Finite-time Synchronization Criteria Research Articles

Finite-time passivity of multi-weighted coupled neural networks with directed topologies and time-varying delay

In this paper, the finite-time passivity (FTP) problem for multi-weighted coupled neural networks (MWCNNs) with directed topologies and time-varying delay is discussed. Firstly, by designing a new state feedback controller, several FTP criteria are given for the considered network. Then, some finite-time synchronization (FTS) criteria are established by employing the FTP results. Secondly, a hybrid impulsive and state feedback controller is first designed, under which different FTP and FTS criteria are presented and the synchronization time is successfully shortened compared to the non-hybrid controller without impulses. Finally, numerical simulations are given to show the effectiveness and superiority of the obtained results.

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.

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.

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 Complex Dynamical Networks via a Novel Hybrid Controller.

The issue of finite-time synchronization (FTS) of complex dynamical networks (CDNs) is investigated in this article. A new control strategy coupling weak finite-time control and finite times of impulsive control is proposed to realize the FTS of CDNs, where the impulses are synchronizing and restricted by maximal impulsive interval (MII), differing from the existing results. In this framework, several global and local FTS criteria are established by using the concept of impulsive degree. The times of impulsive control in the controllers and the settling time, which are all dependent on initial values, are derived optimally. A technical lemma is developed, reflecting the core idea of this article. A simulation example is given to demonstrate the main results finally.

Finite-Time Synchronization of Complex Dynamical Networks With Input Saturation.

In the framework of input saturation, this article studies the problem of finite-time synchronization (FTS) of a class of complex dynamical networks. By designing different classes of saturated controllers, two types of FTS criteria, including leader-follower synchronization and leaderless synchronization, are presented, respectively. A potential relationship between the saturation structure, the settling time, and the domain of attraction is established, which is crucial to achieve FTS. It shows that the saturation structure not only affects the estimation of domain of attraction but also possibly changes the settling time for FTS. Two numerical examples are presented to illustrate the effectiveness of the proposed results.

Finite-time synchronization and topology identification of stochastic multi-layer networks with Markovian switching

The finite-time synchronization and topology identification problems of stochastic multi-layer networks with Markovian switching are investigated in this paper. Compared with previous studies, Markovian switching is considered in stochastic multi-layer networks. First, by using Kirchhoff’s matrix tree theorem in graph theory, the Lyapunov function of the coupling system is constructed indirectly from the Lyapunov function of the vertex system. In view of finite-time stability theory and stochastic analysis technique, some finite-time synchronization criteria of stochastic multi-layer networks are proposed. Moreover, the intra-layer and inter-layer topological structures are successfully identified in finite time. Then, using the pinning control technique, the unknown partial topological structures are also identified in finite time. In the end, two examples for whole and partial topology identification of two-layer small-world networks are given.

Finite-time quantized dynamic event-triggered control for cluster synchronization of Markovian jump complex dynamic networks with time-varying delays and actuator faults

In this article, by employing the quantized dynamic event-triggered (ET) and adaptive fault-tolerant control mechanisms, the finite-time cluster synchronization (FTCS) criterion of Markov jump complex dynamic networks (MJCDNs) with actuator faults is established. A kind of novel adaptive controller is designed and appropriate Lyapunov functions are applied to eliminate the effectiveness of actuator faults. Further on historical ET schemes, a more universal dynamic ET control mechanism for MJCDNs is considered in this article, which can reduce the network load of MJCDNs more effectively. Meanwhile, the Zeno behavior is ruled out availably. Finally, the numerical simulation example is presented to verify the validity of the theory.

Finite-time synchronization of complex networks with partial communication channels failure

This paper addresses the finite-time synchronization problem of complex networks under a new communication constraint. The situation that some communication channels used to transmit sub-information between two nodes may fail is considered, which causes the receiving node to be unable to obtain complete state information. Moreover, due to less information transmission between nodes, the analysis of finite-time synchronization problem becomes more difficult. Therefore, several questions naturally arise here: Under this communication restriction, how to remodel the complex network, and can the network achieve finite-time synchronization? To better solve these questions, the complex network model with partial communication channels failure is established first. Then, based on the finite-time stability theory and state layered method, two finite-time synchronization criteria for complex networks are provided. Finally, the effectiveness of obtained results are verified by numerical simulations.

