A non-singleton type-3 neuro-fuzzy fixed-time synchronizing method

This paper presents a synchronizing approach to chaotic systems with unknown nonlinear dynamics using a Gaussian non-singleton type-3 (NT3) fuzzy logic system (T3-FLS). The proposed method effectively addresses the challenges of parameter uncertainties and external disturbances by utilizing higher-order fuzzy approximations, thereby enhancing robustness and adaptability. By incorporating a projection operator, the control scenario ensures stability. The design includes a fixed-time adaptive synchronization technique that guarantees convergence in a predetermined time frame, independent of the initial values. The presented theoretical analysis proves the superiority of the designed synchronization approach, while simulations demonstrate significant improvements in synchronization performance and resilience against uncertainties. Specifically, the proposed method achieves root mean square errors of 0.1990 and 0.2754 for the tracking errors, representing improvements over 30% compared to the other benchmarking methods. These outcomes demonstrate the robustness of our proposed controller in handling chaotic systems under various operating conditions.