An Improved Adaptive hp Mesh Refinement Method in Solving Optimal Control Problems

Abstract

The adaptive hp pseudospectral method is an effective choice in solving the optimal control problem. In order to improve the computing efficiency of the adaptive hp method, an improved adaptive hp mesh refinement method is proposed in this paper. There are two main cores in this method. The first is to refine the mesh in advance based on the change rate of the control, so that the algorithm can more efficiently deal with the optimal control problem with discontinuous control. And the second is to based on the accumulation of curvature values to ensure that those positions that need to be refined more can be quickly allocated to more mesh points. These two are combined with each other to improve the solving efficiency of the algorithm proposed in this paper, which shortens the required computing time. In addition, the convergence of the algorithm is proved in this paper. The simulation results show the effectiveness and superiority of the algorithm proposed in this paper.

Trajectory Optimization for High-Speed and Long-Range Interceptor Based on Improved Adaptive hp Pseudospectral Method

“…In view of the above considerations, and draw on the ideas of [39], this paper proposes an improved adaptive hp pseudospectral method to solve the trajectory optimization of interceptor based on the combat scenario of high-speed and long-range interceptor defending high-speed strongmaneuvering target. The main innovations are as follows:…”