Finite-time Synchronization Research Articles

Finite-time synchronization criteria on delayed FOCVNNs with uncertain parameters and difference operator

This article analyzes the finite-time synchronization (FTS) issues of delayed complex-valued neural networks (CVNNs) with uncertain parameters and fractional difference operator. Firstly, a significant lemma is derived based on discrete fractional calculus. The proposed lemma can help us reach FTS and estimate the setting time. Next, two controllers with delay terms are established, respectively. The designed control strategies can effectively remove delay terms. By utilizing the proposed lemma, control strategies and inequality techniques, the conditions for FTS are derived. The setting time has also been estimated. Finally, we present two examples to demonstrate the theoretical results.

Adaptive finite-time synchronization of quaternion-valued inertial neural networks with mixed delays under quantized event-triggered impulsive strategy

By incorporating inertial terms, quaternions, and time-varying discrete and distributed delays into traditional neural networks (NNs), this paper establishes a category of drive-response quaternion-valued inertial neural networks (QVINNs) with mixed delays. The issue of adaptive finite-time synchronization (FTS) of the QVINNs with mixed delays is explored. To do this, a fresh and low-cost adaptive controller is devised by combining event-triggered impulsive control (ETIC) with quantized control to greatly lower the amount of communication and economic costs. In virtue of the variable substitution, the Lyapunov method, the comparison principle, the inequality technique, and the concept of average impulsive interval (AII), the novel criteria that the QVINNs can accomplish FTS are derived. Meanwhile, it is possible to determine that Zeno-behavior and chattering are absent, and the settling time is predicted. Ultimately, by performing the numerical instance, the efficiency and accuracy of the theoretical results are confirmed.

Finite-Time Synchronization of Neural Networks With Proportional Delays for RGB-D Image Protection.

Since the depth information of images facilitates the analysis of the spatial distance of objects in computer vision applications, it is necessary to protect the image depth information. Thus this article proposes a novel red-green-blue-depth (RGB-D) image protection algorithm, which is implemented with the finite-time synchronization (FTS) of neural networks (NNs) with proportional delays via the quantized intermittent control to derive the system synchronization criterion based on Lyapunov stability theory. The performance of RGB-D image protection depends on the synchronization error of the system by driving the system sequence to encrypt the RGB-D image and responding to the system sequence to decrypt the encrypted image. Subsequently, the validity of the proposed criteria is verified by simulation examples, and the practical application of RGB-D image protection is verified.

Reinforcement learning-based optimized multi-agent finite-time optimal synchronisation control and its application to the harmonic oscillator

Reinforcement learning-based optimized multi-agent finite-time optimal synchronisation control and its application to the harmonic oscillator

Fractional discrete neural networks with variable order: solvability, finite time stability and synchronization

Fractional discrete neural networks with variable order: solvability, finite time stability and synchronization

Finite-time synchronization of fractional order neural networks via sampled data control with time delay

Finite-time synchronization of fractional order neural networks via sampled data control with time delay

Finite-time and fixed-time function projective synchronization of competitive neural networks with noise perturbation

Finite-time and fixed-time function projective synchronization of competitive neural networks with noise perturbation

An Observer-Based Topology Identification and Synchronization in Finite Time for Fractional Singularly Perturbed Complex Networks via Dynamic Event-Triggered Control

This paper investigates the topology identification and synchronization in finite time for fractional singularly perturbed complex networks (FSPCNs). Firstly, a convergence principle is developed for continuously differential functions. Secondly, a dynamic event-triggered mechanism (DETM) is designed to achieve the network synchronization, and a topology observer is developed to identify the network topology. Thirdly, under the designed DETM, by constructing a Lyapunov functional and applying the inequality analysis technique, the topology identification and synchronization condition in finite time is established in the forms of the matrix inequality. In addition, it is proved that the Zeno behavior can be effectively excluded. Finally, the effectiveness of the main results is verified by an application example.

Dynamic event-triggered synchronization for semi-Markovian switching inertial neural networks with generally uncertain transition rates in finite-time interval

This paper investigates the finite-time synchronization for inertial neural networks with stochastic switching parameters based on dynamic event-triggered protocol. Due to the complexity of network environment, semi-Markovian process is introduced into the modeling of inertial neural networks, in which the transition rates vary with the operating time. The dynamic event-triggered protocol is developed to determine whether the signal is transmitted, in which Zeno phenomenon is eliminated under limited bandwidth resources. The objective is to construct an appropriate dynamic event-triggered control law such that the drive-response system maintains finite-time synchronization under generally uncertain transition rates. Based on the Lyapunov functional theory, finite-time synchronization criterion is proposed for the related inertial neural networks. Furthermore, a dynamic event-triggered controller is constructed in a finite-time interval. A numerical example and an image encryption process are given to show the efficiency of the proposed method.

