adaptive exponential synchronization of delayed chaotic networks abstract this paper deals with the global exponential synchronization of a class of delayed chaotic networks under some simple conditions the global synchronization of a network about its all variables is derived by only considering the global synchronization of its partial variables furthermore based on the halanay inequality technique some delay independent criteria are obtained to ensure the adaptive exponential synchronization of the model and the simpler less conservative and more efficient results are easy to be verified in engineering applications finally an illustrative example is given to demonstrate the effectiveness of the presented synchronization scheme

matrix polynomials and the index problem for elliptic systems the main new results of this paper concern the formulation of algebraic conditions for the fredholm property of elliptic systems of p d e s with boundary values which are equivalent to the lopatinskii condition the lopatinskii condition is reformulated in a new algebraic form based on matrix polynomials which is then used to study the existence of homotopies of elliptic boundary value problems the paper also contains an exposition of the relevant parts of the theory of matrix polynomials and the theory of elliptic systems of p d e s introduction let a denote an elliptic operator in and let b be a boundary operator where is a bounded domain in r in this paper several versions of the algebraic condition for the fredholm property of a b are formulated equivalent to the lopatinskii condition of lo the main new result is the following a square matrix function b defined on the unit cotangent bundle of is constructed from the principal symbols of the coefficients of the boundary operator and a spectral pair for the family of matrix polynomials associated with the principal symbol of the elliptic operator the lopatinskii condition is equivalent to the following condition the function b must have invertible values the proofs use the theory of matrix polynomials due to gohberg lancaster rodman and others for instance see glr chapter 14 in lt and chapter 6 in r there is a natural map defined by a b 7 a going from the space of elliptic boundary value problems to the space of elliptic operators now let a 0 1 be a homotopy of elliptic operators and let b0 be a boundary operator such that a0 b0 satisfies the lopatinksii condition we will show that the given homotopy of elliptic operators can be lifted to a homotopy a b in the space of elliptic boundary value problems satisfying the lopatinskii condition this result is proved in theorem 7 3 and was motivated by the article ge the key element in the proof i e the construction of the boundary operators b requires that we use pseudodifferential operators on and the theory of matrix polynomials mentioned above received by the editors august 16 1994 and in revised form february 12 1996 1991 mathematics subject classification primary 35j45 35j55 15a22

pinning control of complex dynamical networks with general topology abstract recently the researches on pinning control of complex dynamical networks have mainly focused on such networks with very specific coupling schemes e g symmetric coupling uniform coupling and linear coupling however most real networks often consist of local units which interact with each other via asymmetric and heterogeneous connections in this paper pinning control of a continuous time complex dynamical network with general coupling topologies is studied some generic stability criteria based on master stability function msf are derived for such a general controlled network which guarantee that the whole network can be pinned to its equilibrium by placing feedback control only on a small fraction of nodes then these results are extended to discrete time case previous results about symmetric uniform or linear coupled networks in this area are included as special cases of the present work numerical simulations of directed networks with weighted coupling pinned by specifically selective pinning scheme are given for illustration and verification

pinning impulsive synchronization of reaction diffusion neural networks with time varying delays this paper investigates the exponential synchronization of reaction diffusion neural networks with time varying delays subject to dirichlet boundary conditions a novel type of pinning impulsive controllers is proposed to synchronize the reaction diffusion neural networks with time varying delays by applying the lyapunov functional method sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction diffusion neural networks with large and small delay sizes it is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network the technique used in this paper is also applicable to reaction diffusion networks with neumann boundary conditions numerical examples are presented to demonstrate the effectiveness of the theoretical results

brief paper l2 norm performance index of synchronization and lqr control synthesis of complex networks in this paper the synchronizability problem of dynamical networks is addressed where better synchronizability means faster network synchronization with lower vibration the l 2 norm of the error vector e is taken as a performance index to measure this kind of synchronizability for the equilibrium synchronization case it is shown that there is a close relationship between the l 2 norm of the error vector e and the h 2 norm of the transfer function g of the linearized network about the equilibrium point consequently the effect of the network coupling topology on the h 2 norm of the transfer function g is analyzed finally an lqr controller is designed according to the lqr problem in modern control theory which can drive the whole network to its equilibrium point and meanwhile minimize the l 2 norm of the output of the linearized network

synchronization for time varying complex networks based on control in this paper the problem on synchronization is investigated for complex networks with time varying delay and without time varying delay by using control strategy together with some lyapunov krasovskii functions and effective mathematical techniques several conditions are derived to guarantee a class of complex networks with time varying and without time varying delays to be synchronized finally examples are given to illustrate the effectiveness of the proposed methods

lmi based criteria for synchronization of complex dynamical networks this paper considers the problem of controlling a complex dynamical network by means of pinning we point out that the synchronization criterion given in the form of matrix eigenvalues can be equivalent to a linear matrix inequality criterion we further investigate network synchronization via pinning and prove several linear matrix inequality theorems in particular we theoretically provide two typical pinning strategies based on whether the graph which is made up of unpinned nodes and edges between them is irreducible or not numerical simulations including k regular networks star shaped networks and ba scale free networks are shown for illustration and verification

