Finite-Time Synchronization and H∞ Synchronization of Multiweighted Complex Networks With Adaptive State Couplings

Finite-time H∞ output synchronization for DCRDNNs with multiple delayed and adaptive output couplings

This work concentrates on solving the finite-time H∞ output synchronization (FTHOS) issue of directed coupled reaction-diffusion neural networks (DCRDNNs) with multiple delayed and adaptive output couplings in the presence of external disturbances. Based on the output information, an adaptive law to adjust output coupling weights and a controller are respectively developed to ensure that the DCRDNNs achieve FTHOS. Then, in the special case of no external disturbances, a corollary on the finite-time output synchronization (FTOS) of the DCRDNNs with multiple delayed and adaptive output couplings is provided. In addition, a novel adaptive scheme to update output coupling weights is devised to ensure H∞ output synchronization (HOS) in the DCRDNNs with multiple delayed output couplings. Finally, the relevant simulation graphs are provided to certify the validity of several synchronization criteria.

Finite-Horizon H∞ State Estimation for Complex Networks With Uncertain Couplings and Packet Losses: Handling Amplify-and-Forward Relays

This article is concerned with the state estimation problem for a class of complex networks (CNs) with uncertain inner couplings and packet losses over communication networks. The inner couplings are allowed to be uncertain and varying in a specific interval. The amplify-and-forward (AaF) relay protocols are introduced to improve the communication quality and enhance the propagation distance. The Bernoulli random variables are used to characterize the randomly occurring packet losses encountered in communication channels. The focus of this article is on the design of a state estimator for each node of CNs such that a prescribed performance constraint is satisfied for the dynamical error system over a finite horizon. A sufficient condition is first provided to verify the existence of the desired state estimator, and the estimator gain is then determined by solving two coupled backward Riccati difference equations (RDEs). Subsequently, a recursive state estimation algorithm is put forward that is suitable for online computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed estimation method.

Event-triggered hybrid impulsive control for synchronization of fractional-order multilayer signed networks under cyber attacks

In this paper, we consider the exponential bipartite synchronization (EBS) problem of fractional-order multilayer signed networks with time-varying delays (FO-MSNT) under random cyber attacks. In contrast to the existing literature, the proposed hybrid event-triggered controller combines the advantages of feedback controller and impulsive controller, and the event-triggered condition is constructed by applying the network topology and the Lyapunov function of the subsystem, rather than the state function of the subsystem. Based on the Lyapunov-Razumikhin method and the graph theory, some sufficient conditions for achieving EBS of FO-MSNT under cyber attacks which are related to the topology of networks, the event-triggered parameters, the order of fractional derivative and the signal sent by the enemy are obtained. Furthermore, fractional-order coupled Chua's circuits model and fractional-order power systems built on MSNT are established and the EBS issues under cyber attacks are analyzed. Numerical examples and simulations are provided to show the validity of our theories.

Finite-time cluster synchronization for complex dynamical networks under FDI attack: A periodic control approach

In this paper, the finite-time cluster synchronization problem is addressed for complex dynamical networks (CDNs) with cluster characteristics under false data injection (FDI) attacks. A type of FDI attack is taken into consideration to reflect the data manipulation that controllers in CDNs may suffer. In order to improve the synchronization effect while reducing the control cost, a new periodic secure control (PSC) strategy is proposed in which the set of pinning nodes changes periodically. The aim of this paper is to derive the gains of the periodic secure controller such that the synchronization error of the CDN remains at a certain threshold in finite time with the presence of external disturbances and false control signals simultaneously. Through considering the periodic characteristics of PSC, a sufficient condition is obtained to guarantee the desired cluster synchronization performance, based on which the gains of the periodic cluster synchronization controllers are acquired by resolving an optimization problem proposed in this paper. A numerical case is carried out to validate the cluster synchronization performance of the PSC strategy under cyber attacks.

Disturbance rejection for multi-weighted complex dynamical networks with actuator saturation and deception attacks via hybrid-triggered mechanism

In this work, we address hybrid-driven-based robust synchronization problem for multi-weighted complex dynamical networks with actuator saturation and deception attacks. The hybrid-triggered mechanism, which combines a switch between the event-triggered scheme and the time-triggered scheme, is often used to reduce the data transmission and the alleviate network burden. Further, the equivalent-input-disturbance technique is applied to eliminate the unknown disturbance effect of the addressed system. Moreover, a memory controller is designed under actuator saturation to ensure that the resultant augmented system is asymptotically synchronized even in the presence of deception attacks. Finally, three numerical examples are given to show the validity of the obtained theoretical results.