Finite‐time synchronization of network systems with linear and nonlinear couplings via quantized intermittent‐adaptive control

AbstractThis paper investigates the synchronization problem of network systems (NSs) via finite‐time (FIT) control techniques. First, the network systems include two complex networks with linear couplings, nonlinear couplings and different rates of evolution. In order to realize the goal of synchronization, intermittent‐adaptive control schemes with quantizer are designed. Then, several FIT synchronization criteria are established by using the designed controllers whose parameters could be adjusted automatically according to the adaptive laws. At the rest of this article, the numerical simulations are provided to illustrate our results.

Finite-time pinning impulsive synchronization of stochastic complex networks with mixed delays

This paper mainly considers the finite-time synchronization (FTS) of stochastic complex networks with mixed delays via pinning impulsive control. Firstly, a novel pinning impulsive controller is introduced by selecting the nodes of the stochastic complex network with large error norms, which not only saves control resources, but also ensures that stochastic complex network with mixed delays can realize FTS. It is worth noting that the finite-time control strategy constructed is not affected by the sign function. Secondly, a uniform FTS criterion under synchronizing impulses and desynchronizing impulses is derived based on the idea of average impulsive interval. Moreover, the obtained sufficient condition are further extended to general stochastic complex networks and stochastic complex networks with mixed delays under delayed impulses. Finally, the feasibility of the theory results is verified by a numerical example.

Finite-time non-fragile control for synchronization of fractional-order stochastic neural networks

This study concerned with the synchronization problem over a finite-time domain for a class of fractional-order stochastic neural networks via non-fragile controller with discontinuous activation functions. Specifically, the suggested state feedback controller sequentially cope with non-fragile scheme for gain scheduling process. Notably, the main objective of this work is to obtained the finite-time synchronization criterion for the resulting synchronized error system over finite bound with the developed non-fragile controller. For that, some consignment of sufficient conditions is derived systematically by implementing Lyapunov’s indirect method and finite-time stability theory which ensures the finite-time stochastic synchronization of the stipulated neural networks. Later on, the controller gain fluctuations that obeying certain white noise sequels derived from Bernoulli distribution are formulated in terms of linear matrix inequalities. Eventually, the illustrated study are substantiated through two numerical examples and the simulation results manifest the advantage and accuracy of the proposed synchronization criteria.

Delay-dependent finite-time synchronization criterion of fractional-order delayed complex networks

The delay-dependent finite-time synchronization (FTS) is investigated for a class of fractional-order delayed complex networks (FODCNs). First, with the aid of the Young inequality and the rule for fractional derivative of the composition function, a novel delay-dependent fractional-order finite-time convergence principle (FOFTCP) is given. The settling time obtained by this principle is dependent on the time delay, which leads to that obtained FTS criteria by this principle are less conservative than the earlier ones. Second, based on this delay-dependent FOFTCP and the designed feedback controller, a novel FTS criterion of FODCNs is obtained. Finally, two numerical examples are presented to show the effectiveness of the derived results.

Quantized control for finite-time synchronization of delayed fractional-order memristive neural networks: The Gronwall inequality approach

This paper is concerned with the finite-time synchronization (FTS) of delayed fractional-order memristive neural networks (FMNNs) by using quantized control. Firstly, two kinds of quantized controllers are designed to eliminate the residual synchronization errors that appear owing to the characteristics of memristive connection weights. Then, to derive α-dependent FTS criteria for drive–response FMNNs, the Gronwall inequality technique is used by combination with the direct estimation method. Compared with the existing results, the advantages of the derived synchronization criteria are discussed from the aspects of both theory and simulation. In addition, the relationships between the finite-time parameter and the quantization parameters are displayed. It reveals that there is a compromise between the admissible finite-time and the saved network bandwidth. Finally, two examples are given to illustrate the effectiveness of the obtained results.