Synchronization of fractional-order quaternion-valued neural networks with image encryption via event-triggered impulsive control

The finite-time synchronization and impulsive synchronization of fractional-order quaternion-valued neural networks (FOQVNNs) with delay are investigated in this research. To begin, instead of employing a decomposition method, a Lyapunov direct approach is proposed to achieve the finite-time synchronization of FOQVNNs using event-triggered control based on state errors. The settling time is then estimated using a unique fractional differential inequality. The event-triggered impulsive controller, which updates only during triggering instants, is proposed to be more inexpensive and efficient. Then, utilizing fractional Lyapunov theory and the comparison principle, several novel quaternion-valued linear matrix inequalities criteria are defined to assure the impulsive synchronization of the delayed FOQVNNs. Furthermore, the positive lower bound of the inter-event time is obtained to exclude the Zeno behavior. As proof of the feasibility and validity of these theoretical findings obtained, numerical examples are provided. At last, the use of the event-triggered control technique for FOQVNNs in image encryption and decryption is demonstrated and validated.

Almost Finite-time Synchronization of Coronary Artery Systems via Adaptive Fractional-powered-integral-type Sliding Mode Control Method

Almost Finite-time Synchronization of Coronary Artery Systems via Adaptive Fractional-powered-integral-type Sliding Mode Control Method

Finite-Time Adaptive Synchronization and Fixed-Time Synchronization of Fractional-Order Memristive Cellular Neural Networks with Time-Varying Delays

Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems.

Finite-time synchronisation for Markovian master-slave neural networks with weighted try-once-discard protocol and static intermittent control

ABSTRACT This paper studies the finite-time synchronisation (FTS) issue for Markovian master-slave neural networks (NNs). A weighted try-once-discard (WTOD) protocol is introduced to overcome communication constraints, and an intermittent control strategy is employed to surmount energy constraints. A WTOD and parameter dependent static feedback controller is designed for the slave neural networks. Then, sufficient conditions are developed to achieve FTS for the considered master-slave NNs, and the controller design method is obtained. Finally, a numerical example is provided to demonstrate and verify the derived results.

Finite-time synchronization of delayed semi-Markov reaction–diffusion systems: An asynchronous boundary control scheme

This paper tries to study the problem of finite-time synchronization for delayed semi-Markov reaction–diffusion systems. Based on the spatial and parametric characteristics of the considered systems, a new asynchronous boundary control scheme is proposed to ensure the finite-time synchronization of the drive and response systems. In the asynchronous boundary control scheme, only an actuator should be placed at the spatial boundary, which is more easier to implement and economical than the other non-boundary control strategies. Besides, the system parameters and controller follow two asynchronous semi-Markov chains for jumping, which is more practical than obeying one semi-Markov chain. Moreover, for the considered systems, we proposes a new lemma of finite-time stability, and by employing the inequality methods and variable substitution, we derive the criterion of finite-time synchronization and a correlative corollary. Finally, a numerical example and an application example on secure communication are carried out to support the developed approach.

Practical finite-time synchronization of delayed fuzzy cellular neural networks with fractional-order

The practical finite-time (PFT) synchronization of fractional-order delayed fuzzy cellular neural networks (FODFCNNs) is presented in this article. Initially, a useful practical finite time (FT) stable lemma is developed, serving as an efficient instrument for the PFT synchronization of fractional-order systems. Subsequently, a new PFT synchronization criterion for FODFCNNs is derived using the designed controller and the aforementioned lemma. Simultaneously, the settling time for PFT synchronization is determined, relying on specific controller parameters and the initial conditions of the considered systems. Ultimately, the accuracy of the derived outcomes is confirmed through a numerical simulation.

