Coordinated chaos control of urban expressway based on synchronization of complex networks

We investigate the problem of coordinated chaos control on an urban expressway based on pinning synchronization of complex networks. A node coupling model of an urban expressway based on complex networks has been established using the cell transmission model（CTM）. The pinning controller corresponding to multi-ramp coordinated controller was designed by using the delayed feedback control（DFC） method, whose objective is to realize periodical orbits from chaotic states. The concrete pinning control nodes corresponding to the subsystems of regulating the inflows from the on-ramps to the mainline were obtained and the parameters of the controller were optimized by using the stability theory of complex networks to ensure the network synchronization. The validity of the proposed coordinated chaos control method was proven via the simulation experiment. The results of the examples indicated that the order motion on urban expressway can be realized, the wide-moving traffic jam can be suppressed, and the operating efficiency is superior to that of the traditional control methods.

Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control

The finite-time synchronization of fractional-order multi-weighted complex networks(FMCNs)with uncertain parameters and external disturbances is studied.Firstly,based on fractional calculus characteristics and Lyapunov stability theory,quantized controllers are designed to guarantee that FMCNs can achieve synchronization in a limited time with and without coupling delay,respectively.Then,appropriate parameter update laws are obtained to identify the uncertain parameters in FMCNs.Finally,numerical simulation examples are given to validate the correctness of the theoretical results.

Hybrid Synchronization of Fractional-Order Complex Networks Model via Fractional Order Controller

For the purpose of investigating two complex networks' hybrid synchronization,a controller with fractional-order is provided.Regarding hybrid synchronization which includes the outer synchronization and inner synchronization,some hybrid synchronization's sufficient conditions according to the Lyapunov stability theorem and the LaSalle invariance principle are proposed.Theoretical analysis suggests that,only when the state of driving-response networks is outer synchronization and each network is in inner synchronization,two coupled networks' hybrid synchronization under some suitable conditions could be reached.Finally,theoretical results are illustrated and validated with the given numerical simulations.

Pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions

This paper studies pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions. To study a state-feedback pinning-controlled network with N nodes, it first converts the controlled network to an extended network of N＋1 nodes without controls. It is shown that the controlled synchronizability of the given network is determined by the real part of the smallest nonzero eigenvalue of the coupling matrix of its extended network when the synchronized region is unbounded; but it is determined by the ratio of the real parts of the largest and the smallest nonzero eigenvalues of the coupling matrix when the synchronized region is bounded. Both theoretical analysis and numerical simulation show that the portion of controlled nodes has no critical values when the synchronized region is unbounded, but it has a critical value when the synchronized region is bounded. In the former case, therefore, it is possible to control the network to achieve synchronization by pinning only one node. In the latter case, the network can achieve controlled synchronization only when the portion of controlled nodes is larger than the critical value.

Controlled synchronization of complex network with different kinds of nodes

In this paper, a new dynamical network model is introduced, in which the nodes of the network are different. It is shown that by the designed controllers, the state of the network can exponentially synchronize onto a homogeneous stationary state. Some criteria are derived and some examples are presented. The numerical simulations coincide with theoretical analysis.

Impulsive synchronization of a nonlinear coupled complex network with a delay node

We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node. Both delay coupling and non-delay coupling, as well as the symmetrical coupling matrix and the asymmetrical coupling matrix are considered. Based on the comparison theorem of an impulsive differential system, some novel synchronization criteria are derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.

Impulsive synchronization of two coupled complex networks with time-delayed dynamical nodes

In this paper, we investigate the impulsive synchronization between two coupled complex networks with time- delayed dynamical nodes. Based on the Lyapunov stability, the linear feedback control and the impulsive control theories, the linear feedback and the impulsive controllers are designed separately. By using the generalized Barbalat＇s lemma, the global asymptotic impulsive synchronization of the drive-response complex networks is derived and some corresponding sufficient conditions are also obtained. Numerical examples are presented to verify the effectiveness and the correctness of the synchronization criteria.

Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions

The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory and Barbalat＇s lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.

Cluster synchronization of uncertain complex networks with desynchronizing impulse

Cluster synchronization of nonlinear uncertain complex networks with desynchronizing impulse is explored. First of all, a feedback controller is employed, based on the Lyapunov stability theorem and Lipschitz condition, to guarantee that the uncertain complex networks with desynchronizing impulse synchronize with an object trajectory. Furthermore, a synchronizing impulse controller is presented, which is more efficiently and directly used to achieve the cluster synchronization. Finally, numerical examples are examined to show the effectiveness of the proposed methods.

Generalized projective synchronization of two coupled complex networks of different sizes

We investigate a new generalized projective synchronization between two complex dynamical networks of different sizes. To the best of our knowledge, most of the current studies on projective synchronization have dealt with coupled networks of the same size. By generalized projective synchronization, we mean that the states of the nodes in each network can realize complete synchronization, and the states of a pair of nodes from both networks can achieve projective synchronization. Using the stability theory of the dynamical system, several sufficient conditions for guaranteeing the existence of the generalized projective synchronization under feedback control and adaptive control are obtained. As an example, we use Chua’s circuits to demonstrate the effectiveness of our proposed approach.

Pinning sampled-data synchronization for complex networks with probabilistic coupling delay

We deal with the problem of pinning sampled-data synchronization for a complex network with probabilistic time-varying coupling delay. The sampling period considered here is assumed to be less than a given bound. Without using the Kronecker product, a new synchronization error system is constructed by using the property of the random variable and input delay approach. Based on the Lyapunov theory, a delay-dependent pinning sampled-data synchronization criterion is derived in terms of linear matrix inequalities （LMIs） that can be solved effectively by using MATLAB LMI toolbox. Numerical examples are provided to demonstrate the effectiveness of the proposed scheme.

