Fixed-time Synchronization Criteria Research Articles

New fixed-time synchronization results for discontinuous dynamic networks: A novel two-stage analysis approach

This paper concerns the issue of fixed-time synchronization (FXTS) for complex networks composed of dynamical nodes with discontinuous dynamics, abbreviated as discontinuous dynamic networks, under the concept of Filippov solution. In terms of [Formula: see text]-norm and [Formula: see text]-norm, two types of simple control schemes without the linear feedback part are, respectively, designed to compel the considered discontinuous dynamic network to fixed-timely synchronize with a desired trajectory. By utilizing a novel two-stage analysis approach, some new FXTS criteria are derived. Compared with the existing research works, the established theoretical results not only are more relaxed, but also improve the estimation accuracy of synchronous settling time. Finally, the validity of the analytical results is verified via numerical simulations.

Fault-tolerant fixed/preassigned-time synchronization control of uncertain singularly perturbed complex networks with time-varying delay and stochastic disturbances

This paper focuses on the fixed-time (FXT) and preassigned-time (PAT) synchronization of uncertain singularly perturbed complex networks (SPCNs) with time-varying delay and stochastic disturbances. Firstly, the fault-tolerant quantized state feedback control strategy for the SPCNs systems to reach PAT and FXT synchronization is considered for the first time. Besides, by adopting suitable Lyapunov functional with parameter ɛ, with an approach of comparison system and mathematical techniques, the FXT synchronization criteria can be obtained. Next, the PAT synchronization can also be derived, which the synchronization time will be pre-designed based on the actual case. Finally, two simulation examples are presented to verify the effectiveness of the obtained results.

Fixed-Time Synchronization of Coupled Oscillator Networks with a Pacemaker

This paper investigates the fixed-time synchronization problem of a Kuramoto-oscillator network in the presence of a pacemaker. Based on the framework of the cyber-physical system (CPS), fixed-time synchronization criteria of such network are presented respectively for identical and non-identical oscillators. In virtue of Lyapunov stability analyses, sufficient conditions are deduced for achieving phase agreement and frequency synchronization for arbitrary initial phases and/or frequencies under distributed control strategies. Theoretical analysis shows that synchronization can be achieved in a fixed time, which is unrelated to initial phases/frequencies. Furthermore, the upper bounds of synchronization time are also obtained. Finally, the numerical simulations also verify the effectiveness of the derived results.

Fixed/preassigned-time synchronization for impulsive complex networks with mismatched parameters

This paper is concerned with the issue of fixed-time (FT) and preassigned-time (PT) synchronization of impulsive complex networks (ICNs) with mismatched parameters. Firstly, several more succinct conditions are established to achieve FT stability of impulsive systems and an improved estimation for the stable time is given. Subsequently, based on the improved FT stability results, the FT synchronization criteria for ICNs with mismatched parameters are proposed by designing fixed-time controllers without the linear part. Correspondingly, the PT synchronization problem is also considered by developing several innovative control protocols, where the synchronized time can be arbitrary predefined according to task demands and the control gains are bounded. Ultimately, the presented synchronization criteria are verified by numerical simulation.

Fixed-time synchronization criteria of fuzzy inertial neural networks via Lyapunov functions with indefinite derivatives and its application to image encryption

In this paper, we investigate the fixed-time synchronization for fuzzy inertial neural networks with time-varying coefficients and time delays. The fuzzy inertial neural networks are transformed into two forms of first-order differential systems, and then two kinds of different controllers of time-variable are designed. In these schemes, a series of novel criteria are proposed to ensure the fixed-time synchronization for the drive-response fuzzy inertial neural networks via state feedback control methods. Sufficient conditions of delay-dependent and delay-independent are obtained in terms of algebraic inequalities, not the matrix inequalities. Moreover, these new criteria allow the derivative of the Lyapunov function can be positive, but not negative definite as the earlier work. And the algebraic conditions become easy to be tested under the new criteria. Finally, two examples are added to illustrate effectiveness of the results we obtained. Meanwhile, a new image encryption algorithm is proposed based on the synchronization of drive-response networks, and the effectiveness of this algorithm is also demonstrated.

Fixed-Time Synchronization Control of Delayed Dynamical Complex Networks.

