Class Of Complex Dynamical Networks Research Articles

Finite-Time Synchronization of Complex Dynamical Networks With Input Saturation.

In the framework of input saturation, this article studies the problem of finite-time synchronization (FTS) of a class of complex dynamical networks. By designing different classes of saturated controllers, two types of FTS criteria, including leader-follower synchronization and leaderless synchronization, are presented, respectively. A potential relationship between the saturation structure, the settling time, and the domain of attraction is established, which is crucial to achieve FTS. It shows that the saturation structure not only affects the estimation of domain of attraction but also possibly changes the settling time for FTS. Two numerical examples are presented to illustrate the effectiveness of the proposed results.

Synchronization of switched complex dynamical networks with impulses: state-dependent switching approach

This paper studies the globally exponential synchronization (GES) of a class of complex dynamical networks (CDNs) with switching topology involving impulse action. A novel state-dependent switching (SDS) approach to tune the switching topology of CDNs is designed based on the information of the node dynamics with impulses. Different from the traditional SDS results which are based on continuous state space, some sufficient conditions for network synchronization based on SDS are proposed in the framework of impulse action. A relationship between impulse action, the network structure, and switching topology is established, which is crucial to design the SDS law. Two different impulse actions on the network dynamics are fully considered in this paper, namely, stabilizing continuous dynamics with desynchronizing impulses and destabilizing continuous dynamics with synchronizing impulses. Finally, two numerical simulations are given to demonstrate the effectiveness of the proposed control method.

Predictive-based control of complex dynamic networks

This paper addresses the problem of designing a robust controller for a class of complex dynamical networks (CDNs). This class of CDNs is characterized by a scale-free typical structure with Rossler and Lorenz-type nodes. Direct control of every node in a CDN with a large number of nodes might be unnecessary. Based on the concept of pinning control of continuous-time chaotic systems and the matrix measure theory, some simple stability criteria are derived to guarantee the asymptotic stability of the system states such that all the system states of the closed-loop system converge towards the desired unstable equilibrium points. Consequently, the proposed controller developed here for scale-free networks can be employed to handle a broader class of CDNs with different types of nodes. Numerical simulations are provided to show the effectiveness of the proposed control method.

Dynamic event-triggered synchronisation control for complex dynamical networks with stochastic attacks and actuator faults

ABSTRACT This paper studies the problem of dynamic adaptive event-triggered synchronisation control for a class of complex dynamical networks (CDNs) with parameter uncertainty and stochastic network attacks. In order to save communication resources, reduce the driving burden and overcome the conservatism of fixed parameters, an improved event-triggered control strategy is designed. Firstly, a new synchronisation error model with uncertain of internal coupling weights between nodes and stochastic network attacks on actuator is modelled. Secondly, the Bernoulli stochastic distribution process is used to describe the probability of stochastic attacks, and the actuator failure model is adopted to depict actuator failure. By establishing an appropriate Lyapunov function, some sufficient conditions to ensure the asymptotic stability of the synchronisation error system is derived, which reduces conservatism. In addition, the cooperative design of controller and adaptive event-triggered strategy is solved by solving linear matrix inequality. Eventually, two examples are given to illustrate the effectiveness and potential of the proposed design method.

Synchronization of Complex Dynamical Networks Subject to Noisy Sampling Interval and Packet Loss.

This article focuses on the sampled-data synchronization issue for a class of complex dynamical networks (CDNs) subject to noisy sampling intervals and successive packet losses. The sampling intervals are subject to noisy perturbations, and categorical distribution is used to characterize the sampling errors of noisy sampling intervals. By means of the input delay approach, the CDN under consideration is first converted into a delay system with delayed input subject to dual randomness and probability distribution characteristic. To verify the probability distribution characteristic of the delayed input, a novel characterization method is proposed, which is not the same as that of some existing literature. Based on this, a unified framework is then established. By recurring to the techniques of stochastic analysis, a probability-distribution-dependent controller is designed to guarantee the mean-square exponential synchronization of the error dynamical network. Subsequently, a special model is considered where only the lower and upper bounds of delayed input are utilized. Finally, to verify the analysis results and testify the effectiveness and superiority of the designed synchronization algorithm, a numerical example and an example using Chua's circuit are given.

Impulsive cluster synchronization for complex dynamical networks with packet loss and parameters mismatch

This paper investigates the cluster synchronization (CS) for a class of complex dynamical networks (CDNs) with parameters mismatch to the selected cluster pattern. An impulsive control strategy with multiple control gains is proposed. Particularly, the possible packet loss phenomenon in control input is fully considered, and it is characterized by a series of impulse packet loss rate (iPLR) conditions. In terms of the reverse average dwell time (rADT) condition and the average impulse gain method, some sufficient conditions guaranteing that all the nodes of CDNs can be synchronized to their cluster sets are derived, from which the constraint relationships among rate coefficients, impulsive control law, and iPLR can be revealed. Finally, an example is given to illustrate the correctiveness of our results.

