航空学报 > 2008, Vol. 29 Issue (2): 416-423

基于Hamilton-Jacobi方程的编队飞行控制

宋申民,吕建华,陈兴林,段广仁   

  1. 哈尔滨工业大学 航天学院
  • 收稿日期:2007-03-20 修回日期:2007-10-09 出版日期:2008-03-15 发布日期:2008-03-15
  • 通讯作者: 宋申民

On the Control of Formation Flying Based on Hamilton-Jacobi Equations

Song Shenmin,Lu Jianhua,Chen Xinglin,Duan Guangren   

  1. School of Aeronautics, Harbin Institute of Technology
  • Received:2007-03-20 Revised:2007-10-09 Online:2008-03-15 Published:2008-03-15
  • Contact: Song Shenmin

摘要:

针对椭圆参考轨道的编队飞行控制系统,基于哈密尔顿雅克比(Hamilton-Jacobi)方程,给出一种新的生成函数半解析近似解的计算方法,同时推导了编队飞行控制系统相对运动的线性状态转移矩阵,并且验证了模型的精度。在此基础上,结合一个具体的编队飞行任务,采用线性规划算法得到了队形保持的闭环控制器,该算法得到的是脉冲形式的控制序列,因此更具有实际意义。同时还提出了一种简单的避免生成函数奇异点的方法,从而减少了生成函数间相互转换所带来的计算量。最后的非线性仿真结果验证了控制方法的有效性。

关键词: 编队飞行, Hamilton-Jacobi方程, 线性规划, 脉冲控制, 生成函数

Abstract:

For the formation flying control system with ellipse reference orbit,based on Hamilton-Jacobi equations, a new computation approach of generating functions is presented. Meanwhile, the linear state transformation matrix of the relative motion model for formation flying is derived and model precision has been verified. On the basis of above work, combining on a special task of the formation flying, the closed loop controller for formation keeping is presented based on linear programming algorithm.

Key words: formation , flying,  , Hamilton-Jacobi , equations,  , linear , programming,  , impulsive , control,  , generating , functions

中图分类号: