New Fixed-Time Synchronization Criteria for Fractional-Order Fuzzy Cellular Neural Networks with Bounded Uncertainties and Transmission Delays via Multi-Module Control Schemes

This paper concentrates on fractional-order fuzzy cellular neural networks (FOFCNNs) with bounded uncertainties and transmission delays. To better capture real-world dynamic behaviors, the fuzzy AND and OR operators are employed to construct drive-response systems. For the fixed-time synchronization task of the systems, a novel multi-module feedback controller incorporating three functional terms is designed. These terms aim to eliminate delay effects, ensure fixed-time convergence, and reduce parameter conservativeness. Leveraging the properties of fractional-order operators and our multi-module control scheme, new synchronization criteria of the studied drive-response systems can be established within a predefined time. An upper bound on the settling time is derived, depending on the system size and control parameters, but independent of the initial conditions. A significant corollary is derived for the case of no uncertainties under the nonlinear controller. Numerical experiments discuss the impact of uncertainties and delays on synchronization, and confirm the validity of the results presented in this study.