Fast fixed-time synchronization control analysis for a class of coupled delayed Cohen-Grossberg neural networks

In a fixed-time control system, the convergence rate and the fixed settling time are two important performance indexes. In this paper, a novel fixed-time control law is proposed and designed to control a class of coupled delayed Cohen-Grossberg neural networks to achieve synchronization with fast convergence rate within a fixed settling time. It should be emphasized that the derived settling time approach can provide a tighter settling time to more effectively reflect the performance for fast convergence rate of the considered controlled system. Moreover, to show the advantages of the proposed fixed-time control law and the derived fixed settling time approach, the existing related control laws and fixed settling time approaches are further discussed. In addition, the obtained fixed-time synchronization control theory is applied to a secure communication scenario, which further shows the feasibility and innovation of the addressed theoretical results.     

Adaptive synchronization for delayed neural networks with stochastic perturbation

In this paper, an adaptive feedback controller is designed to achieve complete synchronization of unidirectionally coupled delayed neural networks with stochastic perturbation. LaSalle-type invariance principle for stochastic differential delay equations is employed to investigate the globally almost surely asymptotical stability of the error dynamical system. An example and numerical simulation are given to demonstrate the effectiveness of the theory results.     

Pinning exponential synchronization for inertial coupled neural networks via adaptive aperiodically intermittent control under directed topology

This article is mainly focused on investigating pinning exponential synchronization of inertial coupled neural networks (ICNNs) under different directed topologies. The traditional method of variable substitution is removed and replaced by non-reduced order method to investigate the dynamical behavior of second-order coupled system. Additionally, by constructing Lyapunov-Krasovskii functional and utilizing matrix decomposition theory as well as M-matrix theory, an adaptive aperiodically intermittent controller is introduced to derive several improved sufficient criteria based on linear matrix inequalities (LMIs). Finally, some examples with numerical simulation are exhibited to confirm the availability of the theoretical results.     

Centralized security-guaranteed filtering in multirate-sensor fusion under deception attacks

In this paper, the centralized security-guaranteed filtering problem is studied for linear time-invariant stochastic systems with multirate-sensor fusion under deception attacks. The underlying system includes a number of sensor nodes with a centralized filter, where each sensor is allowed to be sampled at different rate. A new measurement output model is proposed to characterize both the multiple rates and the deception attacks. By exploiting the lifting technique, the multi-rate sensor system is cast into a single-rate discrete-time system. With a new concept of security level, the aim of this paper is to design a filter such that the filtering error dynamics achieves the prescribed level of the security under deception attacks. By using the stochastic analysis techniques, sufficient conditions are first derived such that the filtering error system is guaranteed to have the desired security level, and then the filter gain is parameterized by using the semi-definite programme method with certain nonlinear constraints. Finally, a numerical simulation example is provided to demonstrate the feasibility of the proposed filtering scheme.     

Impulsive control for passivity and exponential synchronization of coupled neural networks with multiple weights

This paper investigates the passivity and synchronization problems for two classes of multiple weighted coupled neural networks (MWCNNs) with or without time delays. Firstly, by utilizing an impulsive control strategy and some inequality techniques, several passivity criteria for MWCNNs with diverse dimensions of output and input are established. Then, based on the Lyapunov functional, some sufficient conditions to ensure the synchronization of MWCNNs via impulsive control are derived. In addition, combined with the comparison principle and the impulsive delay differential inequality, the global exponential synchronization of MWCNNs with time-varying delays is considered under impulsive control. Finally, two numerical examples illustrate the effectiveness of the obtained results.     

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.     

