Global Finite-time Synchronization Research Articles

Global finite-time synchronization for fractional complex network via impulsive control based on a new finite-time stability result

This paper focuses on the finite-time stability (FTS) issue for fractional nonlinear impulsive systems (FNISs). By applying Lyapunov functional approach and fractional calculus, a novel result with respect to the FTS is developed, where stabilizing impulse and destabilizing impulse are introduced in systems simultaneously. The settling time (ST), which is related to the impulse numbers, the impulse gain and the order of systems, is calculated accurately. Moreover, the proposed theoretical results are applied to derive the global finite-time synchronization (GFS) conditions for fractional-order complex dynamic network (FCDNs) under hybrid impulse effects. Finally, a simulation example is provided to substantiate the validity of the obtained 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.

A Novel Delay-Dependent Finite-Time Control of Telerobotics System With Asymmetric Time-Varying Delays

Finite-time stability (FTS) is desirable in teleoperation control as it provides fast transient, high-precision, and better disturbance rejection properties. In most cases, a stringent condition on communication time delays or an additional time-delay estimation method is necessary to guarantee finite-time synchronization with the existing finite-time control schemes for the teleoperation system. This article proposes the first result of global finite-time synchronization control algorithm for the teleoperation system without any approximation function. Specifically, a novel proportional plus damping (P + d) like control algorithm is designed by employing a continuous nonsmooth function on the position synchronization errors and the velocity signals, dexterously. Furthermore, global FTS is proved with the Lyapunov stability theory based on linear-matrix-inequality (LMI) and geometric homogeneous techniques. The delay-dependent FTS criteria are also derived, which can be used to compute the allowable maximal transmission delay with the given control parameters. Finally, simulation results demonstrate the effectiveness of the proposed approach, and experiments on a teleoperated pair of three-degree-of-freedom (DOF) PHANToM robots are also presented to show the superior performances of the control strategy.

Global finite-time distributed attitude synchronization and tracking control of multiple rigid bodies without velocity measurements

This paper considers the global finite-time attitude synchronization and coordinated tracking problems of multiple rigid bodies without angular velocity measurements. First, for the attitude synchronization problem, by combining the hybrid technique and homogeneous theory, a new velocity-free attitude synchronization algorithm is constructed to prevent the unwinding problem and achieve finite-time convergence. In the second place, for the leader-following tracking problem, we firstly propose a nonlinear distributed hybrid observer for each follower such that the leader’s information can be estimated accurately. Then, based on the outputs of the distributed observer, we propose a velocity-free distributed attitude tracking algorithm such that the global finite-time attitude tracking objective is achieved. Finally, simulation results are provided to demonstrate the effectiveness of the proposed algorithms.

Synchronization in finite time for variable-order fractional complex dynamic networks with multi-weights and discontinuous nodes based on sliding mode control strategy

This paper is concerned with the global synchronization in finite time for variable-order fractional complex dynamic networks with multi-weights, where the dynamic nodes are modeled to be discontinuous, and subject to the local Hölder nonlinear growth in a neighborhood of continuous points. Firstly, an inequality with respect to variable-order fractional derivative for convex functions is proposed. On the basis of the proposed inequality, a global convergence principle in finite time for absolutely continuous functions is developed. Secondly, based on proposed convergence principle in finite time, a new sliding mode surface is presented, and an appropriate sliding mode control law is designed to drive the trajectory of the error system to the prescribed sliding mode surface in finite time and remain on it forever. In addition, on the basis of differential inclusions theory and Lur’e Postnikov-type convex Lyapunov function approach, the sufficient conditions with respect to the global stability in finite time are established in terms of linear matrix inequalities for the error system on designed sliding mode surface. Moreover, the upper bound of the settling time is explicitly evaluated. Finally, the effectiveness and correction of synchronization strategies are illustrated through two simulation experiments.

