Multistability for Almost-Periodic Solutions of Takagi-Sugeno Fuzzy Neural Networks With Nonmonotonic Discontinuous Activation Functions and Time-Varying Delays

• Published in: IEEE transactions on fuzzy systems 2021-02, Vol.29 (2), p.400-414
• Main Authors: Wan, Peng, Sun, Dihua, Zhao, Min, Huang, Shuai
• Format: Article
• Language: English
• Subjects: Almost-periodic solution; Artificial neural networks; Attraction; attraction basin; Basins; Control theory; Delays; Fuzzy logic; Fuzzy neural networks; multistability; Neural networks; nonmonotonic discontinuous activation function; Stability analysis; Takagi-Sugeno model; Takagi–Sugeno fuzzy neural networks
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2019.2955886

This article investigates the problem of multistability of almost-periodic solutions of Takagi-Sugeno fuzzy neural networks with nonmonotonic discontinuous activation functions and time-varying delays. Based on the geometrical properties of nonmonotonic activation functions, by using the Ascoli-Arzela theorem and the inequality techniques, it is demonstrated that under some reasonable conditions, the addressed networks have a locally exponentially stable almost-periodic solution in some hyperrectangular regions. We also estimate the attraction basins of the locally stable almost-periodic solutions, which indicates that the attraction basins of the locally exponentially stable almost-periodic solution can be larger than original hyperrectangular regions. These results, which include boundedness, globally attractivity, multiple stability, and attraction basins, generalize and improve the earlier publications, and can be extended to monostability and multistability of Takagi-Sugeno fuzzy neural networks with nonmonotonic discontinuous activation functions. Finally, several numerical examples are given to show the feasibility, the effectiveness, and the merits of the theoretical results.