Delayed Complex Dynamical Networks Research Articles

Adaptive pinning control to topology identification of output stochastic complex dynamical network

This paper concerns partial topology identification problem of stochastic delayed complex dynamical network. Compared with many network models, the novel output coupling is introduced to the network model of this paper, which does not require all state variables of the vertex to be observable. By utilizing the graph-theoretic method and adaptive pinning control technology, the identification criteria of multi-weighted stochastic complex dynamical networks are obtained. Ultimately, the Lorenz system and small-world network are chosen to do numerical simulations. The simulation results indicate that the successful identification time (SIT) of stochastic delayed complex dynamical network with output coupling is reduced by about 56% on average by comparing with the SIT of the network without output coupling, which implies the superiority of output coupling.

Local Synchronization for Delayed Complex Dynamical Networks via Self-Triggered Impulsive Control Involving Delays.

This article investigates the local synchronization for delayed complex dynamical networks (CDNs) under self-triggered impulsive control (STIC) approaches involving delays. With the help of Lyapunov-Razumikhin methods and comparison principle, some design criteria of STIC strategies ensuring local synchronization for delayed CDNs with delayed impulses are provided, and Zeno behavior can be avoided. Compared with the existing results on synchronization of CDNs under STIC, in this article, time delays in both continuous and discrete system dynamics are well considered. Moreover, the proposed self-triggered mechanism (STM) is an explicit expression, under which the next triggering instant can be derived directly, with simple structure and easy implementation. Finally, two numerical examples are provided to validate the proposed theoretical criteria.

Finite-Time Topology Identification of Delayed Complex Dynamical Networks and Its Application

To understand the functional behaviors of systems built on networks, it is essential to determine the uncertain topology of these networks. Traditional synchronization-based topology identification methods generally converge asymptotically or exponentially, resulting in their inability to give timely identification results. The finite-time stability theory is adopted in this paper with the aim of addressing the problem of fast identification of uncertain topology in networks. A novel finite-time topology observer is proposed to achieve finite-time topology identification and synchronization of general complex dynamical networks with time delay and second-order dynamical networks with time delay and nonlinear coupling. In addition, the proposed finite-time identification method is applied to power grids to address the problem of fast detection of line outages. Finally, 2 numerical experiments are provided to demonstrate the effectiveness and rapidity of the proposed finite-time identification method.

Global μ-synchronization for coupling delayed complex dynamical networks via event-triggered delayed impulsive control

This paper mainly focuses on solving the global μ-synchronization issue of complex dynamical networks (CDNs) by a novel event-triggered impulsive control (ETIC) method with time delays. This method combines the advantages of impulsive control and event-triggered control and gets rid of the limitation that the Lyapunov function decreases strictly monotonically with the sequence of event triggers. An event-triggered mechanism is specifically designed to realize μ-synchronization for CDNs in this paper, which means that event-triggered control has been applied to μ-synchronization field for the first time. Compared with periodic impulsive control, ETIC only produces control effects when the event-triggered mechanism are met, which is more in line with the actual situation. By Lyapunov–Razumikhin, recursion, etc, some valid global μ-synchronization criteria of CDNs are obtained and also Zeno behavior is avoided. Additionally, coupled delays and uncertainties are considered in CDNs. Finally, two numerical examples are shown to demonstrate the correctness of the designed ETIC strategy.

Event-based Exponential Synchronization of Delayed Complex Dynamical Networks via Intermittent Control with Actuator Saturation

Event-based Exponential Synchronization of Delayed Complex Dynamical Networks via Intermittent Control with Actuator Saturation

Improved Nonfragile Sampled-Data Event-Triggered Control for the Exponential Synchronization of Delayed Complex Dynamical Networks

The exponential synchronization of complex dynamical networks (CDNs) under improved nonfragile sampled-data event-triggered control (INFSDETC) is investigated in this study. A meaningful yet challenging issue is solved, namely, it can adjust the triggering mode and the triggering frequency to adapt to more situations in the event-triggered scheme in which it is able to adjust the triggering condition exponentially and linearly, and dynamically adjust the triggering according to the time and state. By using control theory and Lyapunov analysis theory, an improved event-triggered controller was constructed for more intelligent control and to ensure exponential synchronization for CDNs. Lastly, significant numerical simulation examples are developed to show the usefulness and the performance of the proposed methods.

Synchronization of delayed complex dynamical networks with actuator failure by event-triggered pinning control

This paper investigates the synchronization problem of delayed complex dynamical networks (DCDNs) with actuator failure under dynamical event-triggered pinning control (ETPC). Firstly, the fault-tolerant control system (FTCS) based on pinning control is introduced for DCDNs with time-varying actuator faults, which can reduce the cost of synchronization control. By setting internal dynamical variables, a new event-triggered control (ETC) strategy is designed. Then, it is proved that this control scheme can not only ensure global exponential synchronization of DCDNs based on Lyapunov theory, but also effectively avoid Zeno behavior and can reduce the burden on networks communication. At last, a simulation example verifies the reliability of the introduced dynamical ETPC strategy.

