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首页> 外文期刊>Journal of guidance, control, and dynamics >Simultaneous Learning Optimization of Hamiltonian Systems and Trajectory Tracking Around an Asteroid
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Simultaneous Learning Optimization of Hamiltonian Systems and Trajectory Tracking Around an Asteroid

机译：哈密​​顿系统的同时学习优化和围绕小行星的轨迹跟踪

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摘要

This paper proposes a simultaneous learning optimization method of feedforward input and adjustable parametersusing variational symmetry, which is a special property of Hamiltonian systems. First, a new input/output mapping ofHamiltonian representation is constructed, in which feedforward control input and a finite number of adjustableparameters are defined as the input to the system. Then, a modified variational symmetry for the present Hamiltoniansystem is derived by introducing two operators. Thanks to the modified variational symmetry, the present learningalgorithm simultaneously calculates the gradient of a given cost function with respect to an arbitrary number offeedforward inputs and parameters included in the Hamiltonian with at most two gradient experiments without usingthe plant system model. Furthermore, the proposed method is applied to trajectory tracking control of a spacecraftnear an asteroid. Here, the feedback gains of a local proportional derivative feedback controller to stabilize the systemand feedforward control input to improve tracking performance are simultaneously optimized by learning. Thepresent numerical simulations verify that the cost function decreases to a local minimum, the maximum trackingerror significantly decreases, and the obtained optimal feedforward input behaves closely to the analyticallycalculated input for perfect tracking.
机译：提出了一种使用变分对称性的前馈输入和可调整参数同时学习优化方法，这是哈密顿系统的一个特殊性质。首先，构建新的哈密顿表示形式的输入/输出映射，其中前馈控制输入和有限数量的可调参数被定义为系统的输入。然后，通过引入两个算子得出本哈密顿系统的修正变分对称性。由于修改了变分对称性，当前的学习算法可以在不使用工厂系统模型的情况下，通过最多两个梯度实验，同时针对哈密顿量中包含的任意数量的前馈输入和参数，同时计算给定成本函数的梯度。此外，该方法被应用于小行星附近航天器的轨迹跟踪控制。在此，通过学习同时优化用于稳定系统的局部比例微分反馈控制器的反馈增益和用于改善跟踪性能的前馈控制输入。当前的数值模拟验证了成本函数减小到局部最小值，最大跟踪误差显着减小，并且所获得的最佳前馈输入的行为与解析计算得到的输入非常接近，从而实现了完美的跟踪。

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