The global finite-time synchronization of a class of chaotic systems via the variable-substitution and feedback control

AbstractThis paper deals with the global finite-time synchronization of a class of third-order chaotic systems with some intersecting nonlinearities, which cover many famous chaotic systems. First, a simple, continuous and dimension-reducible control by the name of the variable-substitution and feedback control is designed to construct a master–slave finite-time synchronization scheme. Then, a global finite-time synchronization criterion for the synchronization scheme is proven and the synchronization time is analytically estimated. Subsequently, the criterion and optimization technique are applied to the well-known brushless direct current motor (BLDCM) system and the classic Lorenz system, respectively, further obtaining some new optimized synchronization criteria in the form of algebra. Two numerical examples for the BLDCM system and a numerical example for the Lorenz system are simulated and analyzed to verify the effectiveness of the theoretical results obtained in this paper.

Global Finite-Time and Fixed-Time Synchronization for Discontinuous Complex Dynamical Networks with Semi-Markovian Switching and Mixed Delays

This paper is concerned with the global finite-time and fixed-time synchronization for a class of discontinuous complex dynamical networks with semi-Markovian switching and mixed time-varying delays. The novel state-feedback controllers, which include integral terms and discontinuous facts, are designed to realize the global synchronization between the drive system and response system. By applying the Lyapunov functional method and matrix inequality analysis technique, the global finite-time and fixed-time synchronization conditions are addressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the feasibility of the proposed control scheme and the validity of theoretical results.

Model and criteria on the global finite-time synchronization of the chaotic gyrostat systems

The aim of this paper is to design a simple and continuous controller, named the variable substitution and feedback controller (VSFC), to investigate global finite-time synchronization of the chaotic gyrostat systems. By constructing the finite-time synchronization model for the master–slave gyrostat systems under the new designed VSFC, a finite-time synchronization criterion is presented with theoretically strict proof and the corresponding synchronization time is estimated by an explicit expression. Subsequently, applying the criterion and the optimization technique, some algebraic criteria with respect to various single VSFCs are further proven and optimized. Finally, three examples are presented to support the obtained results by comparing global asymptotic synchronization of the master–slave gyrostat systems under the VSC suggested in our previous work, with global finite-time synchronization of the master–slave gyrostat systems under the VSFC designed in this paper.

Finite-Time Synchronization for a Class of Multiweighted Complex Networks with Markovian Switching and Time-Varying Delay

In this paper, we investigate the finite-time synchronization control for a class of nonlinear coupled multiweighted complex networks (NCMWCNs) with Markovian switching and time-varying delay analytically and quantitatively. The value of this study lies in four aspects: First, it designs the finite-time synchronization controller to make the NCMWCNs with Markovian switching and time-varying delay achieve global synchronization in finite time. Second, it derives two kinds of finite-time estimation approaches by analyzing the impact of the nonlinearity of nonlinear coupled function on synchronization dynamics and synchronization convergence time. Third, it presents the relationship between Markovian switching parameters and synchronization problems of subsystems and the overall system. Fourth, it provides some numerical examples to demonstrate the effectiveness of the theoretical results.

Global dissipativity and finite-time synchronization of mixed time-varying delayed memristor-based neural networks with discontinuous activations

In this paper, the matters of dissipativity and finite time synchronization for memristor-based neural networks (MNNs) with mixed time-varying discontinuities are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. Then, the global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, some novel sufficient conditions are introduced to guarantee the finite-time synchronization of the drive-response MNNs based on a simple Lyapunov function and two different feedback controllers. Finally, several numerical examples are given to verify the validity of the theoretical results.