Model Following Adaptive Control for a Class of Complex Dynamic Networks Based on the Dynamics of Links

Model Following Adaptive Control for a Class of Complex Dynamic Networks Based on the Dynamics of Links

Robust Dynamic Output Feedback Event-Triggering Synchronization for Complex Dynamical Networks

In this study, we investigate the co-design of dynamic output feedback synchronization controllers and event-triggering conditions for a class of complex dynamical networks (CDNs). The measurement output and control input are transmitted to the controller and actuators asynchronously over the individual communication channels of each network node. We address the sufficient conditions for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula> stability of the error dynamics between the isolated and network nodes in the presence of external disturbances and noise in the measurement outputs and control inputs. Finally, we propose co-design conditions of the dynamic output feedback law and event-triggering conditions in terms of linear matrix inequalities (LMIs). Based on the proposed LMIs, we formulate an optimization problem to reduce the number of transmissions over each channel of the nodes. Numerical example results are provided to show the effectiveness of the proposed method.

Optimal Output Synchronization Control of a Class of Complex Dynamical Networks With Partially Unknown System Dynamics

This paper is concerned with the optimal output synchronization control problem for a class of heterogeneous complex dynamical networks (CDNs) with partially unknown system dynamics. By defining a new quadratic performance index including the information of state couplings, an optimal controller consisting of a feedback control and a compensated feedforward control is then designed. A necessary and sufficient condition for the optimal control minimizing the quadratic performance index is established. Especially, an algebraic Riccati equation (ARE) associated with a discount factor is obtained, and a novel online iteration algorithm by iteratively solving the ARE is proposed to compute the optimal controller gain for the case that the CDNs are with partially unknown system dynamics. Moreover, it is proved that the output synchronization errors converge to zero asymptotically by applying the optimal control laws. Finally, two simulation examples are provided to verify the effectiveness of the proposed control method.

Structural Balance Control of Complex Dynamical Networks Based on State Observer for Dynamic Connection Relationships

This paper investigates the observer-based structural balance control for a class of complex dynamical networks. Generally speaking, a complete complex dynamical network is composed of two coupled subsystems, which are called node subsystem (NS) and connection relationship subsystem (CS), respectively. Similar to synchronization and stabilization of networks, the structural balance is another phenomenon of networks and determined by the state of connection relationships. However, it is not feasible to design the controller for the CS directly because the states of the connection relationships are difficult to be measured accurately in practical applications. In order to solve this problem, a state observer for the CS has been designed. Thus, the structural balance controller in the CS can be directly designed by using the estimation information of the state observer. Then, with the help of the Lyapunov stability theory, it is proved that the CS can asymptotically track a given structural balance matrix under the influence of the observer-based controller. Finally, the results derived from this paper are demonstrated by performing a numerical example.

Uncertainty and disturbance rejections of complex dynamical networks via truncated predictive control

This study investigates the combined problems of uncertainty and disturbance rejections and synchronization of a class of complex dynamical networks with input delay. Specifically, a new uncertainty and disturbance estimator (UDE)-based truncated predictive control approach is used to simultaneously compensate the effects of unknown bounded disturbance and known input delay. The proposed approach relies on the conventional state prediction model to estimate the current state for the feedback by using the delayed state information and the estimation error is treated as an additional disturbance. Then, the effects of uncertainty and disturbance in the system model are robustly canceled with an appropriate filter based on the UDE approach. In addition, a set of sufficient conditions that guarantees the synchronization of the concerned system, the input delay compensation and the asymptotic disturbance rejection is derived with the aid of Lyapunov stability theory. In numerical examples, the proposed control method shows the better state estimation and robust synchronization performance by suppressing the effects of uncertainty and disturbance without any prior knowledge about them.

Adaptive Control of the Structural Balance for a Class of Complex Dynamical Networks

Adaptive Control of the Structural Balance for a Class of Complex Dynamical Networks

$${H_\infty }$$/passive synchronization for complex dynamical networks with semi-Markovian jump and coupling time-varying delays based on sampled-data control

This paper investigates $${H_\infty }$$/passive synchronization for a class of complex dynamical networks with semi-Markovian jump and coupling time-varying delays based on sampled-data control. The main purpose is to design a sampled-data controller, using discrete controller approach, to ensure $${H_\infty }$$/passive synchronization of the closed-loop error system. By constructing a novel Lyapunov–Krasovskii functional, in which the characteristics of the sampled-data are fully considered, then combining some integral inequalities, free weighting matrices and convex combination method, we establish the $${H_\infty }$$/passive synchronization criterion for a class of complex dynamical networks with semi-Markovian jump. Moreover, the proposed synchronization criterion can be simplified into the form of linear matrix inequalities using Matlab toolbox. Finally, two numerical examples are given to verify the validity and practicability of the theoretical results.

Finite-time synchronization of uncertain complex dynamic networks with time-varying delay

This study investigates the finite-time synchronization of uncertain nonlinear complex dynamic networks with time-varying delay. For a class of complex network models with time-varying delay and uncertain system parameters, the time delay changes infrequently, uncertain terms are unknown but bounded, and the matching conditions are satisfied. The coupling relationship between nodes is a nonlinear function with time delay, and the function satisfies the Lipschitz condition. A new criterion for the finite-time synchronization of a class of complex dynamical networks with variable delay is obtained, and the upper bound of the time for the system to achieve synchronization is presented by constructing a suitable Lyapunov–Krasovskii function, designing a nonlinear controller, and combining analysis techniques, such as matrix inequality. Finally, the validity of finite-time synchronization is verified through computer simulation.