Finite-Time Synchronization for Delayed Complex Dynamical Networks With Synchronizing or Desynchronizing Impulses.

In this article, the finite-time synchronization problem of delayed complex dynamical networks (CDNs) with impulses is studied, where two types of impulses, namely, synchronizing impulses and desynchronizing impulses, are fully considered, respectively. Since the existence of impulses makes the discontinuity of the states, which means that the classical result for finite-time stability is inapplicable in such a case, the key challenge is how to guarantee the finite-time stability and estimate the settling time in impulse sense. We apply impulsive control theory and finite-time stability theory to CDNs and establish some sufficient conditions for finite-time synchronization, where two kinds of memory controllers are designed for synchronizing impulses and desynchronizing impulses, respectively. Moreover, the upper bounds for settling time of synchronization, which depends on the impulse sequences, are effectively estimated. It shows that the synchronizing impulses can shorten the settling time of synchronization; conversely, the desynchronizing impulses can delay it. Finally, the theoretical analysis is verified by two simulation examples.

Aperiodically intermittent pinning outer synchronization control for delayed complex dynamical networks with reaction-diffusion terms

In this paper, we mainly study the outer synchronization problem of complex dynamical networks (CDNs) involving delays and reaction-diffusion terms by aperiodically intermittent pinning control (AIPC). By using piecewise function and Lyapunov-Krasovskii functional method, some criteria for the complete and exponential outer synchronization of the corresponding CDNs with and without the coupling delay are obtained. Furthermore, two numerical examples are provided to illustrate the effectiveness of the obtained results.

Quasi-synchronization analysis for fractional-order delayed complex dynamical networks

This paper studies the global exponential quasi-synchronization for fractional-order delayed dynamical networks via periodically intermittent pinning control. Firstly, we present some new fractional-order delayed differential inequalities. Then based on the obtained inequalities, the Lyapunov method as well as the periodically intermittent pinning controller, sufficient conditions for achieving global exponential quasi-synchronization is derived for the addressed networks. Finally, numerical simulations are provided to verify the theoretical results.

Observer-based output feedback synchronisation control of delayed complex dynamical networks with two-channel dynamic event-triggered schemes and quantisations

Based on a distributed state observer, the problem of output feedback synchronisation control for a class of discrete-time delayed complex dynamical networks is studied. In order to solve the energy consumption and communication constraints, dynamic event-triggered mechanisms on sensor and controller sides are proposed by introducing two internal dynamical variables, respectively. Compared with traditional static event-triggered schemes, it effectively reduces the frequency of controller and observer update. Meanwhile, the effects of quantisation occurring in both input and output channels are considered. By means of the linear matrix inequality approach, the distributed state observer and output feedback controller of delayed complex dynamical networks can be designed simultaneously. The exponentially ultimately boundedness of synchronisation errors and estimation errors of complex dynamical networks is guaranteed via the Lyapunov stability theory. Finally, the circuit realisations for the proposed dynamic event-triggered synchronisation control approach are given, and the effectiveness of the obtained theoretical results is demonstrated through the simulation.

Event‐triggered approach for finite‐time state estimation of delayed complex dynamical networks with random parameters

SummaryThis article emphasizes the finite‐time state estimation problem for delayed complex dynamical networks with random parameters. In order to reduce the amount of transmission process, an aperiodic sampled‐data event‐triggered mechanism is introduced to determine whether the measurement output should be released at certain time points which incorporate an appropriate triggering condition and sampling moments. Furthermore, a concept of finite‐time boundedness in the pth moment is proposed to access the performance of state estimator. The objective of this article is to design an event‐triggered state estimator to estimate the states of nodes such that, in the presence of time delays, uncertainties, and randomly changing coupling weights, the estimation error system is finite‐time bounded in the pth moment related to a given constant. Some sufficient conditions in form of linear matrix inequalities and algebraic inequalities are established to guarantee finite‐time boundedness. Finally, a numerical example is presented to show the effectiveness of the theoretical results.

Pinning Synchronization of Stochastic T-S Fuzzy Delayed Complex Dynamical Networks with Heterogeneous Impulsive Delays

Pinning Synchronization of Stochastic T-S Fuzzy Delayed Complex Dynamical Networks with Heterogeneous Impulsive Delays

Novel results on nonfragile sampled‐data exponential synchronization for delayed complex dynamical networks

SummaryThis article investigates exponential synchronization for complex dynamical networks (CDNs) with nonfragile sampled‐data feedback control. An important yet challenging problem that contains the time delays of the controller, the uncertainties occurrence and randomness of controller gain fluctuation due to the packet loss, and time delays during data transmission is to be solved. A novel Lyapunov‐Krasovskii functional (LKF) that allows for more free matrix terms and slacks certain one of the terms to nonpositive definite is first constructed based upon special refined block matrices. By employing the novel LKF and functional analysis theory, the nonfragile sampled‐data feedback controller is developed to guarantee the exponential synchronization of CDNs and make a more optimal bound estimation of the sampled period. Finally, compared simulation examples are performed as significant to demonstrate the effective performance and the superiority of the proposed methods.

