Synchronization of General Chaotic Neural Networks With Nonuniform Sampling and Packet Missing: A Switched System Approach

Fast Finite-Time Observer-Based Event-Triggered Consensus Control for Uncertain Nonlinear Multiagent Systems with Full-State Constraints

This article studies a class of uncertain nonlinear multiagent systems (MASs) with state restrictions. RBFNNs, or radial basis function neural networks, are utilized to estimate the uncertainty of the system. To approximate the unknown states and disturbances, the state observer and disturbance observer are proposed to resolve those issues. Moreover, a fast finite-time consensus control technique is suggested in order to accomplish fast finite-time stability without going against the full-state requirements. It is demonstrated that every signal could be stable and boundless, and an event-triggered controller is considered for the saving of resources. Ultimately, the simulated example demonstrates the validity of the developed approach.

Partial-Neurons-Based Proportional-Integral Observer Design for Artificial Neural Networks: A Multiple Description Encoding Scheme

This article is concerned with a new partial-neurons-based proportional-integral observer (PIO) design problem for a class of artificial neural networks (ANNs) subject to bounded disturbances. For the purpose of improving the reliability of the data transmission, the multiple description encoding mechanisms are exploited to encode the measurement data into two identically important descriptions, and the encoded data are then transmitted to the decoders via two individual communication channels susceptible to packet dropouts, where Bernoulli-distributed stochastic variables are utilized to characterize the random occurrence of the packet dropouts. An explicit relationship is discovered that quantifies the influences of the packet dropouts on the decoding accuracy, and a sufficient condition is provided to assess the boundedness of the estimation error dynamics. Furthermore, the desired PIO parameters are calculated by solving two optimization problems based on two metrics (i.e., the smallest ultimate bound and the fastest decay rate) characterizing the estimation performance. Finally, the applicability and advantage of the proposed PIO design strategy are verified by means of an illustrative example.

Sampled-Data Control for Exponential Synchronization of Delayed Inertial Neural Networks With Aperiodic Sampling and State Quantization

This article is devoted to dealing with exponential synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) under the framework of aperiodic sampling and state quantization. First, by taking the effect of aperiodic sampling and state quantization into consideration, a novel quantized sampled-data (QSD) controller with time-varying control gain is designed to tackle the exponential synchronization of INNs. Second, considering the available information of the lower and upper bounds of each HTVD, a refined Lyapunov-Krasovskii functional (LKF) is proposed. Meanwhile, an improved looped-functional method is utilized to fully capture the characteristic of practical sampling patterns and further relax the positive definiteness requirement for LKF. Consequently, less conservative exponential synchronization conditions with extra flexibility are derived. Finally, a numerical example is employed to demonstrate the effectiveness and advantages of the proposed synchronization method.

Event-Triggered Exponential Synchronization of the Switched Neural Networks With Frequent Asynchronism

The synchronization for a class of switched uncertain neural networks (NNs) with frequent asynchronism based on event-triggered control is researched in this article. Compared with existing works that require one switching during an inter-event interval, frequent switching is allowed in this article. By employing controller-mode-dependent Lyapunov-Krasovskii functionals (LKFs), we devise the control strategy to guarantee that the switched NNs can be synchronized. The proposed LKFs can make full use of system information. Using an improved integral inequality, some sufficient stability conditions formed by linear matrix inequalities (LMIs) are derived for the synchronization of switched uncertain NNs. Average dwell time (ADT) is obtained in the form of inequality that includes the maximum inter-event interval. In addition, the existence of lower bound of inter-event interval is discussed to avoid Zeno behavior. At last, the feasibility of the proposed method is proven by a numerical example.