Finite-Time Synchronization of Uncertain Complex Dynamic Networks with Nonlinear Coupling

The finite-time synchronization control is studied in this paper for a class of nonlinear uncertain complex dynamic networks. The uncertainties in the network are unknown but bounded and satisfy some matching conditions. The coupling relationship between network nodes is described by a nonlinear function satisfying the Lipchitz condition. By introducing a simple Lyapunov function, two main results regarding finite-time synchronization of a class of complex dynamic networks with parameter uncertainties are derived. By employing some analysis techniques like matrix inequalities, suitable controllers can be designed based on the obtained synchronization criteria. Moreover, with the obtained control input, the time instant required for the system to achieve finite-time synchronization can be estimated if a set of LMIs are feasible or an assumption on the eigenvalues of some matrices can be satisfied. Finally, the effectiveness of the proposed results is verified by numerical simulation.

Cluster synchronization for a class of complex dynamical network system with randomly occurring coupling delays via an improved event-triggered pinning control approach

This paper discusses the cluster synchronization problem for a class of complex dynamical networks with coupling time delays. Under the randomly occurring coupling time delays condition, a novel complex network model is established to express the dynamical behavior of the nodes more precisely. An improved event-triggered mechanism is proposed for two purpose containing the reduction of network burden and improvement of cluster synchronization efficiency. The pinning control strategy is adopted for cluster synchronization via controlling a small fraction of the network nodes. By employing Lyapunov–Krasovskii functional method, a stability criterion is obtained to ensure the achievement of cluster synchronization and a event-triggered pinning controller is constructed. Finally, a simulation example is expressed to verify the effectiveness of our main results.

Synchronisation for complex dynamical networks with hybrid coupling time-varying delays via pinning adaptive control

ABSTRACTThis paper is concerned with the problem of synchronisation for complex networks with hybrid coupling time delays. The control strategy consisting of adaptive control and pinning adaptive control is considered. Together with an augment Lyapunov–Krasovskii functional and using the effective mathematical techniques, several conditions are derived to guarantee a class of complex dynamical networks with hybrid coupling time-varying delays to be synchronised. Finally, some representative examples are simulated to demonstrate the effectiveness of the proposed approach.

Fault-tolerant passive synchronization for complex dynamical networks with Markovian jump based on sampled-data control

This paper investigates fault-tolerant passive synchronization for a class of complex dynamical networks with Markovian jump and coupling time-varying delays based on sampled-data control. The main purpose is to design a fault-tolerant sampled-data controller to ensure that the closed-loop error system is passively synchronous in the presence of actuator failure. By constructing a novel Lyapunov–Krasovskii functional, in which the characteristics of the sampled-data are fully considered. Then combining some integral inequalities, free weighting matrices and convex combination method, we establish the passive synchronization criterion for a class of complex dynamical networks with Markovian jump. Moreover, the proposed passive synchronization criterion can be simplified into the form of linear matrix inequalities (LMIs) using Matlab toolbox. Finally, two numerical examples are given to verify the validity and practicability of the theoretical results.

Global pinning synchronization of stochastic delayed complex networks

In this paper, the global pinning synchronization problem of a class of complex dynamical networks with hybrid couplings, time delays, random data packet dropouts and multiple stochastic disturbances is investigated. The hybrid couplings are portrayed in three forms: constant couplings, discrete-delay couplings and distributed-delay couplings. The phenomenon of random packet dropouts is described as a binary random variable which obeys the Bernoulli distribution taking values of 0 and 1 with a certain probability. Multiple noisy processes herein are characterized by Brownian motions, which act on all coupling terms as well as the overall dynamics equation. By applying the Lyapunov method and stochastic analysis technique, sufficient conditions are established to ensure the considered stochastic delayed complex network to globally synchronize to a reference trajectory in the mean-square sense via the developed randomly occurring pinning control strategy. The obtained criteria are within the framework of linear matrix inequations. Finally, a simulation example is presented to verify the feasibility and effectiveness of the derived theoretical results.

Lithium versus valproate: Prescribing profile of mood stabilisers for bipolar disorder in an acute care unit

This paper investigates fault-tolerant passive synchronization for a class of complex dynamical networks with Markovian jump and coupling time-varying delays based on sampled-data control. The main purpose is to design a fault-tolerant sampled-data controller to ensure that the closed-loop error system is passively synchronous in the presence of actuator failure. By constructing a novel Lyapunov–Krasovskii functional, in which the characteristics of the sampled-data are fully considered. Then combining some integral inequalities, free weighting matrices and convex combination method, we establish the passive synchronization criterion for a class of complex dynamical networks with Markovian jump. Moreover, the proposed passive synchronization criterion can be simplified into the form of linear matrix inequalities (LMIs) using Matlab toolbox. Finally, two numerical examples are given to verify the validity and practicability of the theoretical results.