brief paper novel decentralized adaptive strategies for the synchronization of complex networks this paper is concerned with the analysis of the synchronization of networks of nonlinear oscillators through an innovative local adaptive approach in particular time varying feedback coupling gains are considered whose gradient is a function of the local synchronization error over each edge in the network it is shown that under appropriate conditions the strategy is indeed successful in guaranteeing the achievement of a common synchronous evolution for all oscillators in the network the theoretical derivation is complemented by its validation on a set of representative examples

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

decay estimates of solutions for the equations of motion of compressible viscous and heat conductive gases in an exterior domain in ℝ3 we consider the equations of motion of compressible viscous and heat conductive gases in an exterior domain in 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem

decay of the navier stokes poisson equations we establish the time decay rates of the solution to the cauchy problem for the compressible navier stokes poisson system via a refined pure energy method in particular the optimal decay rates of the higher order spatial derivatives of the solution are obtained the h s 0 s 3 2 negative sobolev norms are shown to be preserved along time evolution and enhance the decay rates as a corollary we also obtain the usual lp l2 1 p 2 type of the optimal decay rates compared to the compressible navier stokes system and the compressible irrotational euler poisson system our results imply that both the dispersion effect of the electric field and the viscous dissipation contribute to enhance the decay rate of the density our proof is based on a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis

probabilistic synchronisation of pinning control this paper is concerned with synchronization of complex stochastic dynamical networks in the presence of noise and functional uncertainty a probabilistic control method for adaptive synchronization is presented all required probabilistic models of the network are assumed to be unknown therefore estimated to be dependent on the connectivity strength the state and control values robustness of the probabilistic controller is proved via the liapunov method furthermore based on the residual error of the network states we introduce the definition of stochastic pinning controllability a coupled map lattice with spatiotemporal chaos is taken as an example to illustrate all theoretical developments the theoretical derivation is complemented by its validation on two representative examples

adaptation and parameter estimation in systems with unstable target dynamics and nonlinear parametrization in this paper we propose a solution to the problem of adaptive control and parameter estimation in systems with unstable target dynamics models of uncertainties are allowed to be nonlinearly parameterized and required to be smooth and monotonic functions of linear functionals of the parameters the mere assumption of existence of nonlinear operator gains for the target dynamics is sufficient to guarantee that system solutions are bounded reach a neighborhood of the target set and the mismatches between the modeled uncertainties and their compensator converge to zero with respect to parameter convergence a standard persistent excitation condition suffices to ensure that it is exponential when a weaker nonlinear version of persistent excitation is satisfied asymptotic convergence is guaranteed the spectrum of possible applications ranges from tyre road slip control to asynchronous message transmission in spiking neural oscillators

recurrent neural network based multivariable adaptive control for a class of nonlinear dynamic systems with time varying delay at the beginning an approximate nonlinear autoregressive moving average narma model is employed to represent a class of multivariable nonlinear dynamic systems with time varying delay it is known that the disadvantages of robust control for the narma model are as follows 1 suitable control parameters for larger time delay are more sensitive to achieving desirable performance 2 it only deals with bounded uncertainty and 3 the nominal narma model must be learned in advance due to the dynamic feature of the narma model a recurrent neural network rnn is online applied to learn it however the system performance becomes deteriorated due to the poor learning of the larger variation of system vector functions in this situation a simple network is employed to compensate the upper bound of the residue caused by the linear parameterization of the approximation error of rnn an e modification learning law with a projection for weight matrix is applied to guarantee its boundedness without persistent excitation under suitable conditions the semiglobally ultimately bounded tracking with the boundedness of estimated weight matrix is obtained by the proposed rnn based multivariable adaptive control finally simulations are presented to verify the effectiveness and robustness of the proposed control