Adaptive fixed-time output synchronization for complex dynamical networks with multi-weights

This paper addresses fixed-time output synchronization problems for two types of complex dynamical networks with multi-weights (CDNMWs) by using two types of adaptive control methods. Firstly, complex dynamical networks with multiple state and output couplings are respectively presented. Secondly, several fixed-time output synchronization criteria for these two networks are formulated based on Lyapunov functional and inequality techniques. Thirdly, by employing two types of adaptive control methods, fixed-time output synchronization issues of these two networks are dealt with. At last, the analytical results are verified by two numerical simulations.

New finite-time synchronization conditions of delayed multinonidentical coupled complex dynamical networks

In this article, we mainly focus on the finite-time synchronization of delayed multinonidentical coupled complex dynamical networks. By applying the Zero-point theorem, novel differential inequalities, and designing three novel controllers, we obtain three new criteria to assure the finite-time synchronization between the drive system and the response system. The inequalities occurred in this paper are absolutely different from those in other papers. And the controllers provided here are fully novel. We also illustrate the theoretical results through some examples.

Finite-time synchronization of reaction-diffusion memristive neural networks: A gain-scheduled integral sliding mode control scheme

The finite-time synchronization issue of reaction-diffusion memristive neural networks (RDMNNs) is studied in this paper. To better synchronize the parameter-varying drive and response systems, an innovative gain-scheduled integral sliding mode control scheme is proposed, where the 2ⁿ controller gains can be scheduled and an integral switching surface function that contains a discontinuous term is involved. Moreover, by constructing a novel Lyapunov-Krasovskii functional and combining reciprocally convex combination (RCC) method, a less conservative finite-time synchronization criterion for RDMNNs is derived in the form of linear matrix inequalities (LMIs). Finally, three numerical simulations are exploited to illustrate the effectiveness, superiority and practicability of this paper.

Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method

The finite-time synchronization (FNTS) problem for a class of delayed fractional-order fully complex-valued dynamic networks (FFCDNs) with internal delay and non-delayed and delayed couplings is studied by directly constructing Lyapunov functions instead of decomposing the original complex-valued networks into two real-valued networks. Firstly, a mixed delay fractional-order mathematical model is established for the first time as fully complex-valued, where the outer coupling matrices of the model are not restricted to be identical, symmetric, or irreducible. Secondly, to overcome the limitation of the use range of a single controller, two delay-dependent controllers are designed based on the complex-valued quadratic norm and the norm composed of its real and imaginary parts' absolute values, respectively, to improve the synchronization control efficiency. Besides, the relationships between the fractional order of the system, the fractional-order power law, and the settling time (ST) are analyzed. Finally, the feasibility and effectiveness of the control method designed in this paper are verified by numerical simulation.

A Dynamic Event-Triggered Approach to Recursive Nonfragile Filtering for Complex Networks With Sensor Saturations and Switching Topologies

In this article, the nonfragile filtering issue is addressed for complex networks (CNs) with switching topologies, sensor saturations, and dynamic event-triggered communication protocol (DECP). Random variables obeying the Bernoulli distribution are utilized in characterizing the phenomena of switching topologies and stochastic gain variations. By introducing an auxiliary offset variable in the event-triggered condition, the DECP is adopted to reduce transmission frequency. The goal of this article is to develop a nonfragile filter framework for the considered CNs such that the upper bounds on the filtering error covariances are ensured. By the virtue of mathematical induction, gain parameters are explicitly derived via minimizing such upper bounds. Moreover, a new method of analyzing the boundedness of a given positive-definite matrix is presented to overcome the challenges resulting from the coupled interconnected nodes, and sufficient conditions are established to guarantee the mean-square boundedness of filtering errors. Finally, simulations are given to prove the usefulness of our developed filtering algorithm.

Finite-time H∞ synchronization for complex dynamical networks with time-varying delays based on adaptive control

This paper investigates the problem of finite-time H_∞ synchronization (H_∞FTS) for complex dynamical networks (CDNs) with time-varying delays(TVDs) and unknown internal coupling matrices. External disturbances are also considered into this model. By applying the adaptive control theory, this paper presents the adaptive control method to solve the H_∞FTS of CDNs with external disturbances and TVDs. Some criteria are obtained by utilizing appropriate adaptive controllers and devising a special Lyapunov-Krasovskii function (LKF), which ensure the H_∞FTS of CDNs based on passivity theory. Finally, using some effective mathematical techniques, comparative numerical example and Chua's circuit system are used to explain the advantages and applicability of the results and approaches.

