Reinforcement Learning‐Fuzzy Composite H∞ Tracking Control of Input‐Saturated Nonlinear Singularly Perturbed Systems
Linna Zhou, Gonghe Li, Xiaomin Liu, Chunyu Yang · International Journal of Robust and Nonlinear Control · 2025
ABSTRACT The composite control problem is investigated for a class of nonlinear singularly perturbed systems (SPSs) with input‐saturated and partially unknown model information. For the slow subsystem with unknown model information, we introduce an augmented state and derive the tracking Hamilton‐Jacobi‐Isaacs (HJI) equation, taking into account saturation effects and using the reinforcement learning (RL) method to solve it. For a fast subsystem affected by slow time‐varying parameters, a type‐2 fuzzy model is used to approximate it as several subsystems irrelevant to the slow time‐varying parameters. By using the parallel distributed compensation design, the optimal regulation problem of the fast subsystem is transformed into the optimal regulation problem of linear systems. The problem of the saturation upper bound for the fast and slow controllers is addressed using a hyperbolic tangent functional. The virtual subsystem state is reconstructed using measured data from the original system. Furthermore, a saturation gain parameter is designed for both fast and slow controllers to meet the input saturation condition of the original system and reduce the conservativeness of the controllers. The effectiveness of the method is validated in the context of permanent magnet synchronous motors (PMSM) as a practical application scenario.