Adaptive control-based synchronization of discrete-time fractional-order fuzzy neural networks with time-varying delays
This paper is concerned with complete synchronization for discrete-time fractional-order fuzzy neural networks (DFFNNs) with time-varying delays. First, three original equalities and two Caputo σ-difference inequalities are established based on theory of discrete-time fractional Calculus. Next, a no...
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| Published in: | Neural networks 2023-11, Vol.168, p.59-73 |
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| Main Authors: | , , , , |
| Format: | Article |
| Language: | eng |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | This paper is concerned with complete synchronization for discrete-time fractional-order fuzzy neural networks (DFFNNs) with time-varying delays. First, three original equalities and two Caputo σ-difference inequalities are established based on theory of discrete-time fractional Calculus. Next, a novel discrete-time adaptive controller with time-varying delay is designed, by virtue of 1-norm Lyapunov function and newly established lemmas herein as well as inequality techniques and contradiction method, some judgement conditions are derived to guarantee complete synchronization for the explored DFFNNs. Benefitting from discrete-time adaptive control strategy and our analysis method, the conservatism of the derived synchronization criteria is reduced. Ultimately, the effectiveness of our theoretical results and secure communication scheme are demonstrated through two numerical examples.
•We establish three original equalities, which enrich theory of discrete-time fractional Calculus.•Two Caputo σ-difference inequalities are introduced and proved herein. The first one is bc∇σμ(f(t)−ϱ)2⩽2(f(t)−ϱ)bc∇σμf(t), which can be applied to adaptive control-based asymptotic synchronization of nonlinear systems depicted by Caputo σ -difference equations. The second inequality is bc∇σμ|f(t)|⩽sign(f(t))bc∇σμf(t), which plays a central role in building the relationship between 1-norm Lyapunov function and Caputo σ-difference of state variable.•A universal theoretical framework analyzing adaptive control-based complete synchronization for DFNNs is developed for the first time.•Our results are more general, which can be extended to DFNNs without fuzzy logic or DFNNs without delay.•A secure communication scheme for DFFNNTDs is proposed based on complete synchronization method. |
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| ISSN: | 0893-6080 1879-2782 |