distributed static output feedback control for state synchronization in networks of identical lti systems this paper studies state synchronization of multi agent systems with disturbances using distributed static output feedback opfb control the bounded l 2 gain synchronization problem using distributed static opfb is defined and solved the availability of only output measurements restricts the local controls design while the communication graph topology restricts global information flow among the agents it is shown here that these two types of restriction can be dealt with in a symmetric manner and lead to two similar conditions guaranteeing the existence of bounded l 2 gain static opfb one condition is on the output measurement matrix on a local scale and the other on the graph laplacian matrix on a global scale under additional conditions a distributed two player zero sum game using static opfb is also solved and leads to distributed nash equilibrium on the communication graph as a special case the static opfb globally optimal control is given a new class of digraphs satisfying the above condition on the graph laplacian is studied the synchronizing region for distributed static opfb control is exposed and found to be conical different than the infinite right half plane synchronizing region for distributed state feedback

optimizing the controllability of arbitrary networks with genetic algorithm abstract recently as the controllability of complex networks attracts much attention how to optimize networks controllability has become a common and urgent problem in this paper we develop an efficient genetic algorithm oriented optimization tool to optimize the controllability of arbitrary networks consisting of both state nodes and control nodes under popov belevitch hautus rank condition the experimental results on a number of benchmark networks show the effectiveness of this method and the evolution of network topology is captured furthermore we explore how network structure affects its controllability and find that the sparser a network is the more control nodes are needed to control it and the larger the differences between node degrees the more control nodes are needed to achieve the full control our framework provides an alternative to controllability optimization and can be applied to arbitrary networks without any limitations

pinning synchronization of fractional order delayed complex networks with non delayed and delayed couplings abstractthis paper considers the global synchronization of fractional order delayed complex networks with non delayed and delayed couplings based on pinning control with the help of comparison theorems for fractional order linear systems with multiple time delays some novel and useful synchronisation criteria are presented by adding linear error feedback controllers to certain selected nodes here the coupling matrices need not be symmetric or irreducible what is more it is shown that the model and results in the paper are more general than those in the literature a numerical example is given to demonstrate the effectiveness and feasibility of the obtained results

coordination of multi agent systems on interacting physical and communication topologies abstract a new framework is given for coordination of multi agent systems that are interconnected by a physical coupling digraph the edges of this graph represent physical couplings between agents that are fixed due to dynamical interactions on top of the physical graph distributed control protocols are designed where the allowed communications between agents for control purposes are prescribed by a second fixed communication digraph the physical and communication digraphs are generally different and the combination of these two graphs forms a cyber physical system the interactions between physical and communication graphs are the focus of this paper we consider different interactions between two graphs including the case when their pinned laplacian commutes the case of the communication graph with diagonalizable pinned laplacian and the case of two general graphs moreover within each graph the relations between the agents can be either collaborative or antagonistic to capture this the theory of bipartite consensus is used coordination protocols for different cases are designed that are distributed with respect to the communication graph and overcome the detrimental effects of the signed physical graph the proposed control methods are illustrated by simulation examples

synchronization of linear dynamical networks on time scales this paper studies the synchronization problem of complex dynamical networks cdns on time scales a pinning impulsive control scheme that takes into account of time delay effects is designed to achieve synchronization of cdns on time scales with the state of an isolated node based on the theory of time scales and the direct lyapunov method a synchronization criterion is established for linear cdns on general time scales our result shows that by impulsive control a small portion of nodes the consensus of cdns on time scales can be achieved according to our pinning impulsive control scheme different numbers of nodes will be selected at each impulsive instant and time delay is considered in the pinning impulses the modeling framework developed in this paper is a unification and generalization of many existing continuous time and discrete time cdn models while the pinning impulsive control scheme is an extension of the existing control scheme for synchronization of continuous time cdns moreover the idea of studying dynamical systems on time scales provide a unified approach to investigate continuous time system and its discrete time counterpart simultaneously numerical simulations are given to illustrate the effectiveness of the theoretical analysis

studies on controllability of directed networks with extremal optimization abstract almost all natural social and man made engineered systems can be represented by a complex network to describe their dynamic behaviors to make a real world complex network controllable with its desired topology the study on network controllability has been one of the most critical and attractive subjects for both network and control communities in this paper based on a given directed weighted network with both state and control nodes a novel optimization tool with extremal dynamics to generate an optimal network topology with minimum control nodes and complete controllability under kalman s rank condition has been developed the experimental results on a number of popular benchmark networks show the proposed tool is effective to identify the minimum control nodes which are sufficient to guide the whole network s dynamics and provide the evolution of network topology during the optimization process we also find the conclusion the sparse networks need more control nodes than the dense and the homogeneous networks need fewer control nodes compared to the heterogeneous liu et al 2011 18 is also applicable to network complete controllability these findings help us to understand the network dynamics and make a real world network under the desired control moreover compared with the relevant research results on structural controllability with minimum driver nodes the proposed solution methodology may also be applied to other constrained network optimization problems beyond complete controllability with minimum control nodes

