Synchronization of Hierarchical Time-Varying Neural Networks Based on Asynchronous and Intermittent Sampled-Data Control

Sampled-Data-Based Secure Synchronization Control for Chaotic Lur'e Systems Subject to Denial-of-Service Attacks

This article investigates the sampled-data-based secure synchronization control problem for chaotic Lur'e systems subject to power-constrained denial-of-service (DoS) attacks, which can block data packets' transmission in communication channels. To eliminate the adverse effects, a resilient sampled data control scheme consisting of a secure controller and communication protocol is designed by considering the attack signals and periodic sampling mechanism simultaneously. Then, a novel index, i.e., the maximum anti-attack ratio, is proposed to measure the secure level. On this basis, a multi-interval-dependent functional is established for the resulting closed-loop system model. The main feature of the developed functional lies in that it can fully use the information of resilient sampling intervals and DoS attacks. In combination with the convex combination method, discrete-time Lyapunov theory, and some inequality estimate techniques, two sufficient conditions are, respectively, derived to achieve sampled-data-based secure synchronization of drive-response systems against DoS attacks. Compared with the existing Lyapunov functionals, the advantages of the proposed multi-interval-dependent functional are analyzed in detail. Finally, a synchronization example and an application to secure communication are provided to display the effectiveness and validity of the obtained results.

A Switched Integral-Based Event-Triggered Control of Uncertain Nonlinear Time-Delay System With Actuator Saturation

This article explores the asymptotic stabilization criteria of the uncertain nonlinear time-delay system subject to actuator saturation. A switched integral-based event-triggered scheme (IETS) is established to reduce the redundant data transmission over the networks. The switched IETS condition uses the integration of system states over a time period in the past. A fixed waiting time is included to avoid the Zeno behavior. In order to estimate a larger domain of attraction, a delay-dependent polytopic representation method is presented to deal with the effects of actuator saturation in the proposed model. A new series of less conservative linear matrix inequalities (LMIs) is proposed on the basis of delay-dependent Lyapunov-Krasovskii functional (LKF) to ensure the stability of nonlinear time-delay system subject to actuator saturation using the proposed IETS. Numerical examples are used to confirm the effectiveness and advantages of the proposed IETS approach.

Observer-Based Dissipativity Control for T-S Fuzzy Neural Networks With Distributed Time-Varying Delays

An observer-based dissipativity control for Takagi-Sugeno (T-S) fuzzy neural networks with distributed time-varying delays is studied in this article. First, the network channel delays are modeled as a distributed delay with its kernel. To make full use of kernels of the distributed delay, a Lyapunov-Krasovskii functional (LKF) is established with the kernel of the distributed delay. It is noted that the novel LKF and delay-dependent reciprocally convex inequality plays an important role in dealing with global asymptotical stability and strict (Q, S,R) - α -dissipativity of the T-S fuzzy delayed model. Through the constructed LKF, a new set of less conservative linear matrix inequality (LMI) conditions is presented to obtain an observer-based controller for the T-S fuzzy delayed model. This proposed observer-based controller ensures that the state of the closed-loop system is globally asymptotically stable and strictly (Q, S,R) - α -dissipative. Finally, the effectiveness of the proposed results is shown in numerical simulations.

Simplifying Complex Network Stability Analysis via Hierarchical Node Aggregation and Optimal Periodic Control

In this study, the stability of a hierarchical network with delayed output is discussed by applying a kind of optimal periodic control. To reduce the number of the nodes of the original hierarchical network, an aggregation algorithm is first presented to take some nodes with the same information as an aggregated node. Furthermore, the stability of the original hierarchical network can be guaranteed by the optimal periodic control of the aggregated hierarchical network. Then, an optimal control scheme is proposed to reduce the bandwidth waste in information transmission. In the control scheme, the time sequence is separated into two parts: the deterministic segment and the dynamic segment. With the optimal control scheme, two targets are achieved: 1) the outputs of the original and aggregated hierarchical system are both asymptotically stable and 2) the nodes with slow convergent rate can catch up with the convergence speeds of other nodes.

Master-Slave Synchronization of Delayed Neural Networks With Time-Varying Control

This brief investigates the master-slave synchronization problem of delayed neural networks with general time-varying control. Assuming a linear feedback controller with time-varying control gain, the synchronization problem is recast into the stability problem of a delayed system with a time-varying coefficient. The main theorem is established in terms of the time average of the control gain by using the Lyapunov-Razumikhin theorem. Moreover, the proposed framework encompasses some general intermittent control schemes, such as the switched control gain with external disturbance and intermittent control with pulse-modulated gain function, while some useful corollaries are consequently deduced. Interestingly, our theorem also provides a solution for regaining stability under control failure. The validity of the theorem and corollaries is further demonstrated with numerical examples.

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.

