基于凸优化的有限推力远程转移轨迹优化

Optimal Remote Transfer with Finite Thrust Based on Convex Optimization

针对轨迹优化问题中动力学方程对凸优化方法的限制,建立了有限推力远程转移轨迹优化问题的凸优化问题模型,并提出一种迭代逼近算法,使得在每步迭代中状态矩阵保持为线性,从而实现了凸优化在远程轨迹优化中的应用,仿真分析证明了所提出的迭代逼近算法对优化问题的收敛性,所得轨迹迅速收敛至最优轨迹,并与最优控制序列所得实际轨迹保持一致。本文构建的凸优化问题模型及提出的迭代逼近算法对这类远程轨迹优化问题是可行的。

Aiming at the limitation of the kinetic equation against convex optimization application in the remote transfer trajectory, the convex optimization model of remote transfer trajectory optimization with finite thrust is established, and an iterative approximation algorithm is proposed to keep the state matrix linear in each iteration, thereby, the convex optimization can solve the problem smoothly. It is proven that the convergence of proposed iterative approximation algorithm for the optimization problem and the optimal trajectory and control law are simultaneously solved. Through analysis and verification, the resulting optimal control law is in accord with the optimal control sequences, meanwhile, the resulting optimal trajectory and actual trajectory are consistent. The convex optimization model established and the iterative approximation algorithm proposed are valuable and feasible for the remote trajectory optimization.