Global synchronization in finite time for fractional-order coupling complex dynamical networks with discontinuous dynamic nodes

The global Mittag–Leffler synchronization and global synchronization problem in finite time for fractional-order complex networks which with discontinuous nodes is studied in this paper. When the coupling matrix is time-varying and unknown, under the designed adaptive law with respect to the coupling matrix, by utilizing nonsmooth analysis method and Lyapunov functional approach as well as Laplace transform technique, the conditions of global Mittag–Leffler synchronization are achieved in terms of linear matrix inequalities (LMIs). When the coupling matrix is invariable and known, under the designed feedback controller, and by constructing a Lur’e Postnikov-type Lyapunov functional, the conditions of global synchronization in finite time are established, which are in the form of LMIs, and the upper bound of the settling time is explicitly evaluated. Finally, two examples are provided to illustrate the validity of the proposed design method and theoretical results.

Global Synchronization in Finite-time of Fractional-order Complexvalued Delayed Hopfield Neural Networks

This paper deals with the synchronization issue of fractional-order complex-valued Hopfield neural networks with time delay. In this paper, by means of properties of the fractional-order inequality, such as Holder inequality and Gronwall inequality, sufficient conditions are presented to guarantee the finite-time synchronization of the fractional-order complex-valued delayed neural networks when 1/2 ≤ γ < 1 and 0 < γ < 1/2. Finally, two numerical simulations are provided to show the effectiveness of the obtained results.

Global Nonfragile Synchronization in Finite Time for Fractional-Order Discontinuous Neural Networks With Nonlinear Growth Activations.

This paper is concerned with the global nonfragile Mittag-Leffler synchronization and the global synchronization in finite time for fractional-order discontinuous neural networks, where activation functions are discontinuous at 0, or modeled as a local Hölder functions with the nonlinear growth property in a neighborhood of 0. First, two lemmas concerned with the convergence with respect to an absolutely continuous function are developed. Second, a new property, which introduces an inequality of the fractional derivative for the variable upper limit integral with respect to the nonsmooth integrable function, is presented and applied in the synchronization results' analysis. In addition, under the fractional Filippov differential inclusion framework, by utilizing the Lur'e Postnikov-type Lyapunov functional, nonsmooth analysis method, and the convergence properties developed in this paper, the synchronization conditions are derived in the form of linear matrix inequalities. Moreover, the upper bound of the setting time for the global nonfragile synchronization in finite time is calculated accurately. Finally, two illustrations are presented to verify the correctness of the theoretical results.

Global Finite-Time Multi-Switching Synchronization of Externally Perturbed Chaotic Oscillators

Quick recovery of the information signals in secure communications restricts the hacking duration. The short synchronization convergence time is a crucial parameter for faster recovery. This paper develops a novel nonlinear finite-time synchronization control algorithm. This controller accomplishes the global finite-time multi-switching synchronization between two externally perturbed chaotic systems in the drive–response system synchronization scheme. The proposed controller assures the global convergence of the error dynamics in finite-time based on the Lyapunov theory. This implicitly guarantees the global stability of the closed loop. This paper considers Lp(0 < p < 1) norm inequality for the construction of the Lyapunov function. This method provides a means to determine the parameters of the proposed finite-time controller. This paper also studies the significance of structural components of the proposed controller that are responsible for the finite-time synchronization convergence. Computer simulation results of ‘two identical chaotic Lorenz systems’ and ‘chaotic Lorenz and Chen systems’ validate the theoretical findings. The paper discusses the simulation results and compares them with peer works as well.

Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays

This paper is concerned with the global Mittag-Leffler synchronization and the synchronization in finite time for fractional-order neural networks (FNNs) with discontinuous activations and time delays. Firstly, the properties with respect to Mittag-Leffler convergence and convergence in finite time, which play a critical role in the investigation of the global synchronization of FNNs, are developed, respectively. Secondly, the novel state-feedback controller, which includes time delays and discontinuous factors, is designed to realize the synchronization goal. By applying the fractional differential inclusion theory, inequality analysis technique and the proposed convergence properties, the sufficient conditions to achieve the global Mittag-Leffler synchronization and the synchronization in finite time are addressed in terms of linear matrix inequalities (LMIs). In addition, the upper bound of the setting time of the global synchronization in finite time is explicitly evaluated. Finally, two examples are given to demonstrate the validity of the proposed design method and theoretical results.