Projective Synchronization Analysis of Fractional-Order Neural Networks With Mixed Time Delays

In this article, we analyze the projective synchronization of fractional-order neural networks with mixed time delays. By introducing an extended Halanay inequality that is applicable for the case of fractional differential equations with arbitrary initial time and multiple types of delays, sufficient criteria are deduced for ensuring the projective synchronization of fractional-order neural networks with both discrete time-varying delays and distributed delays. Furthermore, sufficient criteria are presented for ensuring the projective synchronization in the Mittag-Leffler sense if there is no delay in fractional-order neural networks. The results derived herein include complete synchronization, anti-synchronization, and stabilization of fractional-order neural networks as particular cases. Moreover, the testable criteria in this article are a meaningful extension of projective synchronization of neural networks with mixed time delays from integer-order to fractional-order ones. A numerical simulation with four cases is provided to verify the validity of the obtained results.

Finite-Time Passivity and Synchronization of Multi-Weighted Complex Dynamical Networks Under PD Control

This article focuses on finite-time passivity (FTP) and finite-time synchronization (FTS) for complex dynamical networks with multiple state/derivative couplings based on the proportional-derivative (PD) control method. Several criteria of FTP for complex dynamical networks with multiple state couplings (CDNMSCs) are formulated by utilizing the PD controller and constructing an appropriate Lyapunov function. Furthermore, FTP is further used to investigate the FTS in CDNMSCs under the PD controller. In addition, the FTP and FTS for complex dynamical networks with multiple derivative couplings (CDNMDCs) are also studied by exploiting the PD control method and some inequality techniques. Finally, two numerical examples are worked out to demonstrate the validity of the presented PD controllers.

Finite-Time Output Synchronization of Multiple Weighted Reaction-Diffusion Neural Networks With Adaptive Output Couplings

This article mainly considers the output synchronization (OS) problem of multiple weighted and adaptive output coupled reaction-diffusion neural networks (RDNNs) without and with coupling delays in finite time. Without coupling delays, an adaptive control law and an output feedback controller are, respectively, proposed to ensure that the multiple weighted and output coupled RDNNs are output synchronized and output synchronized in finite time. With coupling delays, an adaptive coupling weights control scheme and a novel feedback controller are put forward to make the multiple weighted RDNNs with output couplings achieve OS in finite time. Moreover, the finite-time OS is considered in the presence of external disturbances. By the Lyapunov approach, several finite-time OS and OS criteria are given. Finally, two simulation examples are presented to justify the effectiveness of the proposed adaptive control laws and controllers.

Finite-Time H∞ State Estimation for Two-Time-Scale Complex Networks Under Stochastic Communication Protocol

The issue of finite-time H_∞ state estimation is studied for a class of discrete-time nonlinear two-time-scale complex networks (TTSCNs) whose measurement outputs are transmitted to a remote estimator via a bandwidth-limited communication network under the stochastic communication protocol (SCP). To reflect different time scales of state evolutions, a new discrete-time TTSCN model is devised by introducing a singular perturbation parameter (SPP). For the sake of avoiding/alleviating the undesirable data collisions, the SCP is adopted to schedule the data transmissions, where the transition probabilities involved are assumed to be partially unknown. By constructing a new Lyapunov function dependent on the information of the SCP and SPP, a sufficient condition is derived which ensures that the resulting error dynamics is stochastically finite-time bounded and satisfies a prescribed H_∞ performance index. By resorting to the solutions of several matrix inequalities, the gain matrices of the state estimator are given and the admissible upper bound of the SPP can be evaluated simultaneously. The performance of the designed state estimator is demonstrated by two examples.

Finite-Time Output Synchronization and H∞ Output Synchronization of Coupled Neural Networks With Multiple Output Couplings

This article investigates the finite-time output synchronization and H_∞ output synchronization problems for coupled neural networks with multiple output couplings (CNNMOC), respectively. By choosing appropriate state feedback controllers, several finite-time output synchronization and H_∞ output synchronization criteria are proposed for the CNNMOC. Moreover, a coupling-weight adjustment scheme is also developed to guarantee the finite-time output synchronization and H_∞ output synchronization of CNNMOC. Finally, two numerical examples are given to verify the effectiveness of the presented criteria.

H∞ State Estimation for Neural Networks With General Activation Function and Mixed Time-Varying Delays

This article deals with H_∞ state estimation of neural networks with mixed delays. In order to make full use of delay information, novel delay-product Lyapunov-Krasovskii functional (LKF) by using parameterized delay interval is first constructed. Then, generalized free-weighting-matrix integral inequality is used to estimate the derivative of LKF to reduce the conservatism. Also, a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model. Finally, sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed H_∞ performance. Numerical examples are simulated to show the benefits of our proposed method.

