hp自适应伪谱法在滑翔弹道快速优化中的应用

摘要

基于一种求解最优控制问题的新方法—hp自适应伪谱法对滑翔弹道快速优化设计问题进行了研究；该方法将全局伪谱法与有限兀法的思想进行结合,采用双层优化策略对细化单元上的配点数和插值多项式的阶次进行自适应调节以满足快速性及精度要求；对滑翔弹道优化问题进行了数值仿真计算,用极小值原理验证了仿真所得的弹道是最优弹道,并与Guass伪谱法的仿真结果进行了对比分析；结果表明该优化方法在求解周期性跳跃滑翔弹道时具有更合理的配点分布及更少的计算时间,对初始控制量不敏感、鲁棒性强,具有一定的工程应用价值.%Based on hp-adaptive pseudospectral method, this paper presents a new optimal control method to solve the rapid gliding trajectory optimization. In order to meet the speed and precision requirements, this new theory combines the global pseudospectral method with the finite element method, adopts double layer optimization strategy to adjust adaptively the segment breaks and the polynomial degree in each segment. The simulation based on hp-adaptive pseudospectral method is carried out, the result is validated by Pontryagin minimum principle, and compared with the result of Gauss pseudospectral method. The results show that when solving the problem of gliding trajectory optimization the algorithm has more logical distribution and less calculation time, is robust and not sensitive to the initial control values, has a great value in the practical applications.