adaptive pinning control for the projective synchronization of drive response dynamical networks abstract this paper studies the projective synchronization of a drive response dynamical network of partially linear systems the coupling configuration matrix of the network is not necessarily symmetric two adaptive pinning control strategies are derived based on the barbalat s lemma in the first control strategy the pinning control gain is adaptively updated to realize the projective synchronization in the second control strategy both the pinning control gain and the coupling strength between nodes are adaptively updated numerical simulation results show that the coupling strength needed in the second control strategy is smaller than that in the first control strategy to achieve the projective synchronization of the network

controlling collective dynamics in complex minority game resource allocation systems resource allocation takes place in various kinds of real world complex systems such as traffic systems social services institutions or organizations or even ecosystems the fundamental principle underlying complex resource allocation dynamics is boolean interactions associated with minority games as resources are generally limited and agents tend to choose the least used resource based on available information a common but harmful dynamical behavior in resource allocation systems is herding where there are time intervals during which a large majority of the agents compete for a few resources leaving many other resources unused accompanying the herd behavior is thus strong fluctuations with time in the number of resources being used in this paper we articulate and establish that an intuitive control strategy namely pinning control is effective at harnessing the herding dynamics in particular by fixing the choices of resources for a few agents while leaving the majority of the agents free herding can be eliminated completely our investigation is systematic in that we consider random and targeted pinning and a variety of network topologies and we carry out a comprehensive analysis in the framework of mean field theory to understand the working of control the basic philosophy is then that when a few agents waive their freedom to choose resources by receiving sufficient incentives the majority of the agents benefit in that they will make fair efficient and effective use of the available resources our work represents a basic and general framework to address the fundamental issue of fluctuations in complex dynamical systems with significant applications to social economical and political systems

multi agent differential graphical games online adaptive learning solution for synchronization with optimality multi agent systems arise in several domains of engineering and can be used to solve problems which are difficult for an individual agent to solve strategies for team decision problems including optimal control n player games h infinity control and non zero sum and so on are normally solved for off line by solving associated matrix equations such as the coupled riccati equations or coupled hamilton jacobi equations however using that approach players cannot change their objectives online in real time without calling for a completely new off line solution for the new strategies therefore in this paper we bring together cooperative control reinforcement learning and game theory to present a multi agent formulation for the online solution of team games the notion of graphical games is developed for dynamical systems where the dynamics and performance indices for each node depend only on local neighbor information it is shown that standard definitions for nash equilibrium are not sufficient for graphical games and a new definition of interactive nash equilibrium is given we give a cooperative policy iteration algorithm for graphical games that converges to the best response when the neighbors of each agent do not update their policies and to the cooperative nash equilibrium when all agents update their policies simultaneously this is used to develop methods for online adaptive learning solutions of graphical games in real time along with proofs of stability and convergence

consensus in a heterogeneous influence network we consider a dynamical network model in which a number of agents all move on the plane with the same constant absolute velocity at each time step each agent s direction is updated as the average of its direction plus the directions of other agents who can influence it the influencing capability of each agent is represented by its influencing radius which is randomly chosen according to a power law distribution with a scaling exponent between 2 and ensuremath infty as the value of the scaling exponent decreases the radius distribution becomes more heterogeneous and the network becomes much easier to achieve direction consensus among agents due to the leading roles played by a few hub agents furthermore almost all agents will finally move in the same desired direction in a strong heterogeneous influence network if and only if a small fraction of hub agents can be controlled to move in the desired direction these results also reflect the robust yet fragile feature of a heterogeneous influence network

projective synchronization in drive response dynamical networks abstract projective synchronization characterized by a scaling factor and its control have recently been well investigated in two coupled chaotic oscillators but it has not been realized yet in the case of more than two chaotic systems in this paper we study the projective synchronization in 1 n coupled chaotic systems by introducing a drive response dynamical networks model furthermore pinning control techniques are also adopted to direct the scaling factor onto the desired value it is also shown that the projection synchronization of the drive response dynamical networks can be realized by controlling only one node numerical simulations on the chaotic lorenz system are illustrated to verify the theoretical results

synchronization control for nonlinear stochastic dynamical networks pinning impulsive strategy in this paper a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling pinning state feedback controllers have been proved to be effective for synchronization control of state coupled dynamical networks we will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks some generic mean square stability criteria are derived in terms of algebraic conditions which guarantee that the whole state coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes an effective method is given to select the nodes which should be controlled at each impulsive constants the proportion of the controlled nodes guaranteeing the stability is explicitly obtained and the synchronization region is also derived and clearly plotted numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper

