Mode-Mixed Effects Based Intralayer-Dependent Impulsive Synchronization for Multiple Mismatched Multilayer Neural Networks

This article focuses on the intralayer-dependent impulsive synchronization of multiple mismatched multilayer neural networks (NNs) with mode-mixed effects. Initially, a novel multilayer NN model that removes the one-to-one interlayer coupling constraint and introduces nonidentical model parameters is first established to meet diverse modeling requirements in complex applications. To help the multilayer target NNs with mismatched connection coefficients and time delays achieve synchronization, the hybrid controller is designed using intralayer-dependent impulsive control and switched feedback control approaches. Furthermore, the mode-mixed effects caused by the intralayer coupling delays and switched intralayer topologies are incorporated into the novel model and analysis method to ensure that the subsystems operating within the current switching interval can effectively use the topology information of the previous switching intervals. Then, a novel analysis framework including super-Laplacian matrix, augmented matrix, and mode-mixed methods is developed to derive the synchronization results. Finally, the main results are verified via the numerical simulation with secure communication.

Stability and synchronization for complex-valued neural networks with stochastic parameters and mixed time delays

In this paper, a class of complex-valued neural networks (CVNNs) with stochastic parameters and mixed time delays are proposed. The random fluctuation of system parameters is considered in order to describe the implementation of CVNNs more practically. Mixed time delays including distributed delays and time-varying delays are also taken into account in order to reflect the influence of network loads and communication constraints. Firstly, the stability problem is investigated for the CVNNs. In virtue of Lyapunov stability theory, a sufficient condition is deduced to ensure that CVNNs are asymptotically stable in the mean square. Then, for an array of coupled identical CVNNs with stochastic parameters and mixed time delays, synchronization issue is investigated. A set of matrix inequalities are obtained by using Lyapunov stability theory and Kronecker product and if these matrix inequalities are feasible, the addressed CVNNs are synchronized. Finally, the effectiveness of the obtained theoretical results is demonstrated by two numerical examples.

Impulsive strategies in nonlinear dynamical systems: A brief overview

The studies of impulsive dynamical systems have been thoroughly explored, and extensive publications have been made available. This study is mainly in the framework of continuous-time systems and aims to give an exhaustive review of several main kinds of impulsive strategies with different structures. Particularly, (i) two kinds of impulse-delay structures are discussed respectively according to the different parts where the time delay exists, and some potential effects of time delay in stability analysis are emphasized. (ii) The event-based impulsive control strategies are systematically introduced in the light of several novel event-triggered mechanisms determining the impulsive time sequences. (iii) The hybrid effects of impulses are emphatically stressed for nonlinear dynamical systems, and the constraint relationships between different impulses are revealed. (iv) The recent applications of impulses in the synchronization problem of dynamical networks are investigated. Based on the above several points, we make a detailed introduction for impulsive dynamical systems, and some significant stability results have been presented. Finally, several challenges are suggested for future works.

Synchronization of Neural Networks via Periodic Self-Triggered Impulsive Control and Its Application in Image Encryption

In this article, a periodic self-triggered impulsive (PSTI) control scheme is proposed to achieve synchronization of neural networks (NNs). Two kinds of impulsive gains with constant and random values are considered, and the corresponding synchronization criteria are obtained based on tools from impulsive control, event-driven control theory, and stability analysis. The designed triggering protocol is simpler, easier to implement, and more flexible compared with some previously reported algorithms as the protocol combines the advantages of the periodic sampling and event-driven control. In addition, the chaotic synchronization of NNs via the presented PSTI sampling is further applied to encrypt images. Several examples are also utilized to illustrate the validity of the presented synchronization algorithm of NNs based on PSTI control and its potential applications in image processing.

Input-to-State Stability of Impulsive Systems via Event-Triggered Impulsive Control

This article investigates input-to-state stability (ISS) and integral ISS (iISS) of nonlinear impulsive systems based on the event-triggered impulsive control (ETIC) strategy, where the impulse sequence is generated by some predesigned event conditions. Unlike traditional event-triggered control, ETIC means that the controller is activated only when some state-dependent event conditions are triggered and moreover, there is not any control transmission between two consecutive triggered impulse instants. Event-triggered impulses are usually regarded as a class of state-dependent impulses, where the event-triggered mechanism (ETM) is an impulse generator. By using the ETIC strategy, some Lyapunov-based criteria are established, which can effectively avoid infinitely fast triggering behavior and guarantee ISS/iISS of nonlinear impulsive systems. Then, the theoretical results are applied to nonlinear system, where a class of ETMs and impulsive control gain are derived with the help of LMIs. Finally, two numerical examples are presented to illustrate the validity of our control strategies.

