Synchronization Of Fractional-order Neural Networks Research Articles

Synchronization for fractional-order neural networks with unbounded delays

This paper deals with synchronization analysis problem for a class of fractional-order neural networks with unbounded delays. Using the Lyapunov function method combined with fractional Halanay inequality, we derive a novel sufficient condition for asymptotic stability of the error system resulting in two neural networks are synchronized. The obtained conditions are given in terms of linear matrix inequalities, which therefore can be efficiently checked. A numerical example is proposed to illustrate the effectiveness of the obtained results.

Quantized Control for Local Synchronization of Fractional-Order Neural Networks with Actuator Saturation

This brief discusses the use of quantized control with actuator saturation to achieve the local synchronization of master–slave fractional-order neural networks (FONNs). A refined sector condition (RSC) is proposed that addresses the issue of the simultaneous quantizer effects and actuator constraints. The RSC is used in the theoretical analysis of local synchronization in drive-response systems. The analysis employs inequality techniques on the Mittag–Leffler function and fractional-order Lyapunov theory. Additionally, this paper presents two convex optimization algorithms that aim to minimize the actuator’s costs and expand the admissible initial area (AIA). Finally, this paper employs a three-neuron FONN to demonstrate the efficacy of the proposed methods.

Event-based delayed impulsive control for fractional-order dynamic systems with application to synchronization of fractional-order neural networks

Event-based delayed impulsive control for fractional-order dynamic systems with application to synchronization of fractional-order neural networks

Synchronization Analysis of Fractional-Order Neural Networks With Adaptive Intermittent-Active Control

This paper concentrates on the study of adaptive control for the synchronization of fractional-order neural networks. Instead of classical adaptive control updating method, an intermittent-active updating strategy is proposed to adaptively tune the control gain in a fractional-order fashion. Moreover, quantization is brought into the control design to take into account the restricted bandwidth in signal transmission. Note that the suggested controller is basic yet effective in terms of the fractional-order system. The main theorem is established with the method of reduction to absurdity as well as Lyapunov stability theorem. Finally, simulation calculation is conducted to validate the effectiveness of our proposed method.

Projective Synchronization Analysis of Fractional-Order Neural Networks With Mixed Time Delays.

In this article, we analyze the projective synchronization of fractional-order neural networks with mixed time delays. By introducing an extended Halanay inequality that is applicable for the case of fractional differential equations with arbitrary initial time and multiple types of delays, sufficient criteria are deduced for ensuring the projective synchronization of fractional-order neural networks with both discrete time-varying delays and distributed delays. Furthermore, sufficient criteria are presented for ensuring the projective synchronization in the Mittag-Leffler sense if there is no delay in fractional-order neural networks. The results derived herein include complete synchronization, anti-synchronization, and stabilization of fractional-order neural networks as particular cases. Moreover, the testable criteria in this article are a meaningful extension of projective synchronization of neural networks with mixed time delays from integer-order to fractional-order ones. A numerical simulation with four cases is provided to verify the validity of the obtained results.

Global Mittag-Leffler Synchronization of Fractional-Order Neural Networks With Time-Varying Delay via Hybrid Sliding Mode Control

In this paper, the global Mittag-Leffler synchronization (GMLS) for fractional-order neural networks with time-varying delay (FNNTVD) is studied based on hybrid sliding mode control (HSMC). First, a class of sliding surface is designed to study the dynamic behavior of FNNTVD by using the integer order Lyapunov direct method, which resolves the problem that the activation function of FNNTVD cannot be applied to the construction of Lyapunov function in the previous literature. Then, a new HSMC with the fixed signal transmission time delay is developed to ensure GMLS of FNNTVD. Next, based on Lyapunov direct method and the designed HSMC, some criteria are put forward to achieve GMLS of FNNTVD. Finally, two examples are given to verify the effectiveness of the proposed synchronization criteria for FNNTVD.

Impulsive control strategy for the Mittag-Leffler synchronization of fractional-order neural networks with mixed bounded and unbounded delays

<abstract> <p>In this paper we apply an impulsive control method to keep the Mittag-Leffler stability properties for a class of Caputo fractional-order cellular neural networks with mixed bounded and unbounded delays. The impulsive controls are realized at fixed moments of time. Our results generalize some known criteria to the fractional-order case and provide a design method of impulsive control law for the impulse free fractional-order neural network model. Examples are presented to demonstrate the effectiveness of our results.</p> </abstract>

Asymptotic Stability and Synchronization of Fractional-Order Neural Networks With Unbounded Time-Varying Delays

This article deals with the asymptotic stability and synchronization of fractional-order neural networks (FONNs) with unbounded time-varying delays, in which FONNs can be the general nonlinear system. First, the existence of the equilibrium point of the nonlinear system is obtained, and the μ-type stability of fractional-order nonlinear systems is proved by the analytical method. Second, several sufficient conditions are derived to guarantee the μ-type stability of FONNs by taking easily implemented parameters. Moreover, the μ-type synchronization of drive-response systems is established by designing the linear controller. Especially, μ-type stability is the general stability, including Mittag-Leffler stability and power-stability, which is the extension of the Mittag-Leffler stability of FONNs. Finally, two numerical examples are presented to show the effectiveness of the results.

