Pinning control of complex Lur'e networks

This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur'e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur'e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua's oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.     

Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks

This paper is concerned with the robust H∞ synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities (LMIs). The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Robust H∞ observer-based of a class of complex control for synchronization dynamical networks

This paper is concerned with the robust Hoo synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities （LMIs）. The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Robust H_∞ control of piecewise-linear chaotic systems with random data loss

<正>This paper studies the problem of robust H_∞control of piecewise-linear chaotic systems with random data loss. The communication links between the plant and the controller are assumed to be imperfect(that is,data loss occurs intermittently,which appears typically in a network environment).The data loss is modelled as a random process which obeys a Bernoulli distribution.In the face of random data loss,a piecewise controller is designed to robustly stabilize the networked system in the sense of mean square and also achieve a prescribed H_∞disturbance attenuation performance based on a piecewise-quadratic Lyapunov function.The required H_∞controllers can be designed by solving a set of linear matrix inequalities(LMIs).Chua's system is provided to illustrate the usefulness and applicability of the developed theoretical results.     

Pinning consensus analysis of multi-agent networks with arbitrary topology

In this paper the pinning consensus of multi-agent networks with arbitrary topology is investigated. Based on the properties of M-matrix, some criteria of pinning consensus are established for the continuous multi-agent network and the results show that the pinning consensus of the dynamical system depends on the smallest real part of the eigenvalue of the matrix which is composed of the Laplacian matrix of the multi-agent network and the pinning control gains. Meanwhile, the relevant work for the discrete-time system is studied and the corresponding criterion is also obtained. Particularly, the fundamental problem of pinning consensus, that is, what kind of node should be pinned, is investigated and the positive answers to this question are presented. Finally, the correctness of our theoretical findings is demonstrated by some numerical simulated examples.     

Robust H_∞ control for uncertain systems with heterogeneous time-varying delays via static output feedback

This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties.The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties.By constructing an appropriate Lyapunov-Krasvskii functional,a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality.From the derived criterion,the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically.A simulation example is given to illustrate the effectiveness of the proposed design method.     

Cost and effect of pinning control for network synchronization

The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabási--Albert model and various star-shaped networks are performed for verification and illustration.     

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.     

Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics

This paper considers the global stability of controlling an uncertain complex network to a homogeneous trajectory of the uncoupled system by a local pinning control strategy. Several sufficient conditions are derived to guarantee the network synchronisation by investigating the relationship among pinning synchronisation, network topology, and coupling strength. Also, some fundamental and yet challenging problems in the pinning control of complex networks are discussed: (1) what nodes should be selected as pinned candidates? (2) How many nodes are needed to be pinned for a fixed coupling strength? Furthermore, an adaptive pinning control scheme is developed. In order to achieve synchronisation of an uncertain complex network, the adaptive tuning strategy of either the coupling strength or the control gain is utilised. As an illustrative example, a network with the Lorenz system as node self-dynamics is simulated to verify the efficacy of theoretical results.     

Mixed H_∞ and Passive Projective Synchronization for Fractional Order Memristor-Based Neural Networks with Time-Delay and Parameter Uncertainty

This paper investigates the mixed H∞ and passive projective synchronization problem for fractional-order(FO) memristor-based neural networks. Our aim is to design a controller such that, though the unavoidable phenomena of time-delay and parameter uncertainty are fully considered, the resulting closed-loop system is asymptotically stable with a mixed H∞ and passive performance level. By combining active and adaptive control methods, a novel hybrid control strategy is designed, which can guarantee the robust stability of the closed-loop system and also ensure a mixed H∞ and passive performance level. Via the application of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequality techniques. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.     

Robust H_∞ cluster synchronization analysis of Lurie dynamical networks

The cluster synchronization problem of complex dynamical networks with each node being a Lurie system with exter- nal disturbances and time-varying delay is investigated in this paper. Some criteria for cluster synchronization with desired H∞ performance are presented by using a local linear control scheme. Firstly, sufficient conditions are established to realize cluster synchronization of the Lurie dynamical networks without time delay. Then, the notion of the cluster synchronized region is introduced, and some conditions guaranteeing the cluster synchronized region and unbounded cluster synchro- nized region are derived. Furthermore, the cluster synchronization and cluster synchronized region in the Lurie dynamical networks with time-varying delay are considered. Numerical examples are finally provided to verify and illustrate the theoretical results.     