Finite-time synchronization of T-S fuzzy memristive neural networks with time delay

This paper focuses on the study of synchronization problem for T-S fuzzy memristive neural networks with time delay. First, a delay-independent nonlinear fuzzy control is designed. Second, under the designed fuzzy control, two kinds of finite-time synchronization criteria are obtained by comparison method and Lyapunov function method, respectively. Furthermore, the settling time is estimated. Finally, a numerical simulation example is provided to demonstrate the effectiveness and feasibility of the theoretical results, and an application of the obtained theories is also given in the pseudorandom number generator (PRNG).

A novel intermittent sliding mode control approach to finite-time synchronization of complex-valued neural networks

In this work, the issue of finite-time synchronization is discussed for complex-valued neural networks (CVNNs) by applying aperiodically intermittent sliding mode control and a non-separation approach. Firstly, to simplify the theoretical analysis process, some new differential inequalities are established, and new estimated time rules are given. Secondly, to avoid the traditional approach of separating CVNNs, a novel complex-valued aperiodically intermittent sliding mode control strategy is designed, which has never been applied to achieve CVNNs synchronization. Furthermore, by adopting the newly established lemmas, novel controllers and Lyapunov functional, some novel finite-time synchronization criteria of CVNNs are acquired. At last, the validity of the resulting conclusions is indicated by some numerical examples.

New criteria of finite time synchronization of fractional-order quaternion-valued neural networks with time delay

In this paper, to simulate some situations in the real world, a class issue of finite-time synchronization (FTS) about fractional-order quaternion-valued neural networks (FOQVNNs) with time delay is discussed. Firstly, there is no need to divide the QVNNs into several subsystems, some new lemmas related to the sign function of quaternion-valued are established in the quaternion domain. Secondly, based on the proposed sign function framework, a concise and effective controller is directly designed and FTS criteria are derived by constructing the Lyapunov function. Moreover, two settling times of synchronization are effectively estimated. Finally, some examples are shown to testify the correctness of the presented theoretical results.

Finite-time synchronization of reaction–diffusion memristive neural networks: A gain-scheduled integral sliding mode control scheme

The finite-time synchronization issue of reaction–diffusion memristive neural networks (RDMNNs) is studied in this paper. To better synchronize the parameter-varying drive and response systems, an innovative gain-scheduled integral sliding mode control scheme is proposed, where the 2n controller gains can be scheduled and an integral switching surface function that contains a discontinuous term is involved. Moreover, by constructing a novel Lyapunov–Krasovskii functional and combining reciprocally convex combination (RCC) method, a less conservative finite-time synchronization criterion for RDMNNs is derived in the form of linear matrix inequalities (LMIs). Finally, three numerical simulations are exploited to illustrate the effectiveness, superiority and practicability of this paper.

Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays

In this paper, a new fractional differentiation operator is considered the convolution of a power law with a fractal derivative. The novel operator sought to attract more non-local memory effects and self-similarities in chaotic attractors. This paper addresses the problem of fractal-fractional order quaternion-valued neural networks (FFoQVNNs) with time-varying delays. The sufficient conditions for the existence and uniqueness of an equilibrium point are derived for the proposed model by employing contraction mapping. The Lyapunov direct technique and fractal-fractional differential theory achieve the finite-time synchronization criteria by dividing the FFoQVNNs into four real-valued systems. Furthermore, the settling time is determined, which impact by the fractal dimension β, fractional-order α, and control parameters. Finally, a corresponding numerical simulation is demonstrated to show the accuracy of the theoretical results.

Finite-time synchronization of complex dynamical networks under delayed impulsive effects

This paper mainly studies the finite-time synchronization (FTS) of complex dynamical networks (CDNs) with delayed impulses. By constructing proper Lyapunov function, some sufficient criteria for FTS of CDNs under synchronizing and desynchronizing impulses are established, respectively. Firstly, the existing results of FTS are extended to the case with delayed impulses. Secondly, when the impulses in the CDNs are synchronizing, the existing criterion of local FTS (LFTS) is extended to global FTS (GFTS) and the settling time which depends on the initial values and the impulses is estimated. Furthermore, the bound of settling time is estimated explicitly when the CDNs are subjected to desynchronizing impulses. Finally, three examples are given to illustrate the validity of the obtained results.