a method of quickly calculating the number of pinning nodes on pinning synchronization in complex networks in this paper we propose one adaptive pinning synchronization scheme in complex networks whose adaptive law is simple and flexible most of all we find the decreasing law of maximum eigenvalues of the principal submatrices for coupling matrix and give a method of quickly calculating pinning nodes in complex networks with binary search algorithm furthermore we extend the method to the pinning synchronization scheme with linear feedback control numerical simulations give effectiveness of the adaptive pinning synchronization in a scale free network and the relations between maximum eigenvalue sequence of the principal submatrices and the number of pinning nodes under the conditions of three pinning strategies in a scale free network and a small world network respectively

consensus based distributed cooperative learning from closed loop neural control systems in this paper the neural tracking problem is addressed for a group of uncertain nonlinear systems where the system structures are identical but the reference signals are different this paper focuses on studying the learning capability of neural networks nns during the control process first we propose a novel control scheme called distributed cooperative learning dcl control scheme by establishing the communication topology among adaptive laws of nn weights to share their learned knowledge online it is further proved that if the communication topology is undirected and connected all estimated weights of nns can converge to small neighborhoods around their optimal values over a domain consisting of the union of all state orbits second as a corollary it is shown that the conclusion on the deterministic learning still holds in the decentralized adaptive neural control scheme where however the estimated weights of nns just converge to small neighborhoods of the optimal values along their own state orbits thus the learned controllers obtained by dcl scheme have the better generalization capability than ones obtained by decentralized learning method a simulation example is provided to verify the effectiveness and advantages of the control schemes proposed in this paper

adaptive nn controller design for a class of nonlinear mimo discrete time systems an adaptive neural network tracking control is studied for a class of multiple input multiple output mimo nonlinear systems the studied systems are in discrete time form and the discretized dead zone inputs are considered in addition the studied mimo systems are composed of n subsystems and each subsystem contains unknown functions and external disturbance due to the complicated framework of the discrete time systems the existence of the dead zone and the noncausal problem in discrete time it brings about difficulties for controlling such a class of systems to overcome the noncausal problem by defining the coordinate transformations the studied systems are transformed into a special form which is suitable for the backstepping design the radial basis functions nns are utilized to approximate the unknown functions of the systems the adaptation laws and the controllers are designed based on the transformed systems by using the lyapunov method it is proved that the closed loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set the simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm

the pointwise estimates of diffusion wave for the navier stokes systems in odd multi dimensions we study the dissipation of solutions of the isentropic navier stokes equations in odd multi dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygen s principle our approach is based on the detailed analysis of the green function of the linearized system this is used to study the coupling of nonlinear diffusion waves

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

robust consensus for continuous time multiagent dynamics this paper investigates consensus problems for continuous time multiagent systems with time varying communication graphs subject to input noise based on input to state stability and integral input to state stability robust consensus and integral robust consensus are defined with respect to l and l1 norms of the noise function respectively sufficient and or necessary connectivity conditions are obtained for the system to reach robust consensus or integral robust consensus under mild assumptions the results answer the question on how much interaction is required for a multiagent network to converge despite a certain amount of input disturbance the convergence time is obtained for the consensus computation on directed and k bidirectional graphs

analysis and control of output synchronization in directed and undirected complex dynamical networks this research focuses on the problem of output synchronization in undirected and directed complex dynamical networks respectively by applying barbalat s lemma first to ensure the output synchronization several sufficient criteria are established for these network models based on some mathematical techniques such as the lyapunov functional method and matrix theory furthermore some adaptive schemes to adjust the coupling weights among network nodes are developed to achieve the output synchronization by applying the designed adaptive laws several criteria for output synchronization are deduced for the network models in addition a design procedure of the adaptive law is shown finally two simulation examples are used to show the effectiveness of the previous results

