A Time-Varying Fuzzy Parameter Zeroing Neural Network for the Synchronization of Chaotic Systems

Zeroing neural network (ZNN) has been applied to various time-varying problems solving, and numerous ZNN models have been developed in recent years, such as power-type varying-parameter ZNN (PT-VR-ZNN) for solving time-varying quadratic minimization problems, adaptive fuzzy-type ZNN (AFT-ZNN) for solving time-variant matrix inversion and fuzzy power ZNN (FPZNN) for solving time-varying quadratic programming problems. As a time-varying problem and imperative research hot spot in science and engineering, the synchronization of chaotic systems has developed for decades. However, the research on chaos synchronization using ZNN method is rarely reported. Therefore, this paper proposes a time-varying fuzzy parameter ZNN (TVFP-ZNN) model to realize chaotic systems synchronization against the external noises. The most prominent feature of the TVFP- ZNN model is that the time-varying fuzzy parameter generated by the fuzzy logic system is applied in this model. Moreover, the above mentioned three models are also applied to realize the same chaotic systems synchronization for comparison. Compared with above three models, the proposed TVFP-ZNN model not only possesses the fastest convergence speed, but also maintains strongest robustness to noises. Besides, the excellent performances of the TVFP-ZNN model are verified by rigorous mathematical validation. Furthermore, the effectiveness and robustness of the proposed TVFP-ZNN model for chaotic systems synchronization are verified by comparative numerical simulation results. Finally, the process of the proposed TVFP-ZNN model for chaotic system synchronization is displayed on the oscilloscope based on the field programmable gate array (FPGA) to further illustrate its practical application ability.

Automated summary

This paper proposes a new time-varying fuzzy parameter ZNN (TVFP-ZNN) model for achieving synchronization of chaotic systems against external noises. Compared with the other three models, the TVFP-ZNN model not only has the fastest convergence speed, but also exhibits the strongest robustness to noises. Furthermore, the excellent performance of the TVFP-ZNN model is verified through rigorous mathematical validation.