Fixed-time synchronization problem for delayed dynamical complex networks is explored in this paper. Compared with some correspondingly existed results, a few new results are obtained to guarantee fixed-time synchronization of delayed dynamical networks model. Moreover, by designing adaptive controller and discontinuous feedback controller, fixed-time synchronization can be realized through regulating the main control parameter. Additionally, a new theorem for fixed-time synchronization is used to reduce the conservatism of the existing work in terms of conditions and the estimate of synchronization time. In particular, we obtain some fixed-time synchronization criteria for a type of coupled delayed neural networks. Finally, the analysis and comparison of the proposed controllers are given to demonstrate the validness of the derived results from one numerical example.

Finite-/fixed-time synchronization of delayed Clifford-valued recurrent neural networks

This paper investigates the problem of finite-/fixed-time synchronization for Clifford-valued recurrent neural networks with time-varying delays. The considered Clifford-valued drive and response system models are firstly decomposed into real-valued drive and response system models in order to overcome the difficulty of the noncommutativity of the multiplication of Clifford numbers. Then, suitable time-delayed feedback controllers are devised to investigate the synchronization problem in finite-/fixed-time of error system. On the basis of new Lyapunov–Krasovskii functional and new computational techniques, finite-/fixed-time synchronization criteria are formulated for the corresponding real-valued drive and response system models. Two numerical examples demonstrate the effectiveness of the theoretical results.

Fixed-time control of competitive complex networks

This paper aims to establish several synchronization criteria of competitive complex networks (CCNs) by using fixed-time (FDT) control. In CCNs, the variations of different nodes are diverse if they are influenced by external environment. Here, we design two types of controller to deal with the different variations of nodes. Meanwhile, these designed controllers guarantee the synchronization of the CCNs in a given time. The estimated settling time improves corresponding results in the literature. Furthermore, based on rigorous mathematical proof and the structured comparison system, several FDT synchronization criteria are obtained. Some comparisons are presented to show the advantages of these new theoretical results. The validity of our theoretical results is illustrated by numerical simulations.

Finite/fixed-time synchronization for Markovian complex-valued memristive neural networks with reaction–diffusion terms and its application

This paper pays attention to the synchronization issue of complex-valued memristive neural networks (CVMNNs) that contain reaction–diffusion terms and Markovian jump parameters. To better meet the needs of some practical projects, the problem of synchronization investigated in this paper is defined in finite time and fixed time; namely, by designing a suitable controller, the synchronization error system can converge to zero in a finite/fixed time. Additionally, by combining Lyapunov–Krasovskii functional theory and algebraic inequality methods, a novel criterion of finite/fixed-time synchronization for proposed drive and response systems is derived. Note that the finite-time and fixed-time synchronization criteria are integrated into a unified theorem. Finally, two examples are provided, one is a simple numerical example to account for the feasibility of main results, the other realizes the application of this paper in establishing a spatiotemporal chaotic cryptosystem for image encryption, and the proposed cryptosystem has been illustrated that it has obvious advantages of large key space and high security by simulation results.

Finite-time and fixed-time synchronization control of discontinuous fuzzy Cohen-Grossberg neural networks with uncertain external perturbations and mixed time delays

This paper aims to investigate the synchronization control of a class of discontinuous fuzzy Cohen-Grossberg neural networks (DFCGNNs) with uncertain external perturbations and mixed time delays (discrete and distributed time-delays). By using functional differential inclusions theory, inequality technique and the non-smooth analysis of Lyapunov-Krasovskii functional, a simple switching adaptive control is designed and some new criteria are obtained to achieve the finite-time synchronization of the proposed drive-response systems. Besides, the upper bound of the settling time is estimated. Based on the finite-time synchronization, we further present a novel discontinuous state-feedback controller to the response neural system in order to derive the fixed-time synchronization criteria and estimate the settling time. Compared with the previous results which can only fixed-timely synchronize or finite-timely synchronize some simple delayed fuzzy neural network systems with continuous activation functions and without uncertain external perturbations, the DFCGNNs with uncertain external perturbations and mixed time delays addressed and the theoretical results of this paper are more generalized and inclusive. Finally, several simulation examples and remarks are provided to verify the correctness and advantages of the main results.

Cluster stochastic synchronization of complex dynamical networks via fixed-time control scheme

By means of fixed-time (FDT) control technique, cluster stochastic synchronization of complex networks (CNs) is investigated. Quantized controller is designed to realize the synchronization of CNs within a settling time. FDT synchronization criteria are established with the help of Lyapunov functional and comparison system methods. It should be noted that the convergence of synchronization is further improved by comparing with existing FDT synchronization results. Numerical simulations are given to illustrate our results.