brief paper decentralised static output feedback stabilisation and synchronisation of networks in this paper global stabilisation of a complex network is attained by applying local decentralised output feedback control to a minimum number of nodes of the network the stabilisation of the network is treated as a rank constrained problem strict positive realness conditions on the node level dynamics allow nonlinearities uncertainties which satisfy the sector conditions to be considered a network of chua oscillators with 75 nodes is considered to demonstrate the efficacy of the approach

deviation bounds in multi agent systems described by undirected graphs the theory of port hamiltonian systems is used to derive upper bounds for the state deviations in multi agent systems described by undirected graphs pinned to a reference signal the upper bounds for the deviations in networks of first or second order agents respectively depend on the minimal eigenvalue of the extended laplacian of the system in networks of first order agents the deviations decay exponentially with a rate depending on the same minimal eigenvalue in case networks of second order systems meet specific design properties it can be shown that the deviations also decay exponentially with half the rate compared to first order systems

pinning control of complex dynamical networks with heterogeneous delays complex dynamical networks with heterogeneous delays in both continuous and discrete time domains are controlled by applying local feedback injections to a small fraction of nodes in the whole network some generic stability criteria ensuring delay independent stability are derived for such controlled networks in terms of linear matrix inequalities lmi which guarantee that by placing a small number of feedback controllers on some nodes the whole network can be pinned to its equilibrium in some particular cases a single controller can achieve the control objective numerical simulations of various representative networks including a globally coupled network a star coupled network and an extended barabasi albert eba scale free network are finally given for illustration and verification

projective cluster synchronization of fractional order coupled delay complex network via adaptive pinning control abstract this paper investigates the projective cluster synchronization of fractional order coupled delay complex network via adaptive pinning control the pinning control method is employed in designing controllers for guaranteeing projective cluster synchronization based on the lyapunov stability theory and well known barbalat s lemma some new sufficient conditions are derived to guarantee the projective cluster synchronization of the fractional order complex network a numerical simulation is given to verify the effectiveness of the theoretical results

projective cluster synchronization in drive response dynamical networks abstract in this paper we study the projective cluster synchronization in a drive response dynamical network with 1 n coupled partially linear chaotic systems because the scaling factors characterizing the dynamics of projective synchronization remain unpredictable pinning control ideas are adopted to direct the different scaling factors onto the desired values it is also shown that the projection cluster synchronization can be realized by controlling only one node in each cluster numerical simulations on the chaotic lorenz system are illustrated to verify the theoretical results

on distributed pinning observers for a network of dynamical systems in this technical note a distributed observer structure is proposed to estimate the states of a large scale network of semi linear systems interconnected by a positive time varying coupling strength the distributed observer comprises distinct sub observers which require only local node level information and exchange their local state estimates with their neighboring observers the key idea here is to use a minimum number or at least relatively few measurements from the network being monitored to reduce the sensor requirements the problem is formulated as a two stage lmi optimization problem

second order leader following consensus of nonlinear multi agent systems via pinning control abstract without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree this paper studies the second order leader following consensus problem of nonlinear multi agent systems with general network topologies based on graph theory matrix theory and lasalle s invariance principle a pinning control algorithm is proposed to achieve leader following consensus in a network of agents with nonlinear second order dynamics furthermore a pinning consensus protocol is developed for coupled double integrators with a constant reference velocity in particular this paper addresses what kind of agents and how many agents should be pinned and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader numerical simulations are given to verify the theoretical analysis

impulsive effects on quasi synchronization of neural networks with parameter mismatches and time varying delay this paper is concerned with the exponential synchronization issue of nonidentically coupled neural networks with time varying delay due to the parameter mismatch phenomena existed in neural networks the problem of quasi synchronization is thus discussed by applying some impulsive control strategies based on the definition of average impulsive interval and the extended comparison principle for impulsive systems some criteria for achieving the quasi synchronization of neural networks are derived more extensive ranges of impulsive effects are discussed so that impulse could either play an effective role or play an adverse role in the final network synchronization in addition according to the extended formula for the variation of parameters with time varying delay precisely exponential convergence rates and quasi synchronization errors are obtained respectively in view of different types impulsive effects finally some numerical simulations with different types of impulsive effects are presented to illustrate the effectiveness of theoretical analysis

synchronization of fractional order complex dynamical networks abstract in this letter the synchronization of complex dynamical networks with fractional order chaotic nodes is studied a fractional order controller for synchronization of complex network is presented some new sufficient synchronization criteria are proposed based on the lyapunov stability theory and the lasalle invariance principle these synchronization criteria can apply to an arbitrary fractional order complex network in which the coupling configuration matrix and the inner coupling matrix are not assumed to be symmetric or irreducible it means that this method is more general and effective numerical simulations of two fractional order complex networks demonstrate the universality and the effectiveness of the proposed method