Global finite-time synchronization of different dimensional chaotic systems

• Global finite-time synchronization of two different dimensional chaotic systems. • Global finite-time synchronization of two different dimensional chaotic systems with unknown parameters. • Global finite-time synchronization of two different dimensional chaotic systems with adaptive updated control law. • Global finite-time synchronization of two networked different dimensional chaotic systems. This paper addresses the problem of global finite-time synchronization of two different dimensional chaotic systems. Firstly, the definition of global finite-time synchronization of different dimensional chaotic systems are introduced. Based on the finite-time stability methods, the controller is designed such that the chaotic systems are globally synchronized in a finite time. Then, some uncertain parameters are adopted in the chaotic systems, new control law and dynamical parameter estimation are proposed to guarantee that the global finite-time synchronization can be obtained. By considering a dynamical parameter designed in the controller, the adaptive updated controller is also designed to achieve the desired results. At last, the results of two different dimensional chaotic systems are also extended to two different dimensional networked chaotic systems. Finally, three numerical examples are given to verify the validity of the proposed methods.

Scale-Limited Lagrange Stability and Finite-Time Synchronization for Memristive Recurrent Neural Networks on Time Scales.

The existed results of Lagrange stability and finite-time synchronization for memristive recurrent neural networks (MRNNs) are scale-free on time evolvement, and some restrictions appear naturally. In this paper, two novel scale-limited comparison principles are established by means of inequality techniques and induction principle on time scales. Then the results concerning Lagrange stability and global finite-time synchronization of MRNNs on time scales are obtained. Scaled-limited Lagrange stability criteria are derived, in detail, via nonsmooth analysis and theory of time scales. Moreover, novel criteria for achieving the global finite-time synchronization are acquired. In addition, the derived method can also be used to study global finite-time stabilization. The proposed results extend or improve the existed ones in the literatures. Two numerical examples are chosen to show the effectiveness of the obtained results.

Finite-time synchronization of cyclic switched complex networks under feedback control

In this paper, the global finite-time synchronization between two cyclic switched complex dynamical networks is investigated via feedback control. Based on the cyclic dwell time approach, finite-time stability theorem and some inequality techniques, several sufficient criteria are proposed to ensure finite-time synchronization for a class of cyclic switched complex networks (CSCNs) with and without coupling delay. The obtained criteria not only provide a feasible approach to design state feedback controllers but also fully reveal the trade-off among the cyclic dwell time, the finite convergence time and the initial state. Finally, numerical simulations are given to illustrate the effectiveness of the proposed results.

Finite-Time Synchronization of Chaotic Systems with Different Dimension and Secure Communication

Finite-time synchronization of chaotic systems with different dimension and secure communication is investigated. It is rigorously proven that global finite-time synchronization can be achieved between three-dimension Lorenz chaotic system and four-dimension Lorenz hyperchaotic system which have certain parameters or uncertain parameters. The electronic circuits of finite-time synchronization using Multisim 12 are designed to verify our conclusion. And the application to the secure communications is also analyzed and discussed.

Finite-time synchronization of delayed neural networks with Cohen–Grossberg type based on delayed feedback control

This paper is concerned with finite-time synchronization for a class of delayed neural networks with Cohen–Grossberg type. Different from the existing related results, the time-delayed feedback strategy is utilized to investigate finite-time synchronization of delayed Cohen–Grossberg neural networks. By constructing Lyapunov functions and using differential inequalities, several new and effective criteria are derived to realize local and global synchronization in finite time of the addressed neural networks based on two different time-delayed feedback controllers. Besides, the upper bounds of the settling time of synchronization are estimated. Furthermore, as corollaries, some sufficient conditions are given to achieve finite-time synchronization of delayed cellular neural networks. Finally, some numerical examples are provided to verify the theoretical results established in this paper.