稀疏拟谱最优控制法求解Goddard火箭问题  

Sparse pseudospectral optimal control method for solving Goddard rocket problem

作　　者：童科伟[1] 周建平[1] 何麟书[1] 

机构地区：[1]北京航空航天大学宇航学院,北京100083

出　　处：《固体火箭技术》2009年第4期360-364,共5页Journal of Solid Rocket Technology

摘　　要：提出了一种新的基于直接转化法的求解基于常微分方程(ODE)和微分代数方程(DAE)的最优控制问题的数值方法。该方法通过Legendre-Gauss拟谱法同时离散化状态变量和控制变量,把最优控制问题转化为一个非线性规划问题,并利用改进的多相处理方法避免优化无控段,同时基于稀疏矩阵探索其一阶导数信息。数值结果表明,与传统的直接转换法相比,该方法是一种通用高效的精度较高的ODE/DAE最优控制直接数值求解法。最后,从工程观点出发,应用该方法成功求解了终端自由有路径约束的奇异最优控制问题Goddard火箭问题。A novel numerical method for solving optimal control problems based on ordinary differential equations （ODE） or differential-algebra equations （DAE） was proposed. The method is based on direct transcription method that converts an optimal control problem into a nonlinear programming problem using Legendre-Gauss pseudospectral method via simultaneous state and control discretization. Computing time is greatly reduced by using an improved multi-phase method to avoid optimizing non-control phase and using sparse matrix to supply its first order derivative messages. Numerical results show that, compared with other traditional direct transcription methods, the scheme is a general purpose method for solving ODE/DAE optimal control problem which has the advantages of higher precision and lower computational effort. Finally, from engineering views, the proposed method was successfully used for solving Goddard rocket problem, a terminal free, singular optimal control problem with path constraint.

关 键 词：最优控制问题 非线性规划问题 拟谱法 常微分方程 微分代数方程 稀疏矩阵 

分 类 号：V412[航空宇航科学与技术—航空宇航推进理论与工程]