Novel Controller Design for Finite-Time Synchronization of Fractional-Order Nonidentical Complex Dynamical Networks under Uncertain Parameters

The synchronization of complex networks, as an important and captivating dynamic phenomenon, has been investigated across diverse domains ranging from social activities to ecosystems and power systems. Furthermore, the synchronization of networks proves instrumental in solving engineering quandaries, such as cryptography and image encryption. And finite-time synchronization (FTS) controls exhibit substantial resistance to interference, accelerating network convergence speed and heightening control efficiency. In this paper, finite-time synchronization (FTS) is investigated for a class of fractional-order nonidentical complex networks under uncertain parameters (FONCNUPs). Firstly, some new FTS criteria for FONCNUPs are proposed based on Lyapunov theory and fractional calculus theory. Then, the new controller is designed based on inequality theory. Compared to the general controller, it controls all nodes and adds additional control to some of them. When compared to other controllers, it has lower control costs and higher efficiency. Finally, a numerical example is presented to validate the effectiveness and rationality of the obtained results.

Finite-Time Synchronization of Fractional-Order Nonlinear Systems with State-Dependent Delayed Impulse Control

This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order systems. Initially, we employ the aforementioned sufficient conditions to derive stability criteria for general FONSs within the SDDIC framework, employing Linear Matrix Inequality (LMI) techniques. Furthermore, we apply these theoretical findings to tackle the challenge of finite-time synchronization in fractional-order chaotic systems using the proposed SDDIC. We substantiate the efficacy of these theoretical advancements through numerical simulations that vividly demonstrate their capability to achieve finite-time synchronization in fractional-order cellular neural networks and fractional-order Chua’s circuits. Moreover, we introduce an innovative chaos-based multi-image encryption algorithm, thereby contributing significantly to the field. To ensure the algorithm’s robustness, we subject it to rigorous statistical tests, which confidently affirm its capacity to provide the requisite level of security.

Stochastic disturbance with finite-time chaos stabilization and synchronization for a fractional-order nonautonomous hybrid nonlinear complex system via a sliding mode control

This paper provides a novel approach to studying the chaos control and synchronization of fractional-order hybrid Darcy–Brinkman systems (FOHDBs). We use the truncated Galerkin method to transform the system of partial differential equations (PDEs) into ordinary differential equations (ODEs) based on Fourier modes in a nonlinear low-dimensional Brinkman model. In the nonlinear complex system, hybrid nanoparticles and fluid flow physical characteristics are considered to be external disturbances. As a result, the implications of model uncertainty and external disruptions are fully absorbed into the problem, further complicating it and resulting in highly complex and unpredictable behaviors. In addition, To assure the occurrence of the sliding motion in a finite amount of time, an appropriate robust fractional sliding mode technique is proposed. Sliding motion is shown to occur in finite time using the fractional Lyapunov stability. Following that, we discussed control techniques for achieving infinitesimally close to an equilibrium of chaotic states and tracking errors. It is important to note that FOHDBs and external stochastic disturbances can be controlled using the proposed fractional nonsingular terminal sliding mode control technique. Finally, the effectiveness and applicability of the suggested finite-time control technique are graphically illustrated by the analytical and numerical simulations.

Fuzzy sliding mode control based-fast finite-time projective synchronization for fractional-order chaotic systems

This study explores the challenge of achieving a fast finite-time projective synchronization (FFTPS) in chaotic systems characterized by incommensurate fractional orders, unknown master-slave models, and uncertain external disturbances. Utilizing the principles of Lyapunov stability theory, two fuzzy sliding mode control (FSMC) schemes are proposed. Accordingly, two novel non-singular finite-time sliding surfaces are constructed. Fuzzy logic systems are utilized to provide an approximation of the continuous uncertain dynamics within the master-slave system. The sufficient conditions for both controllers are derived to ensure this robust FFTPS. Finally, the proposed controllers are validated through numerical simulations on two projective synchronization examples of fractional-order chaotic systems, demonstrating their feasibility.

Finite-time Mittag-Leffler synchronization of delayed fractional-order discrete-time complex-valued genetic regulatory networks: Decomposition and direct approaches

The complex-valued molecular model of mRNA and protein plays a crucial role in the regulatory mechanisms governing gene expression in the genetic regulatory network (GRN). In this study, we introduced a novel GRN utilizing the fractional-order discrete-time complex-valued molecular model of mRNA and protein. Both decomposition and a direct approach are employed to investigate the nonlinear regulatory function within complex-valued molecular models. New conditions are established to ensure the finite-time Mittag-Leffler synchronization (FTMLS) of the error model dynamics. Feedback controllers are applied to derive the FTMLS conditions for delayed fractional-order discrete-time complex-valued genetic regulatory networks (DFDTCVGRNs). By applying the first-order backward difference on the Lyapunov functional under the definition of fractional Caputo difference and fractional calculus theory, sufficient conditions are derived. Finally, two numerical examples are provided to illustrate the FTMLS criteria obtained.