Exponential synchronization of coupled neural networks under stochastic deception attacks

In this paper, the issue of synchronization is investigated for coupled neural networks subject to stochastic deception attacks. Firstly, a general differential inequality with delayed impulses is given. Then, the established differential inequality is further extended to the case of delayed stochastic impulses, in which both the impulsive instants and impulsive intensity are stochastic. Secondly, by modeling the stochastic discrete-time deception attacks as stochastic impulses, synchronization criteria of the coupled neural networks under the corresponding attacks are given. Finally, two numerical examples are provided to demonstrate the correctness of the theoretical results.

Adaptive Synchronization of Fractional-Order Output-Coupling Neural Networks via Quantized Output Control

This article focuses on the adaptive synchronization for a class of fractional-order coupled neural networks (FCNNs) with output coupling. The model is new for output coupling item in the FCNNs that treat FCNNs with state coupling as its particular case. Novel adaptive output controllers with logarithm quantization are designed to cope with the stability of the fractional-order error systems for the first attempt, which is also an effective way to synchronize fractional-order complex networks. Based on fractional-order Lyapunov functionals and linear matrix inequalities (LMIs) method, sufficient conditions rather than algebraic conditions are built to realize the synchronization of FCNNs with output coupling. A numerical simulation is put forward to substantiate the applicability of our results.

Impulsive Synchronization of Unbounded Delayed Inertial Neural Networks With Actuator Saturation and Sampled-Data Control and its Application to Image Encryption

The article considers the impulsive synchronization for inertial neural networks with unbounded delay and actuator saturation via sampled-data control. Based on an impulsive differential inequality, the difficulties caused by unbounded delay and impulsive effect may be effectively avoid. By applying polytopic representation technique, the actuator saturation term is first considered into the design of impulsive controller, and less conservative linear matrix inequality (LMI) criteria that guarantee asymptotical synchronization for the considered model via hybrid control are given. As special cases, the asymptotical synchronization of the considered model via sampled-data control and saturating impulsive control are also studied, respectively. Numerical simulations are presented to claim the effectiveness of theoretical analysis. A new image encryption algorithm is proposed to utilize the synchronization theory of hybrid control. The validity of image encryption algorithm can be obtained by experiments.

Synchronization of Nonidentical Neural Networks With Unknown Parameters and Diffusion Effects via Robust Adaptive Control Techniques

This paper considers the self-synchronization and tracking synchronization issues for a class of nonidentically coupled neural networks model with unknown parameters and diffusion effects. Using the special structure of neural networks with global Lipschitz activation function, nonidentical terms are treated as external disturbances, which can then be compensated via robust adaptive control techniques. For the case where no common reference trajectory is given in advance, a distributed adaptive controller is proposed to drive the synchronization error to an adjustable bounded area. For the case where a reference trajectory is predesigned, two distributed adaptive controllers are proposed, respectively, to address the tracking synchronization problem with bounded and unbounded reference trajectories, different decomposition methods are given to extract the heterogeneous characteristics. To avoid the appearance of global information, such as the spectrum of the coupling matrix, corresponding adaptive designs on coupling strengths are also provided for both cases. Moreover, the upper bounds of the final synchronization errors can be gradually adjusted according to the parameters of the adaptive designs. Finally, numerical examples are given to test the effectiveness of the control algorithms.

Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms

Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.

Impulsive Control of Nonlinear Systems With Time-Varying Delay and Applications

Impulsive control of nonlinear delay systems is studied in this paper, where the time delays addressed may be the constant delay, bounded time-varying delay, or unbounded time-varying delay. Based on the impulsive control theory and some analysis techniques, a new theoretical result for global exponential stability is derived from the impulsive control point of view. The significance of the presented result is that the stability can be achieved via the impulsive control at certain impulse points despite the existence of impulsive perturbations which causes negative effect to the control. That is, the impulsive control provides a super performance to allow the existence of impulsive perturbations. In addition, we apply the theoretical result to the problem of impulsive control of delayed neural networks. Some results for global exponential stability and synchronization control of neural networks with time delays are derived via impulsive control. Three illustrated examples are given to show the effectiveness and distinctiveness of the proposed impulsive control schemes.

Global Stability of Fractional Order Coupled Systems with Impulses via a Graphic Approach

Based on the graph theory and stability theory of dynamical system, this paper studies the stability of the trivial solution of a coupled fractional-order system. Some sufficient conditions are obtained to guarantee the global stability of the trivial solution. Finally, a comparison between fractional-order system and integer-order system ends the paper.