Adaptive event-triggered synchronization of neural networks under stochastic cyber-attacks with application to Chua's circuit

This paper focuses on the synchronization control problem for neural networks (NNs) subject to stochastic cyber-attacks. Firstly, an adaptive event-triggered scheme (AETS) is adopted to improve the utilization rate of network resources, and an output feedback controller is constructed for improving the performance of the system subject to the conventional deception attack and accumulated dynamic cyber-attack. Secondly, the synchronization problem of master-slave NNs is transformed into the stability analysis problem of the synchronization error system. Thirdly, by constructing a customized Lyapunov-Krasovskii functional (LKF), the adaptive event-triggered output feedback controller is designed to ensure the synchronization error system is asymptotically stable with a given H∞ performance index. Lastly, in the simulation part, two examples, including Chua's circuit, illustrate the feasibility and universality of the related technologies in this paper.

Event-based fixed-time synchronization of neural networks under DoS attack and its applications

In this paper, the fixed-time synchronization control for neural networks with discontinuous data communication is investigated. Due to the transmission blocking caused by DoS attack, it is intractable to establish a monotonically decreasing Lyapunov function like the conventional analysis of fixed-time stability. Therefore, by virtue of recursive and reduction to absurdity approaches, novel fixed-time stability criteria where the estimated upper bound of settling-time is inherently different from existing results are presented. Then, based on the developed conditions, an event-triggered control scheme that can avoid Zeno behavior is designed to achieve synchronization of master-slave neural networks under DoS attack within a prescribed time. For comparison, the established control scheme is further discussed under the case without DoS attack, and the circumstance that there is no attack or event-triggered mechanism, respectively. Simulation results are finally provided to illustrate the significant and validity of our theoretical research. Especially, in terms of encryption and decryption keys generated from the synchronization behavior of chaotic networks, we specifically discuss the application of the proposed fixed-time synchronization scheme to image and audio encryption.

Master-Slave Synchronization of Neural Networks With Unbounded Delays via Adaptive Method

Master-slave synchronization of two delayed neural networks with adaptive controller has been studied in recent years; however, the existing delays in network models are bounded or unbounded with some derivative constraints. For more general delay without these restrictions, how to design proper adaptive controller and prove rigorously the convergence of error system is still a challenging problem. This article gives a positive answer for this problem. By means of the stability result of unbounded delayed system and some analytical techniques, we prove that the traditional centralized adaptive algorithms can achieve global asymptotical synchronization even if the network delays are unbounded without any derivative constraints. To describe the convergence speed of the synchronization error, adaptive designs depending on a flexible ω -type function are also provided to control the synchronization error, which can lead exponential synchronization, polynomial synchronization, and logarithmically synchronization. Numerical examples on delayed neural networks and chaotic Ikeda-like oscillator are presented to verify the adaptive designs, and we find that in the case of unbounded delay, the intervention of ω -type function can promote the realization of synchronization but may destroy the convergence of control gain, and this however will not happen in the case of bounded delay.

Observer-Based Adaptive Optimized Control for Stochastic Nonlinear Systems With Input and State Constraints

In this work, an adaptive neural network (NN) optimized output-feedback control problem is studied for a class of stochastic nonlinear systems with unknown nonlinear dynamics, input saturation, and state constraints. A nonlinear state observer is designed to estimate the unmeasured states, and the NNs are used to approximate the unknown nonlinear functions. Under the framework of the backstepping technique, the virtual and actual optimal controllers are developed by employing the actor-critic architecture. Meanwhile, the tan-type Barrier optimal performance index functions are developed to prevent the nonlinear systems from the state constraints, and all the states are confined within the preselected compact sets all the time. It is worth mentioning that the proposed optimized control is clearly simple since the reinforcement learning (RL) algorithm is derived based on the negative gradient of a simple positive function. Furthermore, the proposed optimal control strategy ensures that all the signals in the closed-loop system are bounded. Finally, a practical simulation example is carried out to further illustrate the effectiveness of the proposed optimal control method.