controlling synchronous patterns in complex networks although the set of permutation symmetries of a complex network could be very large few of them give rise to stable synchronous patterns here we present a general framework and develop techniques for controlling synchronization patterns in complex network of coupled chaotic oscillators specifically according to the network permutation symmetry we design a small size and weighted network namely the control network and use it to control the large size complex network by means of pinning coupling we argue mathematically that for any of the network symmetries there always exists a critical pinning strength beyond which the unstable synchronous pattern associated to this symmetry can be stabilized the feasibility of the control method is verified by numerical simulations of both artificial and real world networks and demonstrated experimentally in systems of coupled chaotic circuits our studies show the controllability of synchronous patterns in complex networks of coupled chaotic oscillators

pinning control of scale free dynamical networks abstract recently it has been demonstrated that many large complex networks display a scale free feature that is their connectivity distributions have the power law form in the present work control of a scale free dynamical network by applying local feedback injections to a fraction of network nodes is investigated the specifically and randomly pinning schemes are considered the specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme the method is applied to an array of chua s oscillators as an example

pinning synchronization of directed networks with switching topologies a multiple lyapunov functions approach this paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies the common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper using tools from m matrix theory and stability analysis of the switched nonlinear systems a new kind of network topology dependent multiple lyapunov functions is proposed for analyzing the synchronization behavior of the whole network it is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed finally some numerical simulations on coupled neural networks are provided to verify the theoretical results

stabilizing weighted complex networks real networks often consist of local units which interact with each other via asymmetric and heterogeneous connections in this paper the v stability problem is investigated for a class of asymmetric weighted coupled networks with nonidentical node dynamics which includes the unweighted network as a special case pinning control is suggested to stabilize such a coupled network the complicated stabilization problem is reduced to measuring the semi negative property of the characteristic matrix which embodies not only the network topology but also the node self dynamics and the control gains it is found that network stabilizability depends critically on the second largest eigenvalue of the characteristic matrix the smaller the second largest eigenvalue is the more the network is pinning controllable numerical simulations of two representative networks composed of non chaotic systems and chaotic systems respectively are shown for illustration and verification

cooperative optimal control for multi agent systems on directed graph topologies this note brings together stability and optimality theory to design distributed cooperative control protocols that guarantee consensus and are globally optimal with respect to a positive semi definite quadratic performance criterion a common problem in cooperative optimal control is that global optimization problems generally require global information which is not available to distributed controllers optimal control for multi agent systems is complicated by the fact that the communication graph topology interplays with the agent system dynamics in the note we use an inverse optimality approach together with partial stability to consider the cooperative consensus and pinning control agents with identical linear time invariant dynamics are considered communication graphs are assumed directed and having fixed topology structured quadratic performance indices are derived that capture the topology of the graph which allows for global optimal control that is implemented using local distributed protocols a new class of digraphs is defined that admits a distributed solution to the global optimal control problem namely those with simple graph laplacian matrices

fractional pi pinning synchronization of fractional complex dynamical networks abstract a novel method for synchronization of fractional order complex dynamical networks using a new fractional proportional integral pi pinning control scheme is presented in this paper stability of this network is proved via the lyapunov stability theorem and the synchronizability criterion is obtained although one can also design a proportional pinning control scheme to synchronize the whole network our proposed fractional pi control is more efficient numerical simulations on lorenz oscillator s interaction over a sample network have shown that the proposed fractional pi controller can provide a faster synchronization with less overshoot to the reference state compared to conventional proportional controller with the same power consumption

chaos synchronization of general complex dynamical networks recently it has been demonstrated that many large scale complex dynamical networks display a collective synchronization motion here we introduce a time varying complex dynamical network model and further investigate its synchronization phenomenon based on this new complex network model two network chaos synchronization theorems are proved we show that the chaos synchronization of a time varying complex network is determined by means of the inner coupled link matrix the eigenvalues and the corresponding eigenvectors of the coupled configuration matrix rather than the conventional eigenvalues of the coupled configuration matrix for a uniform network especially we do not assume that the coupled configuration matrix is symmetric and its off diagonal elements are nonnegative which in a way generalizes the related results existing in the literature

multi agent discrete time graphical games and reinforcement learning solutions this paper introduces a new class of multi agent discrete time dynamic games known in the literature as dynamic graphical games for that reason a local performance index is defined for each agent that depends only on the local information available to each agent nash equilibrium policies and best response policies are given in terms of the solutions to the discrete time coupled hamilton jacobi equations since in these games the interactions between the agents are prescribed by a communication graph structure we have to introduce a new notion of nash equilibrium it is proved that this notion holds if all agents are in nash equilibrium and the graph is strongly connected a novel reinforcement learning value iteration algorithm is given to solve the dynamic graphical games in an online manner along with its proof of convergence the policies of the agents form a nash equilibrium when all the agents in the neighborhood update their policies and a best response outcome when the agents in the neighborhood are kept constant the paper brings together discrete hamiltonian mechanics distributed multi agent control optimal control theory and game theory to formulate and solve these multi agent dynamic graphical games a simulation example shows the effectiveness of the proposed approach in a leader synchronization case along with optimality guarantees

