基于Hamilton-Jacobi方程的编队飞行控制

 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。

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

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.And the controller that is a sequence of impulsive has more practical meaning.Moreover,a simple method of working around the singular points of generating functions is presented,so it can reduce the numerical quantity for transformation of generating functions.Finally,the results of nonlinear simulation illustrate the effectiveness of the method.