Dissipativity-Based Synchronization for Switched Discrete-Time-Delayed Neural Networks With Combined Switching Paradigm

The present study concerns the dissipativity-based synchronization problem for the discrete-time switched neural networks with time-varying delay. Different from some existing research depending on the arbitrary and time-dependent switching mechanisms, all subsystems of the investigated delayed neural networks are permitted to be nondissipative. For reducing the switching frequency, the combined switching paradigm constituted by the time-dependent and state-dependent switching strategies is then constructed. In light of the proposed dwell-time-dependent storage functional, sufficient conditions with less conservativeness are formulated, under which the resultant synchronization error system is strictly (~X,~Y,~Z) - ϑ -dissipative on the basis of the combined switching mechanism or the joint action of the switching mechanism and time-varying control input. Finally, the applicability and superiority of the theoretical results are adequately substantiated with the synchronization issue of two discrete-time switched Hopfield neural networks with time-varying delay, and the relationship among the performance index, time delay, and minimum dwell time is also revealed.

Event-Triggered Output Feedback Synchronization of Master-Slave Neural Networks Under Deception Attacks

The problem of event-triggered synchronization of master-slave neural networks is investigated in this article. It is assumed that both communication channels from the sensor to controller and from controller to actuator are subject to stochastic deception attacks modeled by two independent Markov processes. Two discrete event-triggered mechanisms are introduced for both channels to reduce the number of data transmission through the communication channels. To comply with practical point of view, static output feedback is utilized. By employing the Lyapunov-Krasovskii functional method, some sufficient conditions on the synchronization of master-slave neural networks are derived in terms of linear matrix inequalities, which make it easy to design suitable output feedback controllers. Finally, a numerical example is presented to show the effectiveness of the proposed method.

Nonfragile H∞ State Estimation for Recurrent Neural Networks With Time-Varying Delays: On Proportional-Integral Observer Design

In this article, a novel proportional-integral observer (PIO) design approach is proposed for the nonfragile H_∞ state estimation problem for a class of discrete-time recurrent neural networks with time-varying delays. The developed PIO is equipped with more design freedom leading to better steady-state accuracy compared with the conventional Luenberger observer. The phenomena of randomly occurring gain variations, which are characterized by the Bernoulli distributed random variables with certain probabilities, are taken into consideration in the implementation of the addressed PIO. Attention is focused on the design of a nonfragile PIO such that the error dynamics of the state estimation is exponentially stable in a mean-square sense, and the prescribed H_∞ performance index is also achieved. Sufficient conditions for the existence of the desired PIO are established by virtue of the Lyapunov-Krasovskii functional approach and the matrix inequality technique. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed PIO design scheme.

Distributed H∞ State Estimator Design for Time-Delay Periodic Systems Over Scheduling Sensor Networks

This paper studies the distributed state estimator design method for periodic systems with time-varying delays and periodic communication scheduling strategy over sensor networks. To mitigate the stability attenuation and the performance loss caused by delays, a periodic delay-dependent Lyapunov function is constructed, which relaxes the conservatism and improves the H_∞ performance of the estimators. Then, a periodic scheduling strategy, which updates the correlative innovations of each node during a period in an average way by solving an integer programming problem, is proposed to save energy. Periodic gains of distributed estimators are designed by using analog tool. Finally, a visual example is utilized to describe the periodic communication scheduling. The effectiveness of the strategy and the novel Lyapunov function is demonstrated by the example.

Synchronization of Coupled Time-Delay Neural Networks With Mode-Dependent Average Dwell Time Switching