distributed cooperative adaptive identification and control for a group of continuous time systems with a cooperative pe condition via consensus in this paper we first address the uniformly exponential stability ues problem of a group of distributed cooperative adaptive systems in a general framework inspired by consensus theory distributed cooperative adaptive laws are proposed to estimate the unknown parameters of these systems it is shown that not only is the entire closed loop system stable but also both the identification tracking error and the parameter estimation error converge to zero uniformly exponentially under a cooperative persistent excitation pe condition of a regressor matrix in each system which is weaker than the traditionally defined pe condition the effects of network topology on ues of the closed loop system are also explored if the topology is time invariant it needs to be undirected and connected however when the topology is time varying it is just required that the integration of the topology over an interval with fixed length is undirected and connected the established results are then employed to identify and control several classes of linearly parameterized systems simulation examples are also provided to demonstrate the effectiveness and applications of the proposed distributed cooperative adaptive laws

an extension of lasalle s invariance principle and its application to multi agent consensus in the paper an extension of lasalle s invariance principle to a class of switched linear systems is studied one of the motivations is the consensus problem in multi agent systems unlike most existing results in which each switching mode in the system needs to be asymptotically stable this paper allows that the switching modes are only lyapunov stable under certain ergodicity assumptions an extension of lasalle s invariance principle for global asymptotic stability is obtained then it is used to solve the consensus reaching problem of certain multi agent systems in which each agent is modeled by a double integrator and the associated interaction graph is switching and is assumed to be only jointly connected

on large time behavior of solutions to the compressible navier stokes equations in the half space in r3 the navier stokes equation for compressible viscous fluid is considered on the half space in r3 under the zero dirichlet boundary condition for the momentum with initial data near an arbitrarily given equilibrium of positive constant density and zero momentum time decay properties in l2 norms for solutions of the linearized problem are investigated to obtain the rate of convergence in l2 norms of solutions to the equilibrium when initial data are sufficiently close to the equilibrium in some lower bounds are derived for solutions to the linearized problem one of which indicates a nonlinear phenomenon not appearing in the case of the cauchy problem on the whole space

distributed self tuning consensus and synchronization abstract the problem of self tuning of coupling parameters in multi agent systems is considered agent dynamics are described by a discrete time double integrator with unknown input gain each agent locally tunes the strength of interaction with neighboring agents by using a normalized gradient algorithm nga the tuning algorithm minimizes the square of the error between an individual agent s state velocity and the one step delayed average of its own state and the states of its neighbors assuming that the network graph is strongly connected it is proved that the sequence of coupling parameters is convergent and all velocities converge toward the same constant value

formation stability analysis of unmanned multi vehicles under interconnection topologies in this paper the overall formation stability of an unmanned multi vehicle is mathematically presented under interconnection topologies a novel definition of formation error is first given and followed by the proposed formation stability hypothesis based on this hypothesis a unique extension decomposition aggregation scheme is then employed to support the stability analysis for the overall multi vehicle formation under a mesh topology it is proved that the overall formation control system consisting of n number of nonlinear vehicles is not only asymptotically stable but also exponentially stable in the sense of lyapunov within a neighbourhood of the desired formation this technique is shown to be applicable for a mesh topology but is equally applicable for other topologies a simulation study of the formation manoeuvre of multiple aerosonde uavs unmanned aerial vehicles in 3 d space is finally carried out verifying the achieved formation stability result

a sharp time weighted inequality for the compressible navier stokes poisson system in the critical l p framework abstract the compressible navier stokes poisson system takes the form of usual navier stokes equations coupled with the self consistent poisson equation which is used to simulate the transport of charged particles under the electrostatic potential force in this paper we focus on the large time behavior of global strong solutions in the l p critical besov spaces inspired by the dissipative effect arising from poisson potential we formulate a new regularity assumption of low frequencies and then establish the sharp time weighted inequality which leads to the optimal time decay estimates of strong solutions indeed we see that the decay of density is faster at the half rate than that of velocity which is a different ingredient in comparison with the situation of compressible navier stokes equations our proof mainly depends on tricky and non classical besov product estimates with respect to various sobolev embeddings

