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.
出处
《固体火箭技术》
EI
CAS
CSCD
北大核心
2009年第4期360-364,共5页
Journal of Solid Rocket Technology
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
optimal control problem
nonlinear programming problem
pseudospectral methods
ordinary differential equation
differential-algebra equation
sparse matrix