synchronization criterions and pinning control of general complex networks with time delay the problems of synchronization and pinning control for general time delay complex dynamical networks are investigated in this paper less conservative criterions for both continuous time and discrete time complex dynamical networks with time delay are obtained pinning control strategies are respectively designed to make these complex dynamical networks synchronized moreover the problems of designing controllers are converted into solving optimal problems of a series of linear matrix inequalities which reduces the computation complexity finally numerical simulations verify the effectiveness of our methodology

response of energy envelop in complex oscillator networks to external stochastic excitations the response of energy envelop in complex nonlinear oscillator networks to stochastic excitations is studied first by using the stochastic averaging method for quasi nonintegrable hamiltonian systems the averaged fokker planck kolmogorov equation governing the probability density of the hamiltonian is established then the stationary probability density of the hamiltonian is derived and the stationary probability density of the averaged energy as well as the statistical moments of the hamiltonian is obtained to that end an illustrative example is provided with the analytical relationship between the response and the network parameters as well as the network structure specific solutions are presented for five representative topological structures throughout extensive simulations the effects of system parameters such as the network size coupling strength and intensities of stochastic excitations on the response of the energy envelop of the networks are carefully observed and analyzed

transition to chaos in complex dynamical networks abstract the transition from a non chaotic state to a chaotic state is a commonly concerned issue in the study of coupled dynamical networks in this work we consider a network consisting of nodes that are in non chaotic states with parameters in non chaotic regions before they are coupled together we show that if these non chaotic nodes are linked together through a suitable structural topology positive lyapunov exponents of the coupled network can be generated by choosing a certain uniform coupling strength and the threshold for this coupling strength is determined by the complexity of the network topology moreover we show that topological effects of scale free and random networks which are two basic types of complex network models can be visualized based on their topological sensitivity to random failures and intentional attacks our simulation results on a 1000 node scale free network and a 1000 node random network of the logistic maps have verified that during the transition from non chaotic to chaotic states if the topology is more heterogenous then the coupling strength required to achieve the transition can be decreased

abnormal synchronizing path of delay coupled chaotic oscillators on the edge of stability abstract in this paper the transition of synchronizing path of delay coupled chaotic oscillators in a scale free network is highlighted mainly through the critical transmission delay makes chaotic oscillators be coupled on the edge of stability we find that the transition of synchronizing path is abnormal which is characterized by the following evidences a synchronization process starts with low degree rather than high degree ones b the high degree nodes do not undertake the role of hub c the synchronized subnetworks show a poor small world property as a result of hubs absence d the clustering synchronization behavior emerges even community structure is absent in the scale free network this abnormal synchronizing path suggests that the diverse synchronization behaviors occur in the same topology which implies that the relationship between dynamics and structure of network is much more complicated than the common sense that the structure is the foundation of dynamics moreover it also reveals the potential connection from the transition of synchronization behavior to disorder in real complex networks e g alzheimer disease

cooperative adaptive fuzzy tracking control for networked unknown nonlinear multiagent systems with time varying actuator faults in this paper the cooperative adaptive fault tolerant fuzzy tracking control caftftc problem of networked high order multiagent with time varying actuator faults is studied and a novel caftftc scheme is proposed to guarantee that all follower nodes asymptotically synchronize a leader node with tracking errors converging to a small adjustable neighborhood of the origin in spite of actuator faults the leader node is modeled as a higher order nonautonomous nonlinear system it acts as a command generator giving commands only to a small portion of the networked group each follower is assumed to have nonidentical unknown nonlinear dynamics and the communication network is also assumed to be a weighted directed graph with a fixed topology a distributed robust adaptive fuzzy controller is designed for each follower node such that the tracking errors are cooperative uniform ultimate boundedness cuub moreover these controllers are distributed in the sense that the controller designed for each follower node only requires relative state information between itself and its neighbors the adaptive compensation term of the optimal approximation errors and external disturbances is adopted to reduce the effects of the errors and disturbances which removes the assumption that the upper bounds of unknown function approximation errors and disturbances should be known analysis of stability and parameter convergence of the proposed algorithm are conducted that are based on algebraic graph theory and lyapunov theory comparing with results in the literature the caftftc scheme can minimize the time delay between fault occurrence and accommodation and reduce its adverse effect on system performance in addition the ftc scheme requires no additional fault isolation model which is necessary in the traditional active ftc scheme finally an example is provided to validate the theoretical results

experiments on node to node pinning control of chua s circuits abstract in this paper we study the global intermittent pinning controllability of networks of coupled chaotic oscillators we explore the feasibility of the recently presented node to node pinning control strategy through experiments on chua s circuits we focus on the case of two peer to peer coupled chua s circuits and we build a novel test bed platform comprised of three inductorless chua s oscillators we investigate the effect of a variety of design parameters on synchronization performance including the coupling strength between the oscillators the control gains and the switching frequency of node to node pinning control experimental results demonstrate the effectiveness of this novel pinning control strategy in rapidly taming chaotic oscillator dynamics onto desired reference trajectories while minimizing the overall control effort and the number of pinned network sites from an analytical standpoint we present sufficient conditions for global node to node pinning controllability and we estimate the maximum switching period for network controllability by adapting and integrating available results on lyapunov stability theory and partial averaging techniques