global well posedness for the compressible navier stokes poisson system in the lp framework abstract in this paper we prove the global well posedness for the multi dimensional isentropic compressible navier stokes poisson equations in the l p framework with initial data close to a stable equilibrium this improves the previous results hao and li 2009 12 lin in press 13 in the l 2 framework

novel adaptive strategies for synchronization of linearly coupled neural networks with reaction diffusion terms in this paper two types of linearly coupled neural networks with reaction diffusion terms are proposed we respectively investigate the adaptive synchronization of these two types of complex network models with local information of node dynamics some novel adaptive strategies to tune the coupling strengths among network nodes are designed by constructing appropriate lyapunov functionals and using inequality techniques several sufficient conditions are given for reaching synchronization by using the designed adaptive laws finally two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results

global bounded synchronization of general dynamical networks with nonidentical nodes this note addresses the problem of synchronization for general dynamical networks with nonidentical nodes the coupling strength outer coupling configuration and inner connection in such networks are all time varying neither an equilibrium for each node nor a synchronization manifold is assumed to exist an estimate of the convergence domain for a general class of time varying nonlinear systems is given by introducing the average dynamics of all nodes and based on this estimate a criterion of global synchronization in the sense of boundedness of the maximum state deviation between nodes is developed an explicit bound of the maximum state deviation between nodes is obtained by the maximum difference between each node dynamics and the average dynamics the proposed criterion is an extension of several related synchronization criteria for the case of identical nodes to the case of nonidentical nodes

global existence and large time behavior of weak solutions to the compressible magnetohydrodynamic equations with coulomb force abstract in this paper we consider the equations of magnetohydrodynamics with coulomb force which is of hyperbolic parabolic elliptic mixed type by constructing the approximate solutions to the modified system with an artificial pressure term added global existence of finite energy weak solutions is established via the weak convergence method more careful argument has been paid to overcome the new difficulty arising from the poisson term of coulomb force in two dimensions when the adiabatic exponent is close to one we also investigate the large time behavior of such weak solutions after discussing the regularity and uniqueness of solutions to the stationary problem

how often do simple dynamical processes have infinitely many coexisting sinks this work concerns the nature of chaotic dynamical processes sheldon newhouse wrote on dynamical processes depending on a parameter xx 1 t xn wherex is in the plane such as might arise when studying poincare return maps for autonomous differential equations in ir3 he proved that if the system is chaotic there will very often be existing parameter values for which there are infinitely many periodic attractors coexisting in a bounded region of the plane and that such parameter values would be dense in some interval the fact that infinitely many coexisting sinks can occur brings into question the very nature of the foundations of chaotic dynamical processes we prove for an apparently typical situation that newhouse s construction yields only a set of parameter values of measure zero

the optimal decay estimates on the framework of besov spaces for generally dissipative systems we give a new decay framework for the general dissipative hyperbolic system and the hyperbolic parabolic composite system which allows us to pay less attention to the traditional spectral analysis in comparison with previous efforts new ingredients lie in the high frequency and low frequency decomposition of a pseudo differential operator and an interpolation inequality related to homogeneous besov spaces of negative order furthermore we develop the littlewood paley pointwise energy estimates and new time weighted energy functionals to establish optimal decay estimates on the framework of spatially critical besov spaces for the degenerately dissipative hyperbolic system of balance laws based on the l p mathbb r n embedding and the improved gagliardo nirenberg inequality the optimal l p mathbb r n l 2 mathbb r n 1 leqq p 2 decay rates and l p mathbb r n l q mathbb r n 1 leqq p 2 leqq q leqq infty decay rates are further shown finally as a direct application the optimal decay rates for three dimensional damped compressible euler equations are also obtained