Adaptive Output Synchronization of General Complex Dynamical Network with Time-Varying Delays

This paper is concerned with the output synchronization problems for a class of delayed complex dynamical networks. Based on the invariant principle of functional differential equations and Lyapunov stability theory, the feedback controller and parameter update laws are constructed for a large-scale network with uncertainties. The general complex delayed network can achieve synchronization by adaptively adjusting their feedback gains. Numerical examples are presented to further verify the effectiveness of the proposed control scheme.

Finite-time cluster synchronization for time-varying delayed complex dynamical networks via hybrid control

Throughout this article, the conundrum on finite-time cluster synchronization is investigated for time-varying delayed complex dynamical networks using a kind of new hybrid control scheme. In the light of Lyapunov stability theorem and finite-time control theory, the finite-time cluster synchronization criteria can be achieved. Besides, we introduce the distinction between cluster synchronization and complete synchronization, which is how to select the controlling nodes. We discuss the differences among cluster synchronization with time-varying delays, complete synchronization with time-varying delays, cluster synchronization with a single delay, and cluster synchronization without delay, which is on constructing Lyapunov functional and designing the finite-time hybrid controllers. Finally, numerical simulations are presented to demonstrate the availability of the theoretical consequences.

Sliding mode synchronization of a delayed complex dynamical network in the presence of uncertainties and external disturbances

This paper is concerned with the problem of robust sliding mode [Formula: see text] control of a delayed complex dynamical network subject to parametric uncertainties and external disturbances. In this regard, synchronization error dynamics between the nodes of the complex dynamical network and an individual node are derived. Based on Lyapunov–Krasovskii stability theory, sliding mode [Formula: see text] control laws are designed to force the state trajectories of the error dynamics to sliding manifolds and are maintained thereafter. Moreover, an [Formula: see text] control law is designed to compare its results with the proposed method. By simulating a numerical Chua’s circuit, it is shown that the proposed method is effective at attenuating the effect of the external disturbances and parametric uncertainties.

Nonfragile Sampled-Data Synchronization for Delayed Complex Dynamical Networks With Randomly Occurring Controller Gain Fluctuations

In this paper, the problem of nonfragile sampled-data synchronization of delayed complex dynamical networks with randomly occurring controller gain fluctuations (ROCGFs) is studied. First, more applicable nonfragile memory sampled-data controllers are designed, which involve the signal transmission delay and ROCGFs. The controller gain fluctuations appear in a random way, which obey certain Bernoulli distributed white noise sequences. Second, a modified piecewise Lyapunov-Krasovskii functional (LKF), which involves cubic sawtooth structure term, is constructed for the first time. Third, based on the LKF, less conservative synchronization criteria are established. In comparison with the existing results, the constraint condition of the positive definition of the LKF is less restrictive, since it does not need to be positive definite for all time, but is only required to be positive definite at sampling times. Finally, the effectiveness and advantages of the obtained results are illustrated by two numerical examples.

Non-fragile exponential synchronization of delayed complex dynamical networks with transmission delay via sampled-data control

This paper is devoted to the non-fragile exponential synchronization problem of complex dynamical networks with time-varying coupling delays via sampled-data static output-feedback controller involving a constant signal transmission delay. The dynamics of the nodes contain s quadratically restricted nonlinearities, and the feedback gain is allowed to have norm-bounded time-varying uncertainty. The control design is based on a Lyapunov–Krasovskii functional, which consists of the sum of terms assigned to the individual nodes, i.e., it is constructed without merging the complex dynamical network’s nodes into a single large-scale system. In this way, the proposed design method has substantially reduced computational complexity and improved conservativeness, and guaranties non-fragile exponential stability of the error system. The sufficient stability condition is expressed in terms of linear matrix inequalities that are solvable by standard tools. The efficiency of the proposed method is illustrated by numerical examples.

Consecutive Synchronization of a Delayed Complex Dynamical Network via Distributed Adaptive Control Approach

In this paper, a consecutive synchronization scheme is investigated to synchronize the nodes of a delayed complex dynamical network with an isolated node via an adaptive control approach. The specific feature of this scheme consists in the structure of the communication links: a communication connection is required between the isolated node and one selected node in the network, and further communication links exist between any node and one neighbor node. In this way, all nodes are connected together like a chain. Based on Lyapunov-Krasovskii theory, some conditions are obtained in the form of linear matrix inequalities to guarantee the consecutive synchronization by the designed distributed adaptive control. To make this synchronization scheme more practical, no constraints have been considered for coupling connection matrix such as being symmetric or zero row sum. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method.