consensus analysis of multiagent networks via aggregated and pinning approaches in this paper the consensus problem of multiagent nonlinear directed networks mndns is discussed in the case that a mndn does not have a spanning tree to reach the consensus of all nodes by using the lie algebra theory a linear node and node pinning method is proposed to achieve a consensus of a mndn for all nonlinear functions satisfying a given set of conditions based on some optimal algorithms large size networks are aggregated to small size ones then by applying the principle minor theory to the small size networks a sufficient condition is given to reduce the number of controlled nodes finally simulation results are given to illustrate the effectiveness of the developed criteria

criteria for global pinning controllability of complex networks in this paper we study pinning controllability of networks of coupled dynamical systems in particular we study the problem of asymptotically driving a network of coupled identical oscillators onto some desired common reference trajectory by actively controlling only a limited subset of the whole network the reference trajectory is generated by an exogenous independent oscillator and pinned nodes are coupled to it through a linear state feedback we describe the time evolution of the complex dynamical system in terms of the error dynamics thereby we reformulate the pinning controllability problem as a global asymptotic stability problem by using lyapunov stability theory and algebraic graph theory we establish tractable sufficient conditions for global pinning controllability in terms of the network topology the oscillator dynamics and the linear state feedback

identifying the topology of a coupled fitzhugh nagumo neurobiological network via a pinning mechanism topology identification of a network has received great interest for the reason that the study on many key properties of a network assumes a special known topology different from recent similar works in which the evolution of all the nodes in a complex network need to be received this brief presents a novel criterion to identify the topology of a coupled fitzhugh nagumo fhn neurobiological network by receiving the membrane potentials of only a fraction of the neurons meanwhile although incomplete information is received the evolution of all the neurons including membrane potentials and recovery variables are traced based on schur complement and lyapunov stability theory the exact weight configuration matrix can be estimated by a simple adaptive feedback control the effectiveness of the proposed approach is successfully verified by neural networks with fixed and switching topologies

multi agent zero sum differential graphical games for disturbance rejection in distributed control this paper addresses distributed optimal tracking control of multi agent linear systems subject to external disturbances the concept of differential game theory is utilized to formulate this distributed control problem into a multi player zero sum differential graphical game which provides a new perspective on distributed tracking of multiple agents influenced by disturbances in the presented differential graphical game the dynamics and performance indices for each node depend on local neighbor information and disturbances it is shown that the solution to the multi agent differential graphical games in the presence of disturbances requires the solution to coupled hamilton jacobi isaacs hji equations multi agent learning policy iteration pi algorithm is provided to find the solution to these coupled hji equations and its convergence is proven it is also shown that l 2 bounded synchronization errors can be guaranteed using this technique an online pi algorithm is given to solve the zero sum game in real time a simulation example is provided to show the effectiveness of the online approach

effects of degree correlation on the controllability of networks abstract in this paper we investigate the effects of degree correlation on the controllability of undirected networks with different degree mixing patterns based on simulation analysis considering random pinning max degree pinning and mix degree pinning some relevance factors on controllability such as the control gain and the number of pinned nodes are discussed in detail it is found that disassortative mixing enhances the network controllability contrast to assortative mixing to which the network controllability is sensible furthermore too large or too low value of the feedback gain can reduce the controllability from the viewpoint of practical application mix degree pinning strategy is suggested in assortative network while in disassortative network max degree pinning scheme is better than random pinning

pinning synchronization in t s fuzzy complex networks with partial and discrete time couplings communication constraints which may lead to the degradation of performance are common and unavoidable in a real world network in this paper two kinds of communication constraints are considered during the process of information transmission in takagi sugeno ts fuzzy complex network 1 partial couplings where only some part of nodes state information can be transmitted and the channel matrices are introduced to reflect such a phenomenon and 2 discrete time couplings where the nodes information are sampled at certain time instants this is the first time when both communication constraints are simultaneously considered in fuzzy complex networks compared with the perfect communication much less information is available for synchronization to overcome this difficulty a regrouping method is employed to reconstruct the fuzzy network the concise conditions are then proposed to ensure pinning synchronization of fuzzy complex networks with partial and discrete time couplings simulation examples are also provided to demonstrate the effectiveness of the theoretical results