Fixed-time synchronization of multiplex networks by sliding mode control

Multiplex networks involve different types of synchronization due to their complex spatial structure. How to control multiplex networks to achieve different types of synchronization is an interesting topic. This paper considers the fixed-time synchronization of multiplex networks under sliding mode control (SMC). Firstly, for realizing three types of synchronization of multiplex networks in a fixed time, a unified sliding mode surface (SMS) is established. After that, based on the theory of SMC, a sliding mode controller (SMCr) which is more intelligent and has a simpler form than those in the existing literature is put forward for multiplex networks. It can not only guarantee the emergence of sliding mode motion, but also can realize three different kinds of synchronization by adjusting some parameters or even one parameter of the controller. Based on some theories of fixed-time stability, this paper deduces several sufficient conditions for the trajectories of the system to reach the preset SMS in a fixed time, and derives some sufficient conditions for multiplex networks to realize three different types of fixed-time synchronization. At the same time, the settling time which can reveal what factors determine the fixed-time synchronization in multiplex networks is obtained. Finally, in numerical simulations, different chaotic systems are set for each layer of multiplex networks to represent the nodes of different layers, which can prove that the theoretical results are practical and effective.     

Adaptive fixed-time synchronization of stochastic memristor-based neural networks with discontinuous activations and mixed delays

In this paper, adaptive fixed-time synchronization(FTS) of stochastic memristor-based neural networks(MNNs) with discontinuous activations and mixed delays is investigated. Both continuous and discontinuous activation functions are discussed for stochastic MNNs. Meanwhile, a feedback control strategy and a new adaptive control strategy are proposed to ensure FTS of stochastic MNNs. Since the MNNs are right-hand discontinuous systems, the set-valued mapping and differential inclusion theory are used to deal with its discontinuity. Synchronization criteria and the settling time (ST) are obtained with the aid of some lemmas and mathematical inequalities under corresponding control schemes. It’s worth noting that the ST can be adjusted to desired value by controller parameters regardless of the initial values. Finally, the feasibility of theoretical results are proved via simulation results.     

Global exponential robust stability of Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms

In this paper, the global exponential robust stability is investigated for Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms, this neural network contains time-invariant uncertain parameters whose values are unknown but bounded in given compact sets. Neither the boundedness and differentiability on the activation functions nor the differentiability on the time-varying delays are assumed. By using general Halanay inequality and M-matrix theory, several new sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential robust stability of equilibrium point for Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms. Several previous results are improved and generalized, and three examples are given to show the effectiveness of the obtained results.     

Event-triggered gain-scheduling dissipative synchronization control for switched neural networks under state-dependent switching

The dissipative synchronization problem of delayed Markov jump switched neural networks (MJSNNs) under state-dependent switching by the event-triggered gain-scheduling control scheme is studied in this paper. By the introduction of a Markov jump model, which is used to depict the random variation wherein the connection of MJSNNs, the issues we study can take more generality. Via constructing suitable Lyapunov–Krasovskii functionals (LKFs) and applying some matrix inequality scaling methods, sufficient conditions for dissipative synchronization of delayed MJSNN are established. According to such criteria, the event-triggered gain-scheduling control scheme is adopted to design a controller with less terminal communication costs. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.     

Mean square exponential synchronization in Lagrange sense for uncertain complex dynamical networks

In this paper, the problem of the mean square exponential synchronization in Lagrange sense for the uncertain complex network is investigated. A complex network usually appears some uncertain phenomena, which includes varying topology structure, destroyed nodes, and the noise disturbance from circumstance. Based on the Lyapunov stability theory and the Kronecker product analysis technique, some conditions to guarantee the complex network mean square exponential synchronization in Lagrange sense are provided. Finally, two numerical examples are provided to illustrate the effectiveness of the method proposed.     

Quasi-projective synchronization of discrete-time fractional-order quaternion-valued neural networks

In this article, without decomposing the quaternion-valued neural networks (QVNNs) into two complex-valued subsystems or four real-valued subsystems, quasi-projective synchronization of discrete-time fractional-order QVNNs is investigated. To this end, the sign function for quaternion number is introduced and some related properties are given. Then, two inequalities are built according to the nabla fractional difference and quaternion theory. Subsequently, a simple linear quaternion-valued controller is designed, and some synchronization conditions are given by means of our created inequalities. Finally, numerical simulations are given to prove the feasibility and correctness of the theoretical results.     