In the literature, the effects of switching with average dwell time (ADT), Markovian switching, and intermittent coupling on stability and synchronization of dynamic systems have been extensively investigated. However, all of them are considered separately because it seems that the three kinds of switching are different from each other. This article proposes a new concept to unify these switchings and considers global exponential synchronization almost surely (GES a.s.) in an array of neural networks (NNs) with mixed delays (including time-varying delay and unbounded distributed delay), switching topology, and stochastic perturbations. A general switching mechanism with transition probability (TP) and mode-dependent ADT (MDADT) (i.e., TP-based MDADT switching in this article) is introduced. By designing a multiple Lyapunov-Krasovskii functional and developing a set of new analytical techniques, sufficient conditions are obtained to ensure that the coupled NNs with the general switching topology achieve GES a.s., even in the case that there are both synchronizing and nonsynchronizing modes. Our results have removed the restrictive condition that the increment coefficients of the multiple Lyapunov-Krasovskii functional at switching instants are larger than one. As applications, the coupled NNs with Markovian switching topology and intermittent coupling are employed. Numerical examples are provided to demonstrate the effectiveness and the merits of the theoretical analysis.

Event-Triggered Adaptive Tracking Control for Multiagent Systems With Unknown Disturbances

This paper considers the event-triggered tracking control problem of nonlinear multiagent systems with unknown disturbances. The event-triggering mechanism is considered in the controller update, which decreases the amount of communication and reduces the frequency of the controller update in practice. By designing a disturbance observer, the unknown external disturbances are estimated. Moreover, a part of adaptive parameters are only dependent on the number of followers, which weakens the computational burden. It is shown that all the signals are bounded, and the consensus tracking errors are located in a small neighborhood of the origin based on the Lyapunov stability theory and backstepping approach. Finally, the effectiveness of the approach proposed in this paper is proved by simulation results.

Synchronization Control for Network Systems With Communication Constraints

A novel control strategy for synchronization control for network systems with communication constraints is presented in this paper. The dynamics of nodes in the network are nonidentical. The communication topology of network is weakly connected with communication constraints. The designed distributed controller for each node has two parts: reference generator (RG) and regulator. All RGs adopt the communication channels to exchange local information and track the target trajectory. Meanwhile, regulator can ensure that nonidentical node achieves synchronization with its RG. In order to reduce the communication frequency between node and its regulator, a sampled-date control strategy is utilized. The upper bound of the aperiodic sampling instants is calculated through the small-gain theorem, where the closed-loop system is equivalently formulated as the feedback interconnection of a linear time-invariant system and an integral sampled-data operator. Finally, some simulation results are given to demonstrate the effectiveness of the controller design strategy.

Finite-Horizon l2-l∞ Synchronization for Time-Varying Markovian Jump Neural Networks Under Mixed-Type Attacks: Observer-Based Case

This paper studies the synchronization issue of time-varying Markovian jump neural networks (NNs). The denial-of-service (DoS) attack is considered in the communication channel connecting master NNs and slave NNs. An observer is designed based on the measurements of master NNs transmitted over this unreliable channel to estimate their states. The deception attack is used to destroy the controller by changing the sign of the control signal. Then, the mixed-type attacks are expressed uniformly, and a synchronization error system is established using this function. A finite-horizon l₂-l_∞ performance is proposed, and sufficient conditions are derived to ensure that the synchronization error system satisfies this performance. The controllers are then obtained by a recursive linear matrix inequality algorithm. At last, a simulation result to show the feasibility of the developed results is given.

Filippov Hindmarsh-Rose Neuronal Model With Threshold Policy Control

A Filippov system of Hindmarsh-Rose (HR) neuronal model with threshold policy control is proposed, membrane potential has been taken as the threshold and the corresponding switching function is also established. We first discuss the existence and stability of the equilibria for the two Filippov subsystems based on the 2-D HR model. Subsequently, the sliding dynamics of HR model including the sliding segments, sliding regions, and various equilibria under the Filippov framework are studied. Then, we further consider the equilibria and the sliding bifurcation set of the Filippov system, and find there exist the bistable equilibria and several sliding bifurcation phenomena, such as boundary-node bifurcation, pseudosaddle-node bifurcation, the emergence and disappearance of limit cycles on the sliding line, and so on. Finally, we study the Filippov system of the 3-D HR model, and provide a phase diagram of the system that generates the sliding spiking and the sliding bursting, which lie on the sliding line.