改进的hp自适应网格细化算法及应用  

Improved hp-adaptive Mesh Refinement Algorithm and Its Application

作　　者：王丽英[1] 张友安[2] 赵国荣[2] 

机构地区：[1]海军航空工程学院系统科学与数学研究所,山东烟台264001 [2]海军航空工程学院控制工程系,山东烟台264001

出　　处：《弹道学报》2013年第1期16-21,共6页Journal of Ballistics

基　　金：国家青年科学基金资助项目(61004002)

摘　　要：针对高超再入飞行器的轨迹快速优化问题,提出了一种改进的hp自适应网格细化轨迹快速优化算法。采用hp-LGR伪谱法将多区间连续时间最优控制问题转化为非线性规划问题;以离散的微分-代数约束在采样点上的残差作为解的精度估计准则;在需要提高求解精度的区间,将轨迹曲率作为选择h法或者p法提高求解精度的判据,通过迭代调整子区间的个数、区间内插值多项式的维数达到求解精度要求。仿真结果表明,本文算法能够以较少的计算代价得到较高精度的解,更适合求解多约束条件下轨迹优化问题。Aiming at rapid trajectory optimization problems of hypersonic re-entry vehicle, an improved hp-adaptive mesh refinement algorithm of rapid trajectory optimization was proposed. Multi-intervals optimal control problem was transformed into NLP by using an hp-LGR pseudospectrat method. The accuracy of the solution was assessed by the residual of the discredited differential-algebraic constraints at sample points. For the inaccurate intervals, the curvature of the trajectory was used as the criterion of choosing pseudospectral method or mesh refinement method to improve accuracy. The calculation precision was satisfied by adjusting the number and the degree of the polynomial of subintervals iterativel. Simulation results show that the solution of higher precision can be obtained with less calculation cost by the proposed method,and it is applicable to calculating trajectory optimization under multi-constraints.

关 键 词：伪谱法 网格细化 微分-代数约束 残差 轨迹优化算法 

分 类 号：V412.4[航空宇航科学与技术—航空宇航推进理论与工程]