Outer Synchronization of Complex Networks by Impulse

This paper investigates outer synchronization of complex networks,especially,outer complete synchronizationand outer anti-synchronization between the driving network and the response network.Employing the impulsivecontrol method which is uncontinuous,simple,efficient,low-cost and easy to implement in practical applications,weobtain some sufficient conditions of outer complete synchronization and outer anti-synchronization between two complexnetworks.Numerical simulations demonstrate the effectiveness of the proposed impulsive control scheme.

Fixed-Time and Finite-Time Synchronization for a Class of Output-Coupling Complex Networks via Continuous Control

This paper mainly investigates the finite-time and fixed-time synchronization problem for a class of general output-coupling complex networks with output feedback nodes. The fixed-time and finite-time synchronization protocols are presented based on continuous controller strategies which can efficaciously eliminate chattering phenomenon existing in some previous results. Several sufficient conditions ensuring fixed-time and finite-time synchronization are derived by employing Lyapunov stability theory, linear matrix inequality (LMI) and adaptive technique. Furthermore, aimed at the model of this article, we study the problem of adaptive coupling strength in fixed-time synchronization which is rarely involved in previous results. Finally, several numerical examples are given to illustrate the effectiveness of our results.

Matrix Measure with Application in Quantized Synchronization Analysis of Complex Networks with Delayed Time via the General Intermittent Control

This paper concerned with the quantized synchronization analysis problem. The scope of state vectors of dynamic systems, based on the matrix measure, is estimated. By using the general intermittent control, some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems. Then, both the general intermittent networked controller and the quantized parameters can be designed, which guarantee that the nodes of the complex network are synchronized. Finally, simulation examples are given to illustrate the effectiveness and feasibility of the proposed method.

Decentralized Adaptive Strategies for Synchronization of Fractional-order Complex Networks

This paper focuses on synchronization of fractionalorder complex dynamical networks with decentralized adaptive coupling.Based on local information among neighboring nodes,two fractional-order decentralized adaptive strategies are designed to tune all or only a small fraction of the coupling gains respectively.By constructing quadratic Lyapunov functions and utilizing fractional inequality techniques,Mittag-Leffler function,and Laplace transform,two sufficient conditions are derived for reaching network synchronization by using the proposed adaptive laws.Finally,two numerical examples are given to verify the theoretical results.

Robust adaptive synchronization of uncertain and delayed dynamical complex networks with faulty network

This paper presents a new robust adaptive synchronization method for a class of uncertain dynamical complex networks with network failures and coupling time-varying delays. Adaptive schemes are proposed to adjust controller parameters for the faulty network compensations, as well as to estimate the upper and lower bounds of delayed state errors and perturbations to compensate the effects of delay and perturbation on-line without assuming symmetry or irreducibility of networks. It is shown that, through Lyapunov stability theory, distributed adaptive controllers con- structed by the adaptive schemes are successful in ensuring the achievement of asymptotic synchronization of networks in the present of faulty and delayed networks, and perturbation inputs. A Chua＇s circuit network example is finally given to show the effectiveness of the proposed synchronization criteria.

Modified Function Projective Synchronization of Complex Networks with Multiple Proportional Delays

This paper deals with the modified function projective synchronization problem for general complex networks with multiple proportional delays. With the existence of multiple proportional delays, an effective hybrid feedback control is designed to attain modified function projective synchronization of networks. Numerical example is provided to show the effectiveness of our result.

A novel robust fixed time synchronization of complex network subject to input nonlinearity in the presence of uncertainties and external disturbances

This paper studies the global fixed time synchronization of complex dynamical network,including non-identical nodes with disturbances and uncertainties as well as input nonlinearity.First,a novel fixed time sliding manifold is constructed to achieve the fixed time synchronization of complex dynamical network with disturbances and uncertainties.Second,a novel sliding mode controller is proposed to realize the global fixed time reachability of sliding surfaces.The outstanding feature of the designed control is that the fixed convergence time of both reaching and sliding modes can be adjusted to the desired values in advance by choosing the explicit parameters in the controller,which does not rest upon the initial conditions and the topology of the network.Finally,the effectiveness and validity of the obtained results are demonstrated by corresponding numerical simulations.

Synchronous Control of Complex Networks with Fuzzy Connections

This article is based on the T-S fuzzy control theory and investigates the synchronization control problem of complex networks with fuzzy connections. Firstly, the main stability equation of a complex network system is obtained, which can determine the stability of the synchronous manifold. Secondly, the main stable system is fuzzified, and based on fuzzy control theory, the control design of the fuzzified main stable system is carried out to obtain a coupling matrix that enables the complex network to achieve complete synchronization. The numerical analysis results indicate that the control method proposed in this paper can effectively achieve synchronization control of complex networks, while also controlling the transition time for the network to achieve synchronization.

Synchronization of Markovian jumping complex networks with event-triggered control

This paper investigates event-triggered synchronization for complex networks with Markovian jumping parameters.Nonlinear dynamics with Markovian jumping parameters is considered for each node in a complex network. By utilizing the proposed event-triggered strategy, and based on the Lyapunov functional method and linear matrix inequality technology,some sufficient conditions for synchronization of complex networks are derived whether the transition rate matrix for the Markov process is completely known or not. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical results.