Synchronization Control of Riemann-Liouville Fractional Competitive Network Systems with Time-varying Delay and Different Time Scales

Zhang, Hai; Miao-lin, YE; Cao, Jinde; Alsaedi, Ahmed

doi:10.1007/s12555-017-0371-0

Cited by 25 publications

(10 citation statements)

References 43 publications

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“…In order to use the induction method, let any l with θ ≤ l ≤ N , and for j > l + 1, we assume that H j in 10is strictly positive definite, the optimal feedback controller is presented by (14), A j , B j satisfy the coupled Riccati difference equations (12), (13), and the relationship between λ j−1 and state x j is assumed to satisfy (17).…”

Section: Solution To Problemmentioning

confidence: 99%

“…By substituting the optimal feedback controller as (14) for (25), the minimizing cost function can be calculated as…”

Section: Solution To Problemmentioning

confidence: 99%

“…However, contention based networks may exhibit bandwidth limitations, date packet disordering, limitations arising from data quantization and time-varying sampling period(see [9], [10], [11]). Time delays are normally caused by signal transmission and traffic congestion, and packet losses are by virtue of nodes failure or long time delays(see [12], [13], [14], [15]). For nonlinear NCSs with packet losses, there are some developments in virtue of applications of practical control systems.…”

Section: Introductionmentioning

confidence: 99%

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Control for Multiplicative Noise Systems With Packet Losses and Measurement Delays

Lv¹,

Liang²,

Wang³

et al. 2020

IEEE Access

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This paper mainly considers the control problems for discrete-time multiplicative noise systems with packet losses and measurement delays. The main contributions are twofold. Firstly, based on Pontryagin's maximum principle, the optimal output feedback controller is obtained. Secondly, a necessary and sufficient stabilization condition for multiplicative noise systems is derived in terms of the coupled algebraic Riccati equations. Moreover, it has been proved that the stabilization condition only depends on the eigenvalue of the system matrix and the probability of packet losses which is not related to measurement delays.

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Section: Solution To Problemmentioning

confidence: 99%

“…By substituting the optimal feedback controller as (14) for (25), the minimizing cost function can be calculated as…”

Section: Solution To Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Control for Multiplicative Noise Systems With Packet Losses and Measurement Delays

Lv¹,

Liang²,

Wang³

et al. 2020

IEEE Access

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“…Note that the case of fractional-neural networks with Riemann-Liouville (RL) fractional derivatives is not well studied because of this type of derivative and the required initial condition (see, for example, [10,11,15,27,29]). At the same time, there are some inaccuracies when the RL fractional derivative is applied.…”

Section: Introductionmentioning

confidence: 99%

Mean-square stability of Riemann–Liouville fractional Hopfield’s graded response neural networks with random impulses

et al. 2021

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In this paper a model of Hopfield’s graded response neural network is investigated. A network whose neurons are subject to a certain impulsive state displacement at random times is considered. The model is set up and studied. The presence of random moments of impulses in the model leads to a change of the solutions to stochastic processes. Also, we use the Riemann–Liouville fractional derivative to model adequately the long-term memory and the nonlocality in the neural networks. We set up in an appropriate way both the initial conditions and the impulsive conditions at random moments. The application of the Riemann–Liouville fractional derivative leads to a new definition of the equilibrium point. We define mean-square Mittag-Leffler stability in time of the equilibrium point of the model and study this type of stability. Some sufficient conditions for this type of stability are obtained. The general case with time varying self-regulating parameters of all units and time varying functions of the connection between two neurons is studied.

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“…[21][22][23][24] Because the dynamics of fractional-order calculus have more advantages compared with the dynamics of traditional integer-order calculus to describing the real-world's memory and hereditary properties. Due to the memory properties, many researchers incorporate into neural networks, and a lot of scientific reports have been well-documented in recent literature, see Thuan et al, 25 Yang et al, 26 and Zhang et al 27 Stability theory is the versatile branch of science and engineering that deals with the influence behavior of dynamical structures for both linear and nonlinear systems. According to our literature survey hitherto, the various stability problem of the dynamics of neural networks has been studied by many researchers [28][29][30][31][32][33][34][35] based on the Lyapunov direct method (LDM).…”

Section: Introductionmentioning

confidence: 99%

Stability of discrete‐time fractional‐order time‐delayed neural networks in complex field

Anbalagan

Raja

Cao

et al. 2020

Math Methods in App Sciences

Self Cite

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Dynamics of discrete-time neural networks have not been well documented yet in fractional-order cases, which is the first time documented in this manuscript. This manuscript is mainly considered on the stability criterion of discrete-time fractional-order complex-valued neural networks with time delays. When the fractional-order holds 1 < < 2, sufficient criteria based on a discrete version of generalized Gronwall inequality and rising function property are established for ensuring the finite stability of addressing fractional-order discrete-time-delayed complex-valued neural networks (FODCVNNs). In the meanwhile, when the fractional-order holds 0 < < 1, a global Mittag-Leffler stability criterion of a class of FODCVNNs is demonstrated with two classes of neuron activation function by means of two different new inequalities, fractional-order discrete-time Lyapunov method, discrete version Laplace transforms as well as a discrete version of Mittag-Leffler function. Finally, computer simulations of two numerical examples are illustrated to the correctness and effectiveness of the presented stability results.

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Synchronization Control of Riemann-Liouville Fractional Competitive Network Systems with Time-varying Delay and Different Time Scales

Cited by 25 publications

References 43 publications

Control for Multiplicative Noise Systems With Packet Losses and Measurement Delays

Control for Multiplicative Noise Systems With Packet Losses and Measurement Delays

Mean-square stability of Riemann–Liouville fractional Hopfield’s graded response neural networks with random impulses

Stability of discrete‐time fractional‐order time‐delayed neural networks in complex field

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