Exponential synchronization for coupled complex networks with time-varying delays and stochastic perturbations via impulsive control

This paper is concerned with the problem of exponential synchronization of coupled complex networks with time-varying delays and stochastic perturbations (CCNTDSP). Different from previous works, both the internal time-varying delay and the coupling time-varying delay are taken into account in the network model. Meanwhile, an impulsive controller is designed to realize exponential synchronization in mean square of CCNTDSP. Combining the Lyapunov method with Kirchhoff’s Matrix Tree Theorem, some sufficient criteria are obtained to guarantee exponential synchronization in mean square of CCNTDSP. Furthermore, we apply the theoretical results to study exponential synchronization of stochastic coupled oscillators with the internal time-varying delay and the coupling time-varying delay. And a synchronization criterion is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of our theoretical results and the superiority of impulsive control.     

Finite/fixed-time synchronization control of coupled memristive neural networks

Finite-time and fixed-time synchronization (FAFS) of coupled memristive neural networks (CMNNs) with discontinuous feedback functions are explored in this paper. Firstly, a more comprehensive stability theory is systematically established. Secondly, by designing adaptive feedback controller and discontinuous feedback controller, both finite-time and fixed-time synchronization can be realized through regulating the main control parameter. Thirdly, 1-norm and quadratic-norm Lyapunov functions are considered simultaneously in this article, while in estimating the settling time, the former one is more accurate than the latter one under the same synchronization criteria. Finally, in numerical simulation, the analysis and comparison of the proposed controllers are given to show the effectiveness of the corresponding results.     

Pinning impulsive stabilization for BAM reaction-diffusion neural networks with mixed delays

The exponential stabilization of BAM reaction-diffusion neural networks with mixed delays is discussed in this article. At first, a general pinning impulsive controller is introduced, in which the control functions are nonlinear and the pinning neurons are determined by reordering the state error. Next, based on the designed control protocol and the Lyapunov–Krasovskii functional approach, some novel and useful criteria, which depend on the diffusion coefficients and controlling parameters, are established to guarantee the global exponential stabilization of the considered neural networks. Finally, the effectiveness of the proposed control strategy is shown by two numerical examples.     

Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control

In this paper, we concern the finite-time synchronization problem for delayed dynamical networks via aperiodically intermittent control. Compared with some correspondingly previous results, the intermittent control can be aperiodic which is more general. Moreover, by establishing a new differential inequality and constructing Lyapunov function, several useful criteria are derived analytically to realize finite-time synchronization for delay complex networks. Additionally, as a special case, some sufficient conditions ensuring the finite-time synchronization for a class of coupled neural network are obtained. It is worth noting that the convergence time is carefully discussed and does not depend on control widths or rest widths for the proposed aperiodically intermittent control. Finally, a numerical example is given to demonstrate the validness of the proposed scheme.     

Set stability and synchronization of logical networks with probabilistic time delays

Using the algebraic state space representation (ASSR) method, this paper investigates the set stability and synchronization of Boolean networks with probabilistic time delays (PTDs). Firstly, an equivalent stochastic system is established for the Boolean network with PTDs by using the ASSR method. Secondly, based on the probabilistic state transition matrix of equivalent stochastic system, a necessary and sufficient condition is proposed for the set stability of Boolean networks with PTDs. Thirdly, as an application of set stability, the synchronization of coupled Boolean networks with PTDs is studied, and a necessary and sufficient condition is presented. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained new results.     

Lag synchronization for fractional-order memristive neural networks with time delay via switching jumps mismatch

This paper studies drive-response synchronization in fractional-order memristive neural networks (FMNNs) with switching jumps mismatch. A comparison theorem for fractional-order systems with variable order is provided first. Theories of fractional order Filippov differential inclusions are used to treat FMNNs because the parameters of FMNNs are state dependent and the FMNNs has discontinuous right hand sides. Based on Laplace transform and linear feedback control, some lag quasi-synchronization conditions are obtained with variable order α: 0?<?α?<?1 and 1?<?α?<?2. The error level is estimated and the larger synchronization regain is discussed. Finally, two numerical examples are presented to illustrate the effectiveness of our proposed theorems.     

Finite-time synchronization of delayed complex dynamic networks via aperiodically intermittent control

In this paper, the finite-time synchronization problem of complex dynamic networks with time delay is studied via aperiodically intermittent control. By compared with the existed results concerning aperiodically intermittent control, some new results are obtained to guarantee the synchronization of networks in a finite time. Especially, a new lemma is proposed to reduce the convergence time. In addition, based on aperiodically intermittent control scheme, the essential condition ensuring finite-time synchronization of dynamic networks is also obtained, and the convergence time is closely related to the topological structure of networks and the maximum ratio of the rest width to the aperiodic time span. Finally, a numerical example is provided to verify the validness of the proposed theoretical results.     