A Switched Operation Approach to Sampled-Data Control Stabilization of Fuzzy Memristive Neural Networks With Time-Varying Delay

This paper investigates the issue of sampled-data stabilization for Takagi-Sugeno fuzzy memristive neural networks (FMNNs) with time-varying delay. First, the concerned FMNNs are transformed into the tractable fuzzy NNs based on the excitatory and inhibitory of memristive synaptic weights using a new convex combination technique. Meanwhile, a switched fuzzy sampled-data controller is employed for the first time to tackle stability problems related to FMNNs. Then, the novel stabilization criteria of the FMNNs are established using the fuzzy membership functions (FMFs)-dependent Lyapunov-Krasovskii functional. This sufficiently utilizes information from not only the delayed state and the actual sampling pattern but also the FMFs. Two simulation examples are presented to demonstrate the feasibility and validity of the proposed method.

Cluster Synchronization for Neutral Stochastic Delay Networks via Intermittent Adaptive Control

This paper studies the problem of cluster synchronization at exponential rates in both the mean square and almost sure senses for neutral stochastic coupled neural networks with time-varying delay via a periodically intermittent pinning adaptive control strategy. The network topology can be symmetric or asymmetric, with each network node being described by neutral stochastic delayed neural networks. When considering the exponential stabilization in the mean square sense for neutral stochastic delay system, the delay integral inequality approach is used to circumvent the obstacle arising from the coexistence of random disturbance, neutral item, and time-varying delay. The almost surely exponential stabilization is also analyzed with the nonnegative semimartingale convergence theorem. Sufficient criteria on cluster synchronization at exponential rates in both the mean square and almost sure senses of the underlying networks under the designed control scheme are derived. The effectiveness of the obtained theoretical results is illustrated by two examples.

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.

General Square-Pattern Discretization Formulas via Second-Order Derivative Elimination for Zeroing Neural Network Illustrated by Future Optimization

Previous works provide a few effective discretization formulas for zeroing neural network (ZNN), of which the precision is a square pattern. However, those formulas are separately developed via many relatively blind attempts. In this paper, general square-pattern discretization (SPD) formulas are proposed for ZNN via the idea of the second-order derivative elimination. All existing SPD formulas in previous works are included in the framework of the general SPD formulas. The connections and differences of various general formulas are also discussed. Furthermore, the general SPD formulas are used to solve future optimization under linear equality constraints, and the corresponding general discrete ZNN models are proposed. General discrete ZNN models have at least one parameter to adjust, thereby determining their zero stability. Thus, the parameter domains are obtained by restricting zero stability. Finally, numerous comparative numerical experiments, including the motion control of a PUMA560 robot manipulator, are provided to substantiate theoretical results and their superiority to conventional Euler formula.

Synchronization of Coupled Markovian Reaction-Diffusion Neural Networks With Proportional Delays Via Quantized Control

The asymptotic synchronization of coupled reaction-diffusion neural networks with proportional delay and Markovian switching topologies is considered in this brief where the diffusion space does not need to contain the origin. The main objectives of this brief are to save communication resources and to reduce the conservativeness of the obtained synchronization criteria, which are carried out from the following two aspects: 1) mode-dependent quantized control technique is designed to reduce control cost and save communication channels and 2) Wirtinger inequality is utilized to deal with the reaction-diffusion terms in a matrix form and reciprocally convex technique combined with new Lyapunov-Krasovskii functional is used to derive delay-dependent synchronization criteria. The obtained results are general and formulated by linear matrix inequalities. Moreover, combined with an optimal algorithm, control gains with the least magnitude are designed.

Stability of Singular Discrete-Time Neural Networks With State-Dependent Coefficients and Run-to-Run Control Strategies

In this brief, sustaining and intermittent run-to-run controllers are designed to achieve the stability of singular discrete-time neural networks with state-dependent coefficients. The controllers are designed for two reasons: 1) it is very difficult and almost impossible to only measure the in situ feedback information for the controllers and 2) the controllers may not always exist at any time. The stability is then established for singular discrete-time neural networks with state-dependent coefficients. Finally, numerical simulations are shown to illustrate the usefulness of the obtained criteria.

Synchronization of Nonlinearly and Stochastically Coupled Markovian Switching Networks via Event-Triggered Sampling

This paper studies the exponential synchronization problem for a new array of nonlinearly and stochastically coupled networks via events-triggered sampling (ETS) by self-adaptive learning. The networks include the following features: 1) a Bernoulli stochastic variable is introduced to describe the random structural coupling; 2) a stochastic variable with positive mean is used to model the coupling strength; and 3) a continuous time homogeneous Markov chain is employed to characterize the dynamical switching of the coupling structure and pinned node sets. The proposed network model is capable to capture various stochastic effect of an external environment during the network operations. In order to reduce networks' workload, different ETS strategies for network self-adaptive learning are proposed under continuous and discrete monitoring, respectively. Based on these ETS approaches, several sufficient conditions for synchronization are derived by employing stochastic Lyapunov-Krasovskii functions, the properties of stochastic processes, and some linear matrix inequalities. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results and the superiority of the proposed ETS approach.