Improved exponential stability analysis for delayed recurrent neural networks

In this paper, we investigate the problem of global exponential stability analysis for a class of delayed recurrent neural networks. This class includes Hopfield neural networks and cellular neural networks with interval time-delays. Improved exponential stability condition is derived by employing new Lyapunov-Krasovskii functional and the integral inequality. The developed stability criteria are delay dependent and characterized by linear matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples.     

Probabilistic-constrained tracking control for stochastic time-varying systems under deception attacks: A Round-Robin protocol

The probabilistic-constrained tracking control issue is investigated for a class of time-varying nonlinear stochastic systems with sensor saturation, deception attacks and limited bandwidth in an unified framework. The saturation of sensors is quantified by a sector-bound-based function satisfying certain conditions, and the random deception attacks are considered and modeled by a random indicator variable. To gain more efficient utilization of communication channels, a Round-Robin (RR) protocol is utilized to orchestrate the transmission order of measurements. The main purposes of this study aim to plan an observer-based tracking controller to achieve the following goals: (1) the related performance indicators of the estimation error is less than given bound at each time step; and (2) the violation probability of the tracking error confined in a predefined scope is supposed to be higher than a prescribed scalar and the area is minimized at each instant. In order to reach these requirements, a group of recursive linear matrix inequalities (RLMIs) are developed to estimate the state and design the tracking controller at the same time. Finally, two simulation examples are exploited to illustrate the availability and flexibility of the proposed scheme.     

Aperiodically intermittent control for synchronization of discrete-time delayed neural networks

This paper is concerned with the aperiodically intermittent control (AIC) for the synchronization of discrete-time neural networks with time delay. The synchronization is analyzed by the piecewise Lyapunov function approach and the piecewise Lyapunov–Krasovskii functional approach, respectively. The average activation time ratio of AIC is estimated, which is more general and less conservative than the minimum activation time ratio. Finally, a numerical example is exploited and detailed comparisons are presented to demonstrate the effectiveness and less conservativeness of the obtained results.     

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 synchronization and adaptive synchronization of complex-valued inertial neural networks with time-varying delays in fixed-time interval

This article concentrates on pinning synchronization and adaptive synchronization problems of complex-valued inertial neural networks with time-varying delays in fixed-time interval. First, regarding complex-valued inertial neural networks model as an entirety instead of reducing this system to first-order differential equation, separating the real and imaginary parts of this system into an equivalent real-valued one, and establishing a novel Lyapunov function, the fixed-time stability for the closed-loop error system is guaranteed via partial nodes controlled directly by a new pinning controller which involves the state derivatives and other proper terms. Then, from the point of saving cost and avoiding resources waste, a new pinning adaptive controller is further developed and sufficient condition ensuring the adaptive fixed-time stability for the closed-loop error system is also derived. In the end, the effectiveness of these results is verified by a numerical example.     

Secure synchronization control for a class of complex time-Delay dynamic networks against denial-of-service attacks

In this paper, the secure synchronization control problem of a class of complex time-delay dynamic networks (CTDDNs) under denial of service (DoS) attacks is studied. Based on the pinning control strategy, a non-fragile sampling controller is designed for a small number of nodes in the complex network. It can effectively solve the problem of limited communication resources and has good anti-interference performance. In order to resist the influence of DoS attacks, an improved comparator algorithm is designed to obtain the specific information of DoS attacks, including the upper and lower bounds of the DoS attacks duration, the DoS attacks frequency and the specific active/sleeping interval of DoS attacks. Based on Lyapunov stability theory and by designing the pinning non-fragile sampling controller, new security synchronization criteria are established for CTDDNs. Finally, two numerical examples are given to verify the validity of the theories.