Finite-Time and Fixed-Time Synchronization of Complex-Valued Recurrent Neural Networks with Discontinuous Activations and Time-Varying Delays

Aouiti, Chaouki; Bessifi, Mayssa; Li, Xiaodi

doi:10.1007/s00034-020-01428-4

Cited by 43 publications

(29 citation statements)

References 48 publications

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“…However, the fixed-time controllers in [39], [40] are uncontinuous ones, which may cause chattering phenomenon in engineering applications. Furthermore, the activation functions in [39], [40] are required to be bounded, and the Lyapunov functions in [39], [40] are not derivable. In this paper, we study the fixed-time synchronization of complex-valued neural networks based on the fixed-time stability theorem developed by ourselves.…”

Section: Proof Choose a Lyapunov Functionmentioning

confidence: 99%

“…Since the fixed-time synchronization of CVNNs can be ap-plied in secure communication, image encryption, associative memory, pattern recognition and other potential areas, it is also necessary to analyze the fixed-time synchronization of CVNNs. In fact, there have been some works [39], [40] about the fixed-time synchronization of complex-valued neural networks, which are all based on the fixed-time stability theorem in [1]. However, the fixed-time controllers in [39], [40] are uncontinuous ones, which may cause chattering phenomenon in engineering applications.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, there have been some works [39], [40] about the fixed-time synchronization of complex-valued neural networks, which are all based on the fixed-time stability theorem in [1]. However, the fixed-time controllers in [39], [40] are uncontinuous ones, which may cause chattering phenomenon in engineering applications. Furthermore, the activation functions in [39], [40] are required to be bounded, and the Lyapunov functions in [39], [40] are not derivable.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fixed-Time Synchronization Analysis for Complex-Valued Neural Networks via a New Fixed-Time Stability Theorem

Chen

Qiu

et al. 2020

IEEE Access

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Based on variable substitution, calculating definite integral and solving the minimization problem, in this paper we establish a new fixed-time stability theorem, which can provide a novel upper bound estimate formula for the settling time. By dividing the considered complex-valued neural networks (CVNNs) into double-layer real-valued neural networks, the fixed-time synchronization of CVNNs is analyzed by means of the new fixed-time stability theorem. Both theoretical derivation and numerical simulation show the new upper bound estimate formula for the settling time in this paper is more accurate than that given in the classic fixed-time stability theorem. A numerical example is given to verify the effectiveness of the main results. INDEX TERMS Complex-valued neural networks, Fixed-time stability, Fixed-time synchronization.

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Section: Proof Choose a Lyapunov Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fixed-Time Synchronization Analysis for Complex-Valued Neural Networks via a New Fixed-Time Stability Theorem

Chen

Qiu

et al. 2020

IEEE Access

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“…44 Consequently, the complex-valued neural networks (CVNNs) have received significant research attention. [45][46][47][48] The authors of Reference 46 proposed some sufficient conditions for the existence and uniqueness of the equilibrium point and the global -stability of CVNNs based on homeomorphism mapping, Lyapunov-Krasovskii, and Jensen inequalities. In Reference 45, the finite-time and fixed-time synchronization of CVNNs with discontinuous activations and time-varying delays by dividing the system into two real parts are investigate based on Lyapunov functions and some differential inequalities.…”

Section: Introductionmentioning

confidence: 99%

“…45,[62][63][64][65][66] As an application of fixed-time stability, fixed-time control for RVNNs and CVNNs has received tremendous interest in recent years since it can make system stabilize within a bounded time even if the initial conditions are unknown in advance. 31,32,38,45 The fixed-time controller is added to the model to make it stabilize at a fixed-time. However, there are no results discussed the fixed-time stabilization of quaternion fuzzy neural networks (QFNNs) with time-varying delays which is one of our motivations for conducting this research.…”

Section: Introductionmentioning

confidence: 99%

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

Aouiti

Jallouli

2021

Intl J Robust & Nonlinear

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This article addresses the problems of fixed-time stabilization for a class of quaternion fuzzy neural networks (QFNNs) with time-varying delay. The QFNNs are developed by dividing our system into four real-valued parts based on the Hamilton rule. Then, based on fixed-time stability theory, some inequality techniques, and selecting the appropriate controllers and Lyapunov function, a novel criterion guaranteeing the fixed-time stabilization and the finite-time stabilization of the addressed system is derived. Finally, three numerical examples are presented to show the effectiveness of our theoretical results. K E Y W O R D S finite-time stabilization, fixed-time stabilization, fuzzy neural networks, quaternion neural networks, time-varying delay

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Finite‐time and fixed‐time sliding mode control for discontinuous nonidentical recurrent neural networks with time‐varying delays

Aouiti

Bessifi

2021

Intl J Robust & Nonlinear

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This article investigates the synchronization problem in finite-time and fixed-time of the drive-response delayed recurrent neural networks (RNNs).Moreover, it is assumed that the parameters of the RNNs are nonidentical and the activation functions are discontinuous. For addressing the synchronization problem in finite-time and fixed-time, an improved sliding mode control (SMC) approach is presented. In a first time, by applying the drive-response concept and the synchronization error between the drive-response model, two novel integral sliding mode surfaces are constructed such that the synchronization error can converge to zero in finite-time and fixed-time. In second time, two SMC is created to overcome the finite-time and fixed-time synchronization problem of delayed RNNs. On the basis of Lyapunov stability theory, several sufficient criteria are obtained for the considered discontinuous nonidentical RNNs with time-varying delays models to achieve finite-time synchronization and fixed-time synchronization. Moreover, two types of setting time, which are dependent and independent on the initial values, are given respectively. In the end, three numerical simulations are given to illustrate the effectiveness of the synchronization criteria.

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Finite-Time and Fixed-Time Synchronization of Complex-Valued Recurrent Neural Networks with Discontinuous Activations and Time-Varying Delays

Cited by 43 publications

References 48 publications

Fixed-Time Synchronization Analysis for Complex-Valued Neural Networks via a New Fixed-Time Stability Theorem

Fixed-Time Synchronization Analysis for Complex-Valued Neural Networks via a New Fixed-Time Stability Theorem

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

Finite‐time and fixed‐time sliding mode control for discontinuous nonidentical recurrent neural networks with time‐varying delays

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