论文标题
具有加性和乘法噪声的离散时间系统的无模型最佳控制
Model-free optimal control of discrete-time systems with additive and multiplicative noises
论文作者
论文摘要
本文研究了一类离散时间随机系统的最佳控制问题，但遇到了累加和乘法噪声。为了存在最佳可允许的控制策略，建立了随机Lyapunov方程和随机代数方程。提出了一种无模型的强化学习算法，以使用系统状态的数据和输入的数据来学习最佳的可允许控制策略，而无需了解系统矩阵。事实证明，学习算法会融合到最佳可允许的控制策略。无模型算法的实现基于批处理最小二乘和数值平均值。提出的算法通过数值示例说明，该示例显示了我们的算法优于其他策略迭代算法。
This paper investigates the optimal control problem for a class of discrete-time stochastic systems subject to additive and multiplicative noises. A stochastic Lyapunov equation and a stochastic algebra Riccati equation are established for the existence of the optimal admissible control policy. A model-free reinforcement learning algorithm is proposed to learn the optimal admissible control policy using the data of the system states and inputs without requiring any knowledge of the system matrices. It is proven that the learning algorithm converges to the optimal admissible control policy. The implementation of the model-free algorithm is based on batch least squares and numerical average. The proposed algorithm is illustrated through a numerical example, which shows our algorithm outperforms other policy iteration algorithms.
