Optimal control of nonlinear impulsive systems with free impulse instants and the number of impulses is investigated in this study. A scheme based on adaptive dynamic programming is developed, which leads to a feedback (approximate) solution to the defined optimal impulsive control problem. This is done by proposing a learning algorithm for tuning parameters of a function approximator, which, once tuned offline, provides feedback solution on-the-fly. The scheme is shown to handle single and multiple impulsive actuators with a small online computational burden. Afterward, the controller is applied to a challenging problem, namely, the orbital maneuver of spacecraft with the fixed final time using impulsive actuators. The objective is triggering the actuators in a fuel-optimal manner such that the spacecraft transfers to the desired orbit at a prescribed time. It was shown that the proposed scheme leads to simultaneous and feedback path planning and control for the maneuver. The potentials of the scheme are analyzed in different scenarios, including enforcing a shorter final time, selecting different initial states, and incorporating actuator faults.

中文翻译：

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基于自适应动态规划的最优脉冲控制及其在航天器交会中的应用

本研究研究了具有自由脉冲时刻和脉冲数的非线性脉冲系统的优化控制。开发了一种基于自适应动态规划的方案，该方案导致对定义的最优脉冲控制问题的反馈（近似）解决方案。这是通过提出一种用于调整函数逼近器参数的学习算法来完成的，该算法一旦离线调整，就可以即时提供反馈解决方案。该方案显示出以较小的在线计算负担处理单个和多个脉冲执行器。之后，控制器应用于具有挑战性的问题，即使用脉冲执行器的固定最终时间的航天器轨道机动。目标是以燃料优化的方式触发执行器，以便航天器在规定的时间转移到所需的轨道。结果表明，所提出的方案导致对机动的同步和反馈路径规划和控制。该方案的潜力在不同场景下进行分析，包括强制执行更短的最终时间、选择不同的初始状态以及合并执行器故障。