Chebyshev局部配点法在轨迹优化中的应用

王立峰¹, 汪洋¹, 郭虓¹, 赵晨², 李昊²

(1.北京航空航天大学 航空科学与工程学院, 100191 北京; 2.陆航驻北京地区军事代表室, 100101 北京)�お�



摘要:

伪谱法在轨迹优化中应用广泛,其中Chebyshev伪谱法在求解轨迹优化问题时具有较快的收敛性和较高的精度．为了证明Chebyshev局部配点法在求解轨迹优化等问题的可行性,给Chebyshev局部配点法的应用提供理论基础,研究了Chebyshev局部配点法收敛性和稳定性．文中以Hyper-sensitive问题和Minimum-energy为例,分别用Chebyshev局部配点法与传统插值方法和经典Chebyshev伪谱法求接,计算结果表明:Chebyshev局部配点法是可行和有效的. 该方法不仅在一定程度上相比于传统的插值法精度更高、计算速度更快,和经典Chebyshev伪谱法相比也略有优势．��

关键词:  Chebyshev伪谱法  轨迹优化  最优控制  插值��

DOI：10.11918/j.issn.0367-6234.2013.05.018

分类号:

基金项目:国家国际科技合作专项资助项目(2012DFG61930).��



Application of Chebyshev local collocation method to trajectory optimization

WANG Lifeng¹, WANG Yang¹, GUO Xiao¹, ZHAO Chen², LI Hao²��

(1. School of Aeronautic Science and Engineering, Beihang University, 100191 Beijing, China; ��2. Army Aviation Military Representative Office in Beijing, 100101 Beijing, China)�お�

Abstract:

To improve the trajectory optimization with Chebyshev local collocation method, we study the convergence and stability of Chebyshev local collocation method and provide a theoretical basis for its application. In this paper, the examples of Hyper-sensitive and Minimum-energy problem verify the feasibility and effectiveness of Chebyshev local collocation method which not only is convergent and stable for Hyper-sensitive problem, but also can achieve higher accuracy and faster computation speed in some degree compared with traditional interpolation method and even classic Chebyshev pseudospectral method.��

Key words:  Chebyshev pseudospectral method  trajectory optimization  optimal control  interpolation�お