Intermittent control for finite-time synchronization of fractional-order complex networks

Containment control for fractional-order networked system with intermittent sampled position communication

This paper investigates containment control for fractional-order networked systems. Two novel intermittent sampled position communication protocols, where controllers only need to keep working during communication width of every sampling period under the past sampled position communication of neighbors' agents. Then, some necessary and sufficient conditions are derived to guarantee containment about the differential order, sampling period, communication width, coupling strengths, and networked structure. Taking into account of the delay, a detailed discussion to guarantee containment is given with respect to the delay, sampling period, and communication width. Interestingly, it is discovered that containment control cannot be guaranteed without delay or past sampled position communication under the proposed protocols. Finally, the effectiveness of theoretical results is demonstrated by some numerical simulations.

Synchronization of inertial complex-valued memristor-based neural networks with time-varying delays

The synchronization of inertial complex-valued memristor-based neural networks (ICVMNNs) with time-varying delays was explored in the paper with the non-separation and non-reduced approach. Sufficient conditions required for the exponential synchronization of the ICVMNNs were identified with the construction of comprehensive Lyapunov functions and the design of a novel control scheme. The adaptive synchronization was also investigated based on the derived results, which is easier to implement in practice. What's more, a numerical example that verifies the obtained results was presented.

Proportional-Integral Observer-Based State Estimation for Singularly Perturbed Complex Networks With Cyberattacks

This article investigates the asynchronous proportional-integral observer (PIO) design issue for singularly perturbed complex networks (SPCNs) subject to cyberattacks. The switching topology of SPCNs is regulated by a nonhomogeneous Markov switching process, whose time-varying transition probabilities are polytope structured. Besides, the multiple scalar Winner processes are applied to character the stochastic disturbances of the inner linking strengths. Two mutually independent Bernoulli stochastic variables are exploited to characterize the random occurrences of cyberattacks. In a practical viewpoint, by resorting to the hidden nonhomogeneous Markov model, an asynchronous PIO is formulated. Under such a framework, by applying the Lyapunov theory, sufficient conditions are established such that the augmented dynamic is mean-square exponentially ultimately bounded. Finally, the effectiveness of the theoretical results is verified by two numerical simulations.

Asynchronous Fault Detection for Memristive Neural Networks With Dwell-Time-Based Communication Protocol

This article studies the asynchronous fault detection filter problem for discrete-time memristive neural networks with a stochastic communication protocol (SCP) and denial-of-service attacks. Aiming at alleviating the occurrence of network-induced phenomena, a dwell-time-based SCP is scheduled to coordinate the packet transmission between sensors and filter, whose deterministic switching signal arranges the proper feedback switching information among the homogeneous Markov processes (HMPs) for different scenarios. A variable obeying the Bernoulli distribution is proposed to characterize the randomly occurring denial-of-service attacks, in which the attack rate is uncertain. More specifically, both dwell-time-based SCP and denial-of-service attacks are modeled by means of compensation strategy. In light of the mode mismatches between data transmission and filter, a hidden Markov model (HMM) is adopted to describe the asynchronous fault detection filter. Consequently, sufficient conditions of stochastic stability of memristive neural networks are devised with the assistance of Lyapunov theory. In the end, a numerical example is applied to show the effectiveness of the theoretical method.

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.

Energy scheduling for DoS attack over multi-hop networks: Deep reinforcement learning approach

This paper studies the energy scheduling for Denial-of-Service (DoS) attack against remote state estimation over multi-hop networks. A smart sensor observes a dynamic system, and transmits its local state estimate to a remote estimator. Due to the limited communication range of the sensor, some relay nodes are employed to deliver data packets from the sensor to the remote estimator, which constitutes a multi-hop network. To maximize the estimation error covariance with energy constraint, a DoS attacker needs to determine the energy level implemented on each channel. This problem is formulated as an associated Markov decision process (MDP), and the existence of an optimal deterministic and stationary policy (DSP) is proved for the attacker. Besides, a simple threshold structure of the optimal policy is obtained, which significantly reduces the computational complexity. Furthermore, an up-to-date deep reinforcement learning (DRL) algorithm, dueling double Q-network (D3QN), is introduced to approximate the optimal policy. Finally, a simulation example illustrates the developed results and verifies the effectiveness of D3QN for optimal DoS attack energy scheduling.

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.

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.

Strictly intermittent quantized control for fixed/predefined-time cluster lag synchronization of stochastic multi-weighted complex networks

This article addresses the fixed-time (F-T) and predefined-time (P-T) cluster lag synchronization of stochastic multi-weighted complex networks (SMWCNs) via strictly intermittent quantized control (SIQC). Firstly, by exploiting mathematical induction and reduction to absurdity, a novel F-T stability lemma is proved and an accurate estimation of settling time (ST) is obtained. Subsequently, by virtue of the proposed F-T stability, some simple conditions that ensure the F-T cluster lag synchronization of SMWCNs are derived by developing a SIQC strategy. Furthermore, the P-T cluster lag synchronization is also explored based on a SIQC design, where the ST can be predefined by an adjustable constant of the controller. Note that the designed controllers here are simpler and more economical than the traditional design whose the linear part is still activated during the rest interval. Finally, two numerical examples are provided to verify the effectiveness of the theoretical results.

Exponential Synchronization of Inertial Complex-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays via Periodically Intermittent Control

This paper mainly studies the exponential synchronization issue for the inertial complex-valued fuzzy cellular neural networks (ICVFCNNs) with time-varying delays via periodically intermittent control. To achieve exponential synchronization, we use a non-reduced order and non-separation approach, which is a supplement and innovation to the previous method. Based on directly constructing Lyapunov functional and a novel periodically intermittent control scheme, sufficient conditions for achieving the exponential synchronization of the ICVFCNNs are established. Finally, an example is given to illustrate the validity of the obtained results.

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.

Exponential synchronization for variable-order fractional discontinuous complex dynamical networks with short memory via impulsive control

This paper considers the exponential synchronization issue for variable-order fractional complex dynamical networks (FCDNs) with short memory and derivative couplings via the impulsive control scheme, where dynamical nodes are modeled to be discontinuous. Firstly, the mathematics model with respect to variable-order fractional systems with short memory is established under the impulsive controller, in which the impulse strength is not only determined by the impulse control gain, but also the order of the control systems. Secondly, the exponential stability criterion for variable-order fractional systems with short memory is developed. Thirdly, the hybrid controller, which consists of the impulsive coupling controller and the discontinuous feedback controller, is designed to realize the synchronization objective. In addition, by constructing Lyapunov functional and applying inequality analysis techniques, the synchronization conditions are achieved in terms of linear matrix inequalities (LMIs). Finally, two simulation examples are performed to verify the effectiveness of the developed synchronization scheme and the theoretical outcomes.