Finite-Time Synchronization of Fractional-Order Delayed Fuzzy Cellular Neural Networks With Parameter Uncertainties
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^{...
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| Published in | IEEE transactions on fuzzy systems Vol. 31; no. 6; pp. 1769 - 1779 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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IEEE
01.06.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Abstract | 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. |
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| AbstractList | 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. 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) [Formula Omitted] is extended to the nonlinear case [Formula Omitted], [Formula Omitted], which plays a vital role in the FTS of fractional-order systems. However, for the case of [Formula Omitted], a theoretical cornerstone justifying its use is still missing. To fill this research gap, on the basis of the [Formula Omitted] inequality and the rule for fractional-order derivative of composite function, a nonlinear FOFTI [Formula Omitted], [Formula Omitted] is developed. Furthermore, a nonlinear FOFTI [Formula Omitted] 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. |
| Author | Lu, Jun-Guo Du, Feifei |
| Author_xml | – sequence: 1 givenname: Feifei orcidid: 0000-0003-4725-377X surname: Du fullname: Du, Feifei email: qinjin65@126.com organization: Department of Automation, Shanghai Jiao Tong University, Shanghai, China – sequence: 2 givenname: Jun-Guo orcidid: 0000-0002-5012-5624 surname: Lu fullname: Lu, Jun-Guo email: jglu@sjtu.edu.cn organization: Department of Automation, Shanghai Jiao Tong University, Shanghai, China |
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| Snippet | The finite-time synchronization (FTS) is studied for a class of fractional-order delayed fuzzy cellular neural networks (FODFCNNs) with parameter... |
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| SubjectTerms | 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 |
| Title | Finite-Time Synchronization of Fractional-Order Delayed Fuzzy Cellular Neural Networks With Parameter Uncertainties |
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