Finite-Time Synchronization of Markovian Jumping Complex Networks with Non-Identical Nodes and Impulsive Effects

In this paper, we investigate the finite-time synchronization problem for a class of Markovian jumping complex networks (MJCNs) with non-identical nodes and impulsive effects. Sufficient conditions for the MJCNs are presented based on an M-matrix technique, Lyapunov function method, stochastic analysis technique, and suitable comparison systems to guarantee finite-time synchronization. At last, numerical examples are exploited to illustrate our theoretical results, and they testify the effectiveness of our results for complex dynamic systems.

Global Synchronization of Coupled Fractional-Order Recurrent Neural Networks

This paper presents new theoretical results on the global synchronization of coupled fractional-order recurrent neural networks. Under the assumptions that the coupled fractional-order recurrent neural networks are sequentially connected in form of a single spanning tree or multiple spanning trees, two sets of sufficient conditions are derived for ascertaining the global synchronization by using the properties of Mittag-Leffler function and stochastic matrices. Compared with existing works, the results herein are applicable for fractional-order systems, which could be viewed as an extension of integer-order ones. Two numerical examples are presented to illustrate the effectiveness and characteristics of the theoretical results.

Passivity and Synchronization of Coupled Uncertain Reaction-Diffusion Neural Networks With Multiple Time Delays

This paper presents a complex network model consisting of N uncertain reaction-diffusion neural networks with multiple time delays. We analyze the passivity and synchronization of the proposed network model and derive several passivity and synchronization criteria based on some inequality techniques. In addition, by considering the difficulty in achieving passivity (synchronization) in such a network, an adaptive control scheme is also developed to ensure that the proposed network achieves passivity (synchronization). Finally, we design two numerical examples to verify the effectiveness of the derived passivity and synchronization criteria.

Stability analysis of sample data systems with input missing: A hybrid control approach

In this paper, we establish exponential stability criteria for the sampled-data impulsive control of the linear time-invariant system. With average impulse interval (AII), less conservative conditions are obtained on the exponential stability problem for the sampled-data systems. It is proved that when the AII of the impulsive sequences is fixed, the upper bound of the impulsive intervals could be very large, which guarantees the less conservativeness of the obtained result concerning the sampling intervals. The control input missing is also studied and we establish a new stability criterion for the exponential decay rate and the sampling period which is less conservative than the ones obtained for variable sampling intervals. Two examples are given to show the effectiveness of the obtained result.

Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order

The paper proves a unified analysis for finite-time anti-synchronization of a class of integer-order and fractional-order chaotic systems. We establish an effective controller to ensure that the chaotic system with unknown parameters achieves anti-synchronization in finite time under our controller. Then, we apply our results to the integer-order and fractional-order Lorenz system, respectively. Finally, numerical simulations are presented to show the feasibility of the proposed control scheme. At the same time, through the numerical simulation results, it is show that for the Lorenz chaotic system, when the order is greater, the more quickly is anti-synchronization achieved.

Containment Control of Linear Multiagent Systems With Aperiodic Sampling and Measurement Size Reduction

The containment control problem for generally linear multiagent systems with aperiodic sampling intervals and measurement size reduction is considered in this paper. Under the assumption that the sampling interval changes from a finite set, an improved protocol is proposed, such that a larger sampling interval can be obtained to achieve containment. By using the properties of Laplacian matrix and the newly developed protocol, the containment control problem is transformed into the stability problem of a discrete-time switched linear system. A sufficient condition is obtained that ensures all the followers converge to the convex hull formed by the state of leaders, and such a sufficient condition is presented in terms of linear matrix inequalities, which are independent of the node of network. To further reduce the communication among agents, a switching-type measurement size reduction scheme is introduced. An optimization problem is proposed for the corresponding controller design. Finally, two simulation studies are conducted to show the effectiveness and advantage of the proposed control algorithms.

Neural-Network-Based Adaptive Backstepping Control With Application to Spacecraft Attitude Regulation

This paper investigates the neural-network-based adaptive control problem for a class of continuous-time nonlinear systems with actuator faults and external disturbances. The model uncertainties in the system are not required to satisfy the norm-bounded assumption, and the exact information for components faults and external disturbance is totally unknown, which represents more general cases in practical systems. An indirect adaptive backstepping control strategy is proposed to cope with the stabilization problem, where the unknown nonlinearity is approximated by the adaptive neural-network scheme, and the loss of effectiveness of actuators faults and the norm bounds of exogenous disturbances are estimated via designed online adaptive updating laws. The developed adaptive backstepping control law can ensure the asymptotic stability of the fault closed-loop system despite of unknown nonlinear function, actuator faults, and disturbances. Finally, an application example based on spacecraft attitude regulation is provided to demonstrate the effectiveness and the potential of the developed new neural adaptive control approach.