论文部分内容阅读
挠性卫星最优控制的求解方法,可以分为直接法和间接法。直接法利用极大值原理求解两点边值问题,其难点在于收敛性很难保证;间接法将该问题转化为容易求解的最优化问题,然后利用线性规划或者非线性规划方法求解。由于直接法求解困难,利用间接法思想,将问题转化为一组非线性方程组的求解。求解时,利用同伦连续法得到方程组几乎所有的解,然后利用极大值原理的必要条件验证得到最优解。仿真求解了无阻尼4阶挠性系统的最优解和小阻尼2阶挠性系统的最优解。研究结果表明:3阶以上模态对机动时间和残差影响很小,小挠性阻尼对于总机动时间影响也很小。
Flexible satellite optimal control solution, can be divided into direct and indirect methods. The direct method uses the maximum principle to solve the two-point boundary value problem. The difficulty is that it is hard to guarantee convergence. The indirect method converts the problem into an easy-to-solve optimization problem and then uses linear programming or nonlinear programming. Because of the direct method to solve the problem, the indirect method is used to solve the problem in a set of nonlinear equations. When solving, almost all solutions of the system of equations are obtained by homotopy continuous method, and then the optimal solution is obtained by using the necessary conditions of maximum principle. The optimal solution of the fourth-order flexible system without damping and the optimal solution of the second-order flexible system with small damping are solved by simulation. The results show that the third-order modes have little effect on the maneuvering time and residual, and the small flexible damping has little effect on the total maneuvering time.