用于非线性最优控制的自由 horizon 牛顿法
Free-Horizon Newton Method for Nonlinear Optimal Control
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中文总结 AI 辅助
本文提出一种将控制输入与控制时域均作为设计变量的新型轨迹优化方法，扩展牛顿算法实现能量与时间效率联合优化，通过仿真验证了其在航天器转移问题中的有效性。
中文摘要 AI 辅助
本文提出一种针对非线性 l1 最优控制问题的新型轨迹优化方法，其中控制时域被视为自由变量，可同时计算控制时长与控制输入的 l1 范数。与传统方法在固定控制时域下最小化输入的 l1 范数不同，该方法将控制输入与控制时域均视为设计变量，实现能量与时间效率的联合优化。该方法扩展了基于牛顿的算法以适配此目标，利用对两类变量的梯度信息，无需预先指定控制时域即可找到高保真最优轨迹。通过数值仿真验证了该方法的有效性与鲁棒性：所提算法复现了航天器霍曼转移的解析解，并确定了地月转移的最优控制时域。
英文摘要
This paper presents a novel trajectory optimization method for nonlinear l1-optimal control problems in which the control horizon is treated as a free variable, allowing both the control duration and the l1-norm of the control input to be evaluated. Unlike traditional approaches that minimize the l1-norm of the input under a fixed control horizon, the proposed method treats both the control input and control horizon as design variables, enabling joint optimization of energy and temporal efficiency. The method extends a Newton-based algorithm to accommodate this objective, leveraging gradient information with respect to both variables. This formulation enables one to find high-fidelity optimal trajectories without pre-specifying the control horizon. The effectiveness and robustness of the method are demonstrated through numerical simulations, in which the proposed algorithm recovers the analytical solution to the spacecraft Hohmann transfer, and determines an optimal control horizon for an Earth-Moon transfer.
