In this article, by using singular perturbation theory, reinforcement learning (RL), and Takagi–Sugeno (T-S) fuzzy methods, a RL-fuzzy-based composite suboptimal control method is proposed for nonlinear slow-fast coupled systems (SFCSs) with unknown slow dynamics. First, the SFCSs is decomposed into slow and fast subsystems and the original optimal control problem is reduced to two subproblems. Then, for the slow subsystem, a nonlinear coordinate transformation is introduced to transform the nonquadratic slow utility function into the quadratic form. Unmeasurable virtual slow subsystem state is reconstructed by the state measurements of original system and slow controller design algorithm is proposed in the framework of RL by utilizing the actor-critic neural networks to approximate the controller and cost function. For the fast subsystem, T-S fuzzy model is established and state measurements of the original system are exploited to reconstruct the unmeasurable fast subsystem state. Fast controller is designed with the approach of parallel distributed compensation. The obtained slow and fast controllers form the composite suboptimal controller for the original SFCSs. Considering the state reconstruction error, convergence of the slow controller design algorithm, suboptimality of the composite controller, and stability of the closed-loop SFCSs are analyzed. Finally, the effectiveness of our proposed method is illustrated by examples.

中文翻译：

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使用强化学习和 Takagi-Sugeno 模糊方法的非线性慢-快耦合系统的次优控制

在本文中，利用奇异摄动理论、强化学习（RL）和 Takagi-Sugeno（TS）模糊方法，提出了一种基于 RL 模糊的复合次优控制方法，用于非线性慢-快耦合系统（SFCS）。缓慢的动态。首先，SFCSs 被分解为慢速和快速子系统，并将原来的最优控制问题简化为两个子问题。然后，对于慢子系统，引入非线性坐标变换将非二次慢效用函数转化为二次形式。通过原始系统的状态测量重构不可测量的虚拟慢子系统状态，并在强化学习的框架下提出慢控制器设计算法，利用actor-critic神经网络来逼近控制器和成本函数。对于快速子系统，建立TS模糊模型，并利用原系统的状态测量来重构不可测量的快速子系统状态。快速控制器采用并行分布补偿的方法设计。获得的慢速和快速控制器形成了原始 SFCS 的复合次优控制器。考虑状态重构误差，分析了慢速控制器设计算法的收敛性、复合控制器的次优性和闭环SFCS的稳定性。最后，我们通过例子说明了我们提出的方法的有效性。获得的慢速和快速控制器形成了原始 SFCS 的复合次优控制器。考虑状态重构误差，分析了慢速控制器设计算法的收敛性、复合控制器的次优性和闭环SFCS的稳定性。最后，我们通过例子说明了我们提出的方法的有效性。获得的慢速和快速控制器形成了原始 SFCS 的复合次优控制器。考虑状态重构误差，分析了慢速控制器设计算法的收敛性、复合控制器的次优性和闭环SFCS的稳定性。最后，我们通过例子说明了我们提出的方法的有效性。