Fixed-Time Synchronization of Fuzzy Cellular Neural Networks With Time-Varying Delays and Discontinuous Activations

The present paper investigates the fixed-time synchronization for fuzzy cellular neural networks with time-varying delays and discontinuous activations. In the framework of differential inclusions, new and useful fixed-time synchronization criteria for the networks considered are established by utilizing the discontinuous state feedback control and constructing Lyapunov functionals, which significantly generalize and improve recent works in the literature. Numerical simulations are given to show the effectiveness of the fixed-time synchronization schemes.

Fixed-time outer synchronization of hybrid-coupled delayed complex networks via periodically semi-intermittent control

In this paper, the fixed-time synchronization between two delayed complex networks with hybrid couplings is investigated. The internal delay, transmission coupling delay and self-feedback coupling delay are all included in the network model. By introducing and proving a new and important differential equality, and utilizing periodically semi-intermittent control, some fixed-time synchronization criteria are derived in which the settling time function is bounded for any initial values. It is shown that the control rate, network size and node dimension heavily influence the estimating for the upper bound of the convergence time of synchronization state. Finally, numerical simulations are performed to show the feasibility and effectiveness of the control methodology by comparing with the corresponding finite-time synchronization problem.

Fixed-time synchronization criteria for complex networks via quantized pinning control

In this paper, fixed-time (FDT) synchronization of complex networks (CNs) is considered via quantized pinning controllers (QPCs). New control schemes with logarithmic quantization are designed, which not only can reduce control cost but also can save channel resources. The QPC with sign function can be used more generally than the QPC without sign function, but the QPC without sign function can be utilized to overcome the chattering phenomenon in some existing results. Based on designed Lyapunov function and different control schemes, several FDT synchronization criteria expressed by linear matrix inequalities (LMIs) are presented. Moreover, a numerical example is presented to illustrate the theoretical results.

Finite-Time and Fixed-Time Synchronization Criteria for Discontinuous Fuzzy Neural Networks of Neutral-Type in Hale’s Form

Finite-Time and Fixed-Time Synchronization Criteria for Discontinuous Fuzzy Neural Networks of Neutral-Type in Hale’s Form

Fixed-time synchronization of inertial memristor-based neural networks with discrete delay

This paper is concerned with the fixed-time synchronization control of inertial memristor-based neural networks with discrete delay. We design four different kinds of feedback controllers, under which the considered inertial memristor-based neural networks can realize fixed-time synchronization perfectly. Moreover, the obtained fixed-time synchronization criteria can be verified by algebraic operations. For any initial synchronization error, the settling time of fixed-time synchronization is bounded by a fixed constant, which can be calculated beforehand based on system parameters and controller parameters. Numerical simulations are given to illustrate the effectiveness of our theoretical results.

Fixed-time synchronization of memristor-based fuzzy cellular neural network with time-varying delay

This paper mainly investigates the fixed-time synchronization of memristor-based fuzzy cellular neural network (MFCNN) with time-varying delay. By utilizing differential inclusion, set-valued map theory, the definitions of finite-time and fixed-time stability, we convert the fixed-time synchronization control of the drive-response MFCNN into the equivalent fixed-time stability problem of the error system between the drive-response systems. Some novel sufficient conditions are derived to guarantee the fixed-time synchronization of the drive-response MFCNN based on a simple Lyapunov function and a nonlinear feedback controller. Meanwhile, the settling time can be estimated by simple calculations. Furthermore, these fixed-time synchronization criteria here are easy to validate and extend to the MFCNN without time-varying delay and general memristor-based neural networks. Finally, three numerical examples are given to illustrate the correctness of the main results.

Fixed-Time Stochastic Synchronization of Complex Networks via Continuous Control.

This paper investigates the fixed-time synchronization (FDTS) of complex networks with stochastic perturbations. A new control scheme is designed to realize the synchronization goal. Moreover, the designed controller without sign function is continuous, which means the chattering phenomenon in some previous results can be avoided. By constructing Lyapunov functionals, using the properties of the Weiner process as well as applying a designed comparison system, several FDTS criteria are obtained. Synchronization criteria of this paper are very general and can be utilized in directed and undirected weighted networks. Numerical simulations are given to illustrate the theoretical results.