Nonlinear System Control Based on an Output Recurrent TS Fuzzy Controller

Abstract

The Takagi-Sugeno (TS) fuzzy control design method has been widely utilized for nonlinear system control due to its ability to approximate complex system behaviors. Traditionally, TS fuzzy controllers are designed by computing controller gains offline using the MATLAB linear matrix inequality (LMI) control toolbox, where system parameters are obtained through the linearization of each subsystem. While this simplification reduces computational complexity, it also compromises the nonlinear characteristics of the system, leading to a discrepancy between the mathematical model and the real-world implementation. Moreover, system uncertainties and time-varying dynamics introduce further challenges, as the offline-derived controller gains may become suboptimal during actual operation, limiting the controller's adaptability and robustness. To address these issues, this study proposes an output recurrent Takagi-Sugeno fuzzy controller (ORTSFC), designed to enhance system adaptability and disturbance rejection. The novelty of this research lies in the integration of a recurrent structure within the TS fuzzy framework, transforming it from a static system into a dynamic one. This approach allows the controller to adapt continuously to real-time system dynamics, enhancing responsiveness and performance without requiring complex recalculations. Consequently, the proposed ORTSFC achieves robust control with significantly reduced computational demands. In addition, system stability is rigorously ensured through Lyapunov-based analysis. Overall, the ORTSFC provides a theoretically grounded and practically efficient solution for controlling nonlinear systems, especially under uncertainty and time-varying conditions. The main contributions of this study include: 1) Development of an ORTSFC, which introduces recurrence into the TS fuzzy control framework, improving its ability to capture dynamic system behaviors and adapt to uncertainties. 2) Application of the ORTSFC to a nonlinear control problem, specifically for the omnidirectional inverted pendulum (OIP), demonstrating its superior performance in stabilizing complex systems under uncertain conditions. Extensive simulation results validate the effectiveness of the proposed ORTSFC, showing its advantages over conventional TS fuzzy controllers in terms of adaptability, robustness, and computational efficiency.