Finite-Time Synchronization of Fractional-Order Delayed Fuzzy Cellular Neural Networks With Parameter Uncertainties

• Published in: IEEE transactions on fuzzy systems Vol. 31; no. 6; pp. 1769 - 1779
• Main Authors: Du, Feifei, Lu, Jun-Guo
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Artificial neural networks; Calculus; Cellular communication; Cellular neural networks; Chaos; Composite functions; Control systems design; Feedback control; Finite-time synchronization (FTS); Fractional calculus; fractional-order finite-time inequality (FOFTI); fuzzy cellular neural network (FCNN); Fuzzy logic; Inequalities; Neural networks; parameter uncertainties; Parameter uncertainty; Synchronization; time delay; Time synchronization; Uncertain systems
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2022.3214070

The finite-time synchronization (FTS) is studied for a class of fractional-order delayed fuzzy cellular neural networks (FODFCNNs) with parameter uncertainties. A linear fractional-order finite time inequality (FOFTI) <inline-formula><tex-math notation="LaTeX">{}^{c}_{t_{0}}D^{p}_{t} V(t)\leq -a V(t)-b</tex-math></inline-formula> is extended to the nonlinear case <inline-formula><tex-math notation="LaTeX">{}^{c}_{t_{0}}D^{p}_{t} V(t)\leq -a V^{-\eta }(t)-b</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">\eta \geq 1</tex-math></inline-formula>, which plays a vital role in the FTS of fractional-order systems. However, for the case of <inline-formula><tex-math notation="LaTeX">0< \eta < 1</tex-math></inline-formula>, a theoretical cornerstone justifying its use is still missing. To fill this research gap, on the basis of the <inline-formula><tex-math notation="LaTeX">C_{p}</tex-math></inline-formula> inequality and the rule for fractional-order derivative of composite function, a nonlinear FOFTI <inline-formula><tex-math notation="LaTeX">{}^{c}_{t_{0}}D^{p}_{t} V(t)\leq -a V^{-\eta }(t)-b</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">0< \eta < 1</tex-math></inline-formula> is developed. Furthermore, a nonlinear FOFTI <inline-formula><tex-math notation="LaTeX">{}^{c}_{t_{0}}D^{p}_{t} V(t)\leq -bV^{-\xi }(t)-a V^{-\eta }(t)</tex-math></inline-formula> is also established. These two novel inequalities provide the new tools for the research on the finite time stability and synchronization of fractional-order systems and can greatly extend the pioneer ones. Next, on the basis of these novel inequalities, the feedback controller is designed and two novel FTS criteria of FODFCNNs with parameter uncertainties are obtained. Finally, two examples are presented to verify the effectiveness of the derived results.