Non-fragile exponential synchronization of delayed complex dynamical networks with transmission delay via sampled-data control

This paper is devoted to the non-fragile exponential synchronization problem of complex dynamical networks with time-varying coupling delays via sampled-data static output-feedback controller involving a constant signal transmission delay. The dynamics of the nodes contain s quadratically restricted nonlinearities, and the feedback gain is allowed to have norm-bounded time-varying uncertainty. The control design is based on a Lyapunov–Krasovskii functional, which consists of the sum of terms assigned to the individual nodes, i.e., it is constructed without merging the complex dynamical network’s nodes into a single large-scale system. In this way, the proposed design method has substantially reduced computational complexity and improved conservativeness, and guaranties non-fragile exponential stability of the error system. The sufficient stability condition is expressed in terms of linear matrix inequalities that are solvable by standard tools. The efficiency of the proposed method is illustrated by numerical examples.     

Exponential synchronization of stochastic complex networks with multi-weights: A graph-theoretic approach

This paper concerns the exponential synchronization problem of stochastic complex networks with multiple weights (SCNMW). By the method of network split, SCNMW can be modelled as stochastic coupled systems driven by Brownian motion. By combining graph theory, Lyapunov stability theory and state feedback control technique, drive-response synchronization criteria of SCNMW have been obtained. Two kinds of exponential synchronization criteria are obtained, one is given with Lyapunov functions of vertex systems, and the other is shown with the coefficients of SCNMW. The obtained synchronization principles are closely related to the coupling strength of multiple sub-networks and the intensity of noise perturbation. Finally, a numerical example with some simulations is presented to illustrate the theoretical results.     

Discrete-time stochastic impulsive BAM neural networks with leakage and mixed time delays: An exponential stability problem

In this paper, the stability analysis of impulsive discrete-time stochastic BAM neural networks with leakage and mixed time delays is investigated via some novel Lyapunov–Krasoviskii functional terms and effective techniques. For the target model, stochastic disturbances are described by Brownian motion. Then the result is further extended to address the problem of robust stability of uncertain discrete-time BAM neural networks. The conditions obtained here are expressed in terms of Linear Matrix Inequalities (LMIs), which can be easily checked by MATLAB LMI control toolbox. Finally, few numerical examples are presented to substantiate the effectiveness of the derived LMI-based stability conditions.     

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.     

Novel discontinuous control for exponential synchronization of memristive recurrent neural networks with heterogeneous time-varying delays

This paper investigates the exponential synchronization problem of memristive recurrent neural networks (MRNNs) with heterogeneous time-varying delays (HTVDs). First, a novel discontinuous feedback control is designed, in which a tunable scalar is introduced. The tunable scalar makes the controller more flexible in reducing the upper bound of the control gain. Based on this control scheme, the double integral term can be successfully used to construct the LKF. Second, New method for tackling memristive synaptic weights and new estimation technique are presented. Third, based on the LKF and estimation technique, synchronization criterion is derived. In comparison with existing results, the established criterion is less conservatism thanks to the double integral term of the LKF. Finally, numerical simulations are presented to validate the effectiveness and advantages of the proposed results.     

Exponential synchronization of the switched uncertain neural networks with mixed delays based on sampled-data control

The synchronization for a class of switched uncertain neural networks (NNs) with mixed delays and sampled-data control is researched in this paper. When a switching signal occurs in a sampling interval, the controller cannot switch until the next sampling instant. There is a mismatch between the system and the controller. Thus, we devise the control strategy to guarantee that the switched NNs can be synchronized. The proposed Lyapunov-Krasovskii functional (LKF) can make full use of system information. By use of an improved integral inequality, some sufficient stability conditions formed by linear matrix inequalities (LMIs) are derived for the synchronization of switched NNs. Average dwell time (ADT) is obtained as a form of inequality that includes the sampling interval. At last, the feasibility of the proposed method is proved by some numerical examples.     

Distributed cooperative learning for a group of uncertain systems via output feedback and neural networks

This paper studies the problem of adaptive neural network (NN) output-feedback control for a group of uncertain nonlinear multi-agent systems (MASs) from the viewpoint of cooperative learning. It is assumed that all MASs have identical unknown nonlinear dynamic models but carry out different periodic control tasks, i.e., each agent system has its own periodic reference trajectory. By establishing a network topology among systems, we propose a new consensus-based distributed cooperative learning (DCL) law for the unknown weights of radial basis function (RBF) neural networks appearing in output-feedback control laws. The main advantage of such a learning scheme is that all estimated weights converge to a small neighborhood of the optimal value over the union of all system estimated state orbits. Thus, the learned NN weights have better generalization ability than those obtained by traditional NN learning laws. Our control approach also guarantees the convergence of tracking errors and the stability of closed-loop system. Under the assumption that the network topology is undirected and connected, we give a strict proof by verifying the cooperative persisting excitation condition of RBF regression vectors. This condition is defined in our recent work and plays a key role in analyzing the convergence of adaptive parameters. Finally, two simulation examples are provided to verify the effectiveness and advantages of the control scheme proposed in this paper.     