Hybrid Projective Synchronization of Fractional-order Neural Networks with Different Dimensions

This paper is concerned with the problem of hybrid projective synchronization between two fractional-order neural networks with the order lying in the interval \((1,2)\). The coupled networks have ...

Intermittent control strategy for synchronization of fractional-order neural networks via piecewise Lyapunov function method

In this paper, the synchronization problem of fractional-order neural networks (FNNs) with chaotic dynamics is investigated via the intermittent control strategy. Two types of intermittent control methods, the aperiodic one and the periodic one, are applied to achieve the synchronization of the considered systems. Based on the dynamic characteristics of the intermittent control systems, the piecewise Lyapunov function method is employed to derive the synchronization criteria with less conservatism. The results under the aperiodically intermittent control show more generality than the ones via the periodically intermittent control. For each of the aperiodic and periodic cases, a simple controller design process is presented to show how to design the corresponding intermittent controller. Finally, two numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.

Novel results on projective synchronization of fractional-order neural networks with multiple time delays

This paper investigates a projective synchronization of fractional-order neural networks (FONN) with multiple time delays, and two new synchronization conditions are derived by combining open loop control and linear control. This is achieved by employing stability theorem of linear fractional order systems with multiple delays and comparison principle. Feasibility of the theoretical results is validated through numerical simulations.

Global asymptotic synchronization of nonidentical fractional-order neural networks

Abstract This paper investigates the global asymptotic synchronization problem of nonidentical fractional-order neural networks with Riemann–Liouville derivative. First, by utilizing the properties of fractional calculus and fractional Lyapunov direct method, some novel properties on the fractional calculus and the asymptotic stability theorem of reducing the conservatism for the non-autonomous fractional-order system with Riemann–Liouville derivative are proposed. Then, a new feedback controller is presented to guarantee the global asymptotic synchronization of nonidentical fractional-order neural networks. Via using the proposed the asymptotic stability theorem and matrix inequality techniques, sufficient conditions for global asymptotic synchronization of fractional-order neural networks are presented. Finally, numerical examples are used to demonstrate the effectiveness of the proposed synchronization control scheme for nonidentical fractional-order neural networks.

Synchronization of a class of fractional-order neural networks with multiple time delays by comparison principles

This paper studies the synchronization of fractional-order neural networks with multiple time delays. Based on an inequality of fractional-order and comparison principles of linear fractional equation with multiple time delays, some sufficient conditions for synchronization of master-slave systems are obtained. Example and related simulations are given to demonstrate the feasibility of the theoretical results.

Global Mittag-Leffler projective synchronization for fractional-order neural networks: an LMI-based approach

This paper is concerned with the global projective synchronization issue for fractional neural networks in the Mittag-Leffler stability sense. Firstly, a fractional-order differential inequality in the existing literature for the Caputo fractional derivative, with $0<\alpha< 1$ , is improved, which plays a central role in the synchronization analysis. Secondly, hybrid control strategies are designed via combing open loop control and adaptive control, and unknown control parameters are determined by the adaptive fractional updated laws to achieve global projective synchronization. In addition, applying the fractional Lyapunov approach and Mittag-Leffler function, the projective synchronization conditions are addressed in terms of linear matrix inequalities (LMIs) to ensure the synchronization. Finally, two examples are given to demonstrate the validity of the proposed method.

Global Mittag-Leffler synchronization of fractional-order neural networks with discontinuous activations

This paper is concerned with the global Mittag-Leffler synchronization for a class of fractional-order neural networks with discontinuous activations (FNNDAs). We give the concept of Filippov solution for FNNDAs in the sense of Caputo’s fractional derivation. By using a singular Gronwall inequality and the properties of fractional calculus, the existence of global solution under the framework of Filippov for FNNDAs is proved. Based on the nonsmooth analysis and control theory, some sufficient criteria for the global Mittag-Leffler synchronization of FNNDAs are derived by designing a suitable controller. The proposed results enrich and enhance the previous reports. Finally, one numerical example is given to demonstrate the effectiveness of the theoretical results.

Projective synchronization of fractional-order memristor-based neural networks

This paper investigates the projective synchronization of fractional-order memristor-based neural networks. Sufficient conditions are derived in the sense of Caputo’s fractional derivation and by combining a fractional-order differential inequality. Two numerical examples are given to show the effectiveness of the main results. The results in this paper extend and improve some previous works on the synchronization of fractional-order neural networks.

Projective synchronization for fractional neural networks

In this paper, the global projective synchronization of fractional-order neural networks is investigated. First, a sufficient condition in the sense of Caputo’s fractional derivation to ensure the monotonicity of the continuous and differential functions and a new fractional-order differential inequality are derived, which play central roles in the investigation of the fractional adaptive control. Based on the preparation and some analysis techniques, some novel criteria are obtained to realize projective synchronization of fractional-order neural networks via combining open loop control and adaptive control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the addressed neural networks. Finally, an example with numerical simulations is given to show the effectiveness of the obtained results.