Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field

Zhang, Weiwei; Sha, Chunlin; Cao, Jinde; Wang, Guanglan; Wang, Yuan

doi:10.1016/j.amc.2021.126045

Cited by 24 publications

(19 citation statements)

References 24 publications

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“…Remark 1 Recently, the various synchronization modes [15,27,[33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] were investigated such as finite-time synchronization [34,45,46], asymptotic synchronization [15,[35][36][37], Mittag-Leffler synchronization [38,39,41,44] and projective synchronization [40,42,43]. The different control strategies had been designed to solve synchronization problems for NNs including impulsive control [17,20,23,38,39,47], linear feedback control [44] and sliding mode control [40].…”

Section: Resultsmentioning

confidence: 99%

Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay

Yu-hong

Zhang

et al. 2021

J. Appl. Math. Comput.

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This paper focuses on the global Mittag-Leffler (M-L) synchronization for fractionalorder inertial neural networks (FOINNs) including the Caputo derivative and delay. By choosing an appropriate variable transformation, the considered system including the inertial term is transformed into two fractional-order nonlinearly coupled interconnected subsystems. Combining with the delayed-feedback controller, fractional Lyapunov functional approach and inequality analysis technique, multi sets of novel algebraic criteria on the global M-L synchronization between derive-response systems are established. The main prominent highlight of this paper is that the proposed results are characterized by the algebraic inequalities form, which can simplify the calculation and facilitate the test. Two numerical simulation examples validate the theoretical results.

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Section: Resultsmentioning

confidence: 99%

Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay

Yu-hong

Zhang

et al. 2021

J. Appl. Math. Comput.

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“…and sliding surface (18) and ( 15) are equivalent. Based on the sliding mode control method, when error system (13) moves on sliding surface, the formulas S(t) � 0 and _ S(t) � 0 have to be satisfied.…”

Section: Resultsmentioning

confidence: 99%

“…In [15][16][17], by using different control methods, the authors have researched the PS for FNNs. In [18], Zhang et al have used the adaptive control method to achieve the PS of FNNs in quaternion field. In [19][20][21], researchers have explored the PS for fractional-order memristive neural networks with different characters.…”

Section: Introductionmentioning

confidence: 99%

Sliding Mode Matrix-Projective Synchronization for Fractional-Order Neural Networks

Lei

Jiang

2021

Journal of Mathematics

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This work generalizes the projection scaling factor to a general constant matrix and proposes the matrix-projection synchronization (MPS) for fractional-order neural networks (FNNs) based on sliding mode control firstly. This kind of scaling factor is far more complex than the constant scaling factor, and it is highly variable and difficult to predict in the process of realizing the synchronization for the driving and response systems, which can ensure high security and strong confidentiality. Then, the fractional-order integral sliding surface and sliding mode controller for FNNs are designed. Furthermore, the criterion for realizing MPS is proved, and the reachability and stability of the synchronization error system are analyzed, so that the global MPS is realized for FNNs. Finally, a numerical application is given to demonstrate the feasibility of theory analysis. MPS is more general, so it is reduced to antisynchronization, complete synchronization, projective synchronization (PS), and modified PS when selecting different projective matrices. This work will enrich the synchronization theory of FNNs and provide a feasible method to study the MPS of other fractional-order dynamical models.

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“…Synchronization can be regarded as the dynamic behavior of nodes with the help of relations between nodes, 19 which can be divided simply into two categories, the inner synchronization and the outer synchronization. The inner synchronization means that the synchronous state of all nodes happens within the same network 3,4,6,8,10,11,13‐15,19‐22 . There are many real networks for inner synchronization such as synchronous firing of neurons, 23 the synchronization of several pendulum clocks, 24,25 the data synchronization between multiple computers, 26 the synchronous operation of motors in multi‐conveyor‐belt‐systems 27 and so forth.…”

Section: Introductionmentioning

confidence: 99%

“…2 It is known to not all networks can synchronize naturally, and thus the appropriate control schemes are needed to promote network synchronization. 3,4 In recent years, thanks to the great efforts of researchers, a lot of results on synchronization control schemes are proposed for CDNs, such as the complete synchronization, 5,6 generalized synchronization, 7,8 projective synchronization, [9][10][11] cluster synchronization, [12][13][14][15] global synchronization [16][17][18] and so forth.…”

Section: Introductionmentioning

confidence: 99%

Outer synchronization for a class of discrete‐time complex dynamic networks with unknown bounded interaction

Wang

2022

Adaptive Control & Signal

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This article investigates the outer synchronization for the two discrete-time complex dynamic networks. First, the more universal mathematical models of the networks with unknown coupling and interaction are proposed. Then, based on the available state of networks and the estimation of summarized unknown parameters shown in the models, the adaptive state feedback controller is synthesized to make the outer synchronization error of two networks converge asymptotically to an arbitrarily small neighborhood at the origin. Finally, the results of simulation show the validity and advantages of the controller.

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Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field

Cited by 24 publications

References 24 publications

Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay

Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay

Sliding Mode Matrix-Projective Synchronization for Fractional-Order Neural Networks

Outer synchronization for a class of discrete‐time complex dynamic networks with unknown bounded interaction

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