choosing effective controlled nodes for scale free network synchronization abstract previous studies concerning pinning control of complex network synchronization have very often demonstrated that in an unweighted symmetrical scale free network controlling the high degree nodes is more efficient than controlling randomly chosen ones due to the heterogeneity of the node degree or edge connection distribution of the scale free network small degree nodes have relatively high probabilities of being chosen at random but their control has less influence on the other nodes through the network this raises the question of whether or not controlling the high degree nodes is always better than controlling the small ones in scale free networks our answer to this is yes and no in this study we carry out extensive numerical simulations to show that in an unweighted symmetrical barabasi albert scale free network when the portion of controlled nodes is relatively large controlling the small nodes becomes better than controlling the big nodes and controlling randomly chosen nodes has approximately the same effect as controlling the big ones however we also show that for normalized weighted scale free networks controlling the big nodes is in fact always better than controlling the small ones

a transformed lure problem for sliding mode control and chattering reduction the sliding mode control problem is investigated with the frequency domain approach the authors show that the sliding mode control can be transformed into a lure problem with this formulation it is shown that the conventional sliding mode control with a nonlinear sign function can only guarantee to make the overall system stable but not asymptotically stable the authors also consider a practical situation where the sign nonlinearity may contain a hysteresis loop for this situation they show that even if the hysteresis loop is very small there still exists a limit cycle however chattering phenomenon caused by the limit cycle behavior can be eliminated by a certain class of nonlinearities

multiple scale analysis of complex networks using the empirical mode decomposition method abstract empirical mode decomposition emd method can decompose any complicated data into finite intrinsic mode functions imfs in this paper we use emd method to analyze and discuss the structural properties of complex networks a random walk method is used to collect the data series of network systems utilizing the emd method we decompose the obtained data into finite imfs under different spatial scales the analysis results show that emd method is an effective tool for capturing the topological properties of network systems under different spatial scales such as the modular structures of network systems and their energy densities

analysis of pinning controlled networks a renormalization approach in this paper a renormalization approach is introduced for analyzing pinning controlled networks the renormalization process consists of two operations edge weighting and node reduction and is built on a new concept of passivity comparison in the sense of lyapunov v stability furthermore a cascaded model resulted from the renormalization process in a layer structure is presented for estimating the v stability of a network finally simulation studies are presented for illustration and verification of the theoretical results

the control gain region for synchronization in non diffusively coupled complex networks abstract the control gain region for synchronization of non diffusively coupled networks was studied with respect to three conditions synchronization synchronization in finite time and synchronization in the minimum time based on cancellation control methodology and master stability function formalism we found that a complete feasible control gain region may be bounded unbounded empty or a union of several bounded and unbounded regions with a similar shape to the synchronized region an interesting possibility emerged that a network could be synchronized by both negative and positive feedback control simultaneously by bridging synchronizability and synchronizing response speeds with a settling time index we have developed timed synchronized region tsr as a substitute for the classical synchronized region to study finite time synchronization as for the last condition a graphical method was developed to estimate control gain with the minimum synchronization time cgmst each condition has examples provided for illustration and verification

brief paper distributed adaptive control for synchronization of unknown nonlinear networked systems this paper is concerned with synchronization of distributed node dynamics to a prescribed target or control node dynamics a design method is presented for adaptive synchronization controllers for distributed systems having non identical unknown nonlinear dynamics and for a target dynamics to be tracked that is also nonlinear and unknown the development is for strongly connected digraph communication structures a lyapunov technique is presented for designing a robust adaptive synchronization control protocol the proper selection of the lyapunov function is the key to ensuring that the resulting control laws thus found are implementable in a distributed fashion lyapunov functions are defined in terms of a local neighborhood tracking synchronization error and the frobenius norm the resulting protocol consists of a linear protocol and a nonlinear control term with adaptive update law at each node singular value analysis is used it is shown that the singular values of certain key matrices are intimately related to structural properties of the graph

adaptive pinning synchronization in fractional order complex dynamical networks abstract synchronization of general complex dynamical networks with fractional order dynamical nodes is addressed in this paper based on the stability theory of fractional order differential systems and adaptive pinning control some sufficient local asymptotical synchronization criteria and global asymptotical ones are derived respectively which succeed in solving the problem about how many nodes are need to be controlled and how much coupling strength should be applied to ensure the synchronization of the entire fractional order networks the obtained results are more general and effective than those reported moreover the coupling configuration matrices and the inner coupling matrices are not assumed to be symmetric and irreducible finally a numerical simulation is presented to demonstrate the validity and feasibility of the proposed synchronization criteria

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

brief paper global stabilization of complex networks with digraph topologies via a local pinning algorithm this paper concerns the global stability of controlling a complex network with digraph topology to a homogeneous trajectory of the uncoupled system by the local pinning control algorithm the derived stability condition indicates that the smallest real part of eigenvalues of the laplacian sub matrix corresponding to the unpinned vertices can be used to measure the stabilizability of a digraph with a given pinned vertex set a pinned vertex set can stabilize a directed network to some unstable trajectories for instance to a chaotic trajectory of the uncoupled systems if and only if the pinned vertex set can access all other vertices in the digraph furthermore in the bigraph case the analytical estimation of the stabilizability s lower bound suggests that an optimal pinning strategy should take not only the vertex degree but also the shortest path between pairs of vertices into considerations