Stochastic Koopman Operator-Based Adaptive Fuzzy Control for Nonlinear Systems under Unmodeled Dynamics

Document Type : Research Paper

Authors

1 Faculty of Electrical Engineering, K.N. Toosi University of Technology, Tehran, Iran

2 Department of Electrical Engineering, YI.C., Islamic Azad University, Tehran, Iran.

10.22111/ijfs.2026.52890.9350

Abstract

This paper introduces a novel stochastic Koopman-based adaptive fuzzy control framework that combines Koopman operator theory with Takagi-Sugeno-Kang (TSK) fuzzy logic to effectively manage nonlinear systems under unmodeled dynamics and diverse stochastic disturbances. The core innovation lies in the concurrent online learning of sparse Koopman observables and the fuzzy controller using deep dictionary learning, replacing static feature sets to significantly enhance adaptability. A robust Lyapunov-based stability analysis in the Koopman observable space, supported by linear matrix inequality criteria, guarantees reliable performance across Gaussian and non-Gaussian noise conditions. Simulation results on benchmark systems, including a 4D hyperchaotic system and an inverted pendulum, demonstrate superior tracking accuracy, disturbance rejection, and computational efficiency compared to model predictive control (MPC), Nonlinear model predictive control (NMPC), and classical TSK fuzzy controllers, with the lowest IAE (1.4933, 3.2627) and ISE (2.3226, 5.0745) metrics. The method’s balance of interpretability and data-driven modeling makes it ideal for real-time control of complex, uncertain systems. While offering strong theoretical foundations and addressing critical gaps in robustness and scalability, further empirical validation and enhanced visual representations of the architecture could strengthen its impact. This work advances adaptive fuzzy control and data-driven modeling, with significant potential for applications in robotics, smart infrastructure, and other safety-critical domains.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 4
July and August 2026
Pages 121-143

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