Exponential Stability of Fractional-Order Complex Multi-Links Networks With Aperiodically Intermittent Control

In this article, the exponential stability problem for fractional-order complex multi-links networks with aperiodically intermittent control is considered. Using the graph theory and Lyapunov method, two theorems, including a Lyapunov-type theorem and a coefficient-type theorem, are given to ensure the exponential stability of the underlying networks. The theoretical results show that the exponential convergence rate is dependent on the control gain and the order of fractional derivative. To be specific, the larger control gain, the higher the exponential convergence rate. Meanwhile, when aperiodically intermittent control degenerates into periodically intermittent control, a corollary is also provided to ensure the exponential stability of the underlying networks. Furthermore, to show the practicality of theoretical results, as an application, the exponential stability of fractional-order multi-links competitive neural networks with aperiodically intermittent control is investigated and a stability criterion is established. Finally, the effectiveness and feasibility of the theoretical results are demonstrated through a numerical example.

Synchronization Control for Discrete-Time-Delayed Dynamical Networks With Switching Topology Under Actuator Saturations

This article is concerned with the synchronization control problem for a class of discrete-time dynamical networks with mixed delays and switching topology. The saturation phenomenon of physical actuators is specifically considered in designing feedback controllers. By exploring the mixed-delay-dependent sector conditions in combination with the piecewise Lyapunov-like functional and the average-dwell-time switching, a sufficient condition is first established under which all trajectories of the error dynamics are bounded for admissible initial conditions and nonzero external disturbances, while the l₂ - l_∞ performance constraint is satisfied. Furthermore, the exponential stability of the error dynamics is ensured for admissible initial conditions in the absence of disturbances. Second, by using some congruence transformations, the explicit condition guaranteeing the existence of desired controller gains is obtained in terms of the feasibility of a set of linear matrix inequalities. Then, three convex optimization problems are formulated regarding the disturbance tolerance, the l₂ - l_∞ performance, and the initial condition set, respectively. Finally, two simulation examples are given to show the effectiveness and merits of the proposed results.

Finite-Horizon H∞ State Estimation for Stochastic Coupled Networks With Random Inner Couplings Using Round-Robin Protocol

This article is concerned with the problem of finite-horizon H_∞ state estimation for time-varying coupled stochastic networks through the round-robin scheduling protocol. The inner coupling strengths of the considered coupled networks are governed by a random sequence with known expectations and variances. For the sake of mitigating the occurrence probability of the network-induced phenomena, the communication network is equipped with the round-robin protocol that schedules the signal transmissions of the sensors' measurement outputs. By using some dedicated approximation techniques, an uncertain auxiliary system with stochastic parameters is established where the multiplicative noises enter the coefficient matrix of the augmented disturbances. With the established auxiliary system, the desired finite-horizon H_∞ state estimator is acquired by solving coupled backward Riccati equations, and the corresponding recursive estimator design algorithm is presented that is suitable for online application. The effectiveness of the proposed estimator design method is validated via a numerical example.

Output Synchronization of Complex Dynamical Networks With Multiple Output or Output Derivative Couplings

In this paper, the output synchronization problem for complex dynamical networks (CDNs) with multiple output or output derivative couplings is discussed in detail. Under the help of Lyapunov functional and inequality techniques, an output synchronization criterion is presented for CDNs with multiple output couplings (CDNMOCs). To ensure the output synchronization of CDNMOCs, an adaptive control scheme is also devised. Similarly, we also take into account the adaptive output synchronization and output synchronization of CDNs with multiple output derivative couplings. At last, several numerical examples are designed to testify the effectiveness of the proposed results.

Resilient asynchronous state estimation of Markov switching neural networks: A hierarchical structure approach

This paper deals with the issue of resilient asynchronous state estimation of discrete-time Markov switching neural networks. Randomly occurring signal quantization and packet dropout are involved in the imperfect measured output. The asynchronous switching phenomena appear among Markov switching neural networks, quantizer modes and filter modes, which are modeled by a hierarchical structure approach. By resorting to the hierarchical structure approach and Lyapunov functional technique, sufficient conditions are achieved, and asynchronous resilient filters are derived such that filtering error dynamic is stochastically stable. Finally, two examples are included to verify the validity of the proposed method.

Exponential H∞ Filtering for Continuous-Time Switched Neural Networks Under Persistent Dwell-Time Switching Regularity

This paper focuses on the exponential H_∞ filtering issue for a class of continuous-time switched neural networks (NNs). Our aim is to design a mode-dependent filter acquiring the state of the investigated system, and ensuring the global uniform exponential stability of the resulting filtering error system. The persistent dwell-time (PDT) switching strategy is employed to represent the switching among NNs. By utilizing a suitable Lyapunov function and the switched system theory, some criteria for the solvability of the addressed problem are presented under the full consideration of switching frequency. Finally, the filter gains are derived by a straightforward decoupling method, and with the aid of the algorithm of the continuous-time PDT switching regularity, the availability of the filter is expounded through a numerical example.