论文标题
对非线性约束轨迹优化问题的管随机最佳控制
Tube Stochastic Optimal Control for Nonlinear Constrained Trajectory Optimization Problems
论文作者
论文摘要
最近的低潮空间任务强调了设计轨迹强大的不确定性的重要性。以其完整形式，该过程被公式化为非线性约束随机最佳控制问题。该问题是控制理论中最复杂的问题之一，迄今为止，已经提出了实际上没有适用于低推动轨迹优化问题的方法。本文提出了一种新算法，以解决非线性系统和约束的随机最佳控制问题。所提出的算法使用无气体变换将随机最佳控制问题转换为确定性问题，然后通过轨迹优化方法（例如差分动态编程）来求解。两个数字示例，其中一个将所提出的方法应用于低头轨迹设计，这说明了它自动引入了改善鲁棒性的边距。最后，使用蒙特卡洛模拟来评估溶液的鲁棒性和最佳性。
Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control problem. This problem is among the most complex in control theory, and no practically applicable method to low-thrust trajectory optimization problems has been proposed to date. This paper presents a new algorithm to solve stochastic optimal control problems with nonlinear systems and constraints. The proposed algorithm uses the unscented transform to convert a stochastic optimal control problem into a deterministic problem, which is then solved by trajectory optimization methods such as differential dynamic programming. Two numerical examples, one of which applies the proposed method to low-thrust trajectory design, illustrate that it automatically introduces margins that improve robustness. Finally, Monte Carlo simulations are used to evaluate the robustness and optimality of the solution.