Event-triggered synchronization of delayed neural networks with actuator saturation using quantized measurements

This paper studies event-triggered synchronization control problem for delayed neural networks with quantization and actuator saturation. Firstly, in order to reduce the load of network meanwhile retain required performance of system, the event-triggered scheme is adopted to determine if the sampled signal will be transmitted to the quantizer. Secondly, a synchronization error model is constructed to describe the master-slave synchronization system with event-triggered scheme, quantization and input saturation in a unified framework. Thirdly, on the basis of Lyapunov–Krasovskii functional, sufficient conditions for stabilization are derived which can ensure synchronization of the master system and slave system; particularly, a co-designed parameters of controller and the corresponding event-triggered parameters are obtained under the above stability condition. Lastly, two numerical examples are employed to illustrate the effectiveness of the proposed approach.     

Stability of memristor neural networks with delays operating in the flux-charge domain

The paper considers a class of neural networks where flux-controlled dynamic memristors are used in the neurons and finite concentrated delays are accounted for in the interconnections. Goal of the paper is to thoroughly analyze the nonlinear dynamics both in the flux-charge domain and in the current-voltage domain. In particular, a condition that is expressed in the form of a linear matrix inequality, and involves the interconnection matrix, the delayed interconnection matrix, and the memristor nonlinearity, is given ensuring that in the flux-charge domain the networks possess a unique globally exponentially stable equilibrium point. The same condition is shown to ensure exponential convergence of each trajectory toward an equilibrium point in the voltage-current domain. Moreover, when a steady state is reached, all voltages, currents and power in the networks vanish, while the memristors act as nonvolatile memories keeping the result of computation, i.e., the asymptotic values of fluxes. Differences with existing results on stability of other classes of delayed memristor neural networks, and potential advantages over traditional neural networks operating in the typical voltage-current domain, are discussed.     

Leader-following fixed-time quantized consensus of multi-agent systems via impulsive control

In this paper, we mainly tend to consider distributed leader-following fixed-time quantized consensus problem of nonlinear multi-agent systems via impulsive control. An appropriate quantized criterion and some novel control protocols are proposed in order to solve the problem. The protocols proposed integrates the two control strategies from the point of view of reducing communication costs and constraints, which are quantized control and impulsive control. The fixed-time quantized consensus of multi-agent is analyzed in terms of algebraic graph theory, Lyapunov theory and comparison system theory, average impulsive interval. The results show that if some sufficient conditions are met, the fixed-time consensus of multi-agent systems can be guaranteed under impulsive control with quantized relative state measurements. In addition, compared with finite-time consensus, the settling-time of fixed-time quantized consensus does not depend on the initial conditions of each agent but on the parameters of the protocol. Finally, numerical simulations are exploited to illustrate the effectiveness and performance to support our theoretical analysis.     

Projective synchronization in fixed time for complex dynamical networks with nonidentical nodes via second-order sliding mode control strategy

This paper is concerned with the global projective synchronization in fixed time for complex dynamical networks (CDNs) with nonidentical nodes in the presence of disturbances. Firstly, in order to realize the fixed-time projective synchronization of CDNs with matched disturbances, the second-order sliding mode is established, and the global fixed-time reachability of sliding manifolds is analyzed. The fixed-time stability of the sliding mode dynamics is also proved analytically based on Lyapunov stability theory. Moreover, the fixed convergence time of both reaching and sliding mode phases can be adjusted to any desired values in advance by the choice of the designable parameters. Secondly, in order to realize the fixed-time projective synchronization of CDNs with mismatched disturbances, a super-twisting-like (STL) controller, which does not require the information of the derivative of the sliding variable, is designed, and the synchronization condition is addressed in terms of linear matrix inequalities (LMIs). By the proposed controllers, continuous control signals can be provided to reduce the chattering effect and improve the control accuracy. Finally, two numerical examples are given to demonstrate the validity of the theoretical results and the the feasibility of the proposed approaches.     

A new approach based on discrete-time high-order neural networks with delays and impulses

This paper is concerned with the stability of discrete-time high-order neural networks (HONNs) with delays and impulses. Without applying the Lyapunov function, some sufficient conditions, which ensure the exponential stability and asymptotic stability of considered networks involving delays and impulses, are derived based on the fixed point theory. Finally, several numerical examples are given to demonstrate the effectiveness of the obtained results.