AI 中文总结
本文提出一种代数方法，利用闭式解生成解析梯度优化最优反馈控制的状态、控制与终端状态权重矩阵，无需数值积分，通过数值示例验证了其有效性，可用于多领域控制理论应用。
AI 中文摘要
最优反馈控制算法的构建所需的必要条件已为人所知多年。性能指标中存在自由参数，其形式为状态惩罚矩阵、控制惩罚矩阵与终端状态惩罚矩阵，用于调优最优受控系统的性能。该选择过程通常是实验性且迭代的。为生成最优反馈控制算法的权重矩阵，本文提出了一种优化方法。通常，权重矩阵的优化过程需要多次数值积分，计算成本高昂；本研究通过利用时变Riccati矩阵、状态轨迹、状态转移矩阵及最优性能指标的闭式解，克服了经典的高计算成本问题。闭式代数方程用于生成所有偏导数计算，无需进行数值积分。闭式偏导数用于生成优化步骤的解析梯度。该优化策略旨在最小化反馈控制问题的终端状态值。本文给出了一个数值示例，以证明所提优化算法的有效性。所得计算程序有望广泛应用于科学与工程领域的控制理论应用中。
英文摘要
The necessary conditions for formulating optimal feedback control algorithms have been known for many years. Free parameters exist in the performance index in the form of state and control penalty and terminal state penalty matrices for tuning the performance of the optimally controlled system. The selection process is typically experimental and iterative. To generate the weight matrices for optimal feedback control algorithms, an optimization process is proposed. Typically, the optimization process for the weight matrices requires several numerical integration processes that are computationally expensive; this work overcomes the classical high computational cost by exploiting closed-form solutions for the time-varying Riccati matrix, state trajectories, state transition matrix, and the optimal performance index. Closed-form algebraic equations are used to generate all partial derivative calculations, and no numerical integration is required. The closed-form partial derivatives are used to generate analytic gradients for the optimization steps. The optimization strategy seeks to minimize the terminal state values for the feedback control problem. A numerical example is presented to demonstrate the effectiveness of the proposed optimization algorithm. The resulting computational procedures are expected to be broadly useful for control theory applications in science and engineering.
Comments11 pages, 6 figures, 2021 AAS/AIAA Astrodynamics Specialist Conference