Pinning impulsive synchronization of stochastic delayed coupled networks

In this paper,the pinning synchronization problem of stochastic delayed complex network (SDCN) is investigated by using a novel hybrid pinning controller. The proposed hybrid pinning controller is composed of adaptive controller and impulsive controller,where the two controllers are both added to a fraction of nodes in the network. Using the Lyapunov stability theory and the novel hybrid pinning controller,some sufficient conditions are derived for the exponential synchronization of such dynamical networks in mean square. Two numerical simulation examples are provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed control scheme has a fast convergence rate compared with the conventional adaptive pinning method.     

Synchronization of impulsively coupled complex networks

We investigate the synchronization of complex networks,which are impulsively coupled only at discrete instants.Based on the comparison theory of impulsive differential systems,a distributed impulsive control scheme is proposed for complex dynamical networks to achieve synchronization.The proposed scheme not only takes into account the influence of all nodes to network synchronization,which depends on the weight of each node in the network,but also provides us with a flexible method to select the synchronized state of the network.In addition,it is unnecessary for the impulsive coupling matrix to be symmetrical.Finally,the proposed control scheme is applied to a chaotic Lorenz network and Chua’s circuit network.Numerical simulations are used to illustrate the validity of this control scheme.     

Optimal design of virtual topology reconfiguration in WDM optical networks

Virtual topology of WDM optical networks is often designed for some specific traffic matrix to get the best network performance. When traffic demand imposed on WDM optical networks changes, the network performance may degrade and even become unacceptable. So virtual topology need to be reconfigured. In previous works, virtual topology is reconfigured to achieve the best network performance, in which a large number of lightpaths need to be set up or torn down. In this paper, we try to get a tradeoff between the network performance and traffic disruption (or implementing cost). The problem of virtual topology reconfiguration for changing traffic patterns is formulated as an optimization problem and a mixed integer linear programming (MILP) algorithm is presented. Numerical results show that a large cost reduction of reconfiguration can be achieved at the expense of network performance.     

Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays

In this paper, the problem of exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and Mode-dependent probabilistic time-varying coupling delays is investigated. The sam- pling period is assumed to be time-varying and bounded. The information of probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred complex dynamical network model. Based on the condition, the design method of the desired sampled data controller is proposed. By constructing a new Lyapunov functional with triple integral terms, delay-distribution-dependent exponential synchronization criteria are derived in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.     

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.     

Exponential Synchronization of Uncertain Complex Dynamical Networks with Delay Coupling

This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown coupling functions but bounded. Novel delay-dependent linear controllers are designed via the Lyapunov stability theory. Especially, it is shown that the controlled networks are globally exponentially synchronized with a given convergence rate. An example of typical dynamical network of this class, having the Lorenz system at each node, has been used to demonstrate and verify the novel design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.     

Linear-control-based synchronization of coexisting attractor networks with time delays

This paper introduces the concept of linear-control-based synchronization of coexisting attractor networks with time delays.Within the new framework,closed loop control for each dynamic node is realized through linear state feedback around its own arena in a decentralized way,where the feedback matrix is determined through consideration of the coordination of the node dynamics,the inner connected matrix and the outer connected matrix.Unlike previously existing results,the feedback gain matrix here is decoupled from the inner matrix;this not only guarantees the flexible choice of the gain matrix,but also leaves much space for inner matrix configuration.Synchronization of coexisting attractor networks with time delays is made possible in virtue of local interaction,which works in a distributed way between individual neighbours,and the linear feedback control for each node.Provided that the network is connected and balanced,synchronization will come true naturally,where theoretical proof is given via a Lyapunov function.For completeness,several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme.     

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying,and distributed delay. The aim is to design a delay-dependent robust H∞control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities（LMIs）. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.     

Adaptive synchronization in an array of asymmetric coupled neural networks

This paper investigates the global synchronization in an array of linearly coupled neural networks with constant and delayed coupling. By a simple combination of adaptive control and linear feedback with the updated laws, some sufficient conditions are derived for global synchronization of the coupled neural networks. The coupling configuration matrix is assumed to be asymmetric, which is more coincident with the realistic network. It is shown that the approaches developed here extend and improve the earlier works. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results.