem is formulated by linearizing about a reference trajectory. A linear servomechanism problem, rather than a regulator problem, is solved, leading to a Riccati matrix differential equation and an auxiliary vector differential equation which are solved backwards in time. Successive linearization consists of iteratively generating new trajectories by linearizing about a reference trajectory created from a prior iteration. The cost function is adjusted between iterations to shape the trajectory. Qualitative guidelines for selecting these cost functions are given. Test cases are shown, with emphasis on designing a trajectory to intercept a target point. (Author)