摘要
提出一种新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。本方法基于直接配置法,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。与传统的直接转换法相比,本方法具有精度高、计算量小、结构简单的特点,而且可以求解最优控制"多相"问题。数值结果表明,本方法是一种通用的精度较高的最优控制直接数值求解法,可用于求解ODE/DAE最优控制问题。
A novel numerical method for solving optimal control problems based on ordinary differential equations （ODE） and/or differential-algebra equations （DAE） is proposed. This method is based on the 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. Compared with other standard direct transcription methods,the scheme has the advantages of higher precision and lower computational effort with a simpler structure which can also be used for the so-called optimal control multi-phase problems. Numerical results show the approach is a general purpose higher precision optimal control direct transcription method which can be used for solving ODE/DAE optimal control problems.
出处
《航空学报》
EI
CAS
CSCD
北大核心
2008年第6期1531-1537,共7页
Acta Aeronautica et Astronautica Sinica
关键词
最优控制
非线性规化
直接转换法
拟谱法
常微分方程
微分代数方程
optimal control
nonlinear programming
direct transcription method
pseudospectral method
ordinary differential equation
differential-algebra equation