pointwise estimates of solution for the navier stokes poisson equations in multi dimensions abstract the cauchy problem of the navier stokes poisson equations in multi dimensions n 3 is considered we obtain the pointwise estimates of the solution when it is a perturbation of the constant state then we have the optimal l p r n p 1 convergence rate of the solution

existence of global strong solutions in critical spaces for barotropic viscous fluids this paper is dedicated to the study of viscous compressible barotropic fluids in dimension n 2 we address the question of the global existence of strong solutions for initial data close to a constant state having critical besov regularity first this article shows the recent results of charve and danchin arch ration mech anal 198 1 233 271 2010 and chen et al commun pure appl math 63 1173 1224 2010 with a new proof our result relies on a new a priori estimate for the velocity that we derive via the intermediary of the effective velocity which allows us to cancel out the coupling between the density and the velocity as in haspot well posedness in critical spaces for barotropic viscous fluids 2009 second we improve the results of charve and danchin 2010 and chen et al 2010 by adding as in charve and danchin 2010 some regularity on the initial data in low frequencies in this case we obtain global strong solutions for a class of large initial data which rely on the results of hoff arch rational mech anal 139 303 354 1997 hoff commun pure appl math 55 11 1365 1407 2002 and hoff j math fluid mech 7 3 315 338 2005 and those of charve and danchin 2010 and chen et al 2010 we conclude by generalizing these results for general viscosity coefficients

asymptotic behavior of solutions of the compressible navier stokes equations on the half space asymptotic behavior of solutions of the compressible navier stokes equations on the half space r n n 2 is considered around a given constant equilibrium a solution formula for the linearized problem is derived and l p estimates for solutions of the linearized problem are obtained for 2 p it is shown that as in the case of the cauchy problem the leading part of the solution of the linearized problem is decomposed into two parts one that behaves like diffusion waves and the other one purely diffusively there however are some aspects different from the cauchy problem especially in considering spatial derivatives it is also shown that the solution of the linearized problem approaches for large times the solution of the nonstationary stokes problem in some l p spaces and as a result a solution formula for the nonstationary stokes problem is obtained large time behavior of solutions of the nonlinear problem is then investigated in l p spaces for 2 p by applying the results on the linearized analysis and the weighted energy method the results indicate that there may be some nonlinear interaction phenomena not appearing in the cauchy problem

robust h_ infty group consensus for interacting clusters of integrator agents in this technical note we investigate the h infty group consensus for networks of agents modeled by single integrator with model uncertainty and external disturbance by developing tools from algebraic graph theory matrix analysis as well as lyapunov stability theory we are able to derive some sufficient conditions in terms of the structure and strength of the couplings among agents so as to guarantee the group consensus with desired h infty performance such conditions are structural and easy to check furthermore some adaptation laws are proposed to address the coupling strength problem arising from the consideration that the theoretical value is usually much larger than expected in practice finally some simulation examples are presented to demonstrate the efficiency of the theoretical findings

connectivity and set tracking of multi agent systems guided by multiple moving leaders in this paper we investigate distributed multi agent tracking of a convex set specified by multiple moving leaders with unmeasurable velocities various jointly connected interaction topologies of the follower agents with uncertainties are considered in the study of set tracking based on the connectivity of the time varying multi agent system necessary and sufficient conditions are obtained for set input to state stability and set integral input to state stability for a nonlinear neighbor based coordination rule with switching directed topologies conditions for asymptotic set tracking are also proposed with respect to the polytope spanned by the leaders

asymptotic behavior of classical solutions to the compressible navier stokes poisson equations in three and higher dimensions abstract in this paper we consider the initial value problem for the compressible navier stokes poisson equations in three and higher dimensions firstly global existence and new decay estimate of classical solutions are established the proof is mainly based on the decay properties of solution operator to the compressible navier stokes poisson equations which may be derived from the pointwise estimate of the solution operator to a linear wave equation that is corresponding to the density function while the pointwise estimate of solution operator to the linear wave equation may be established by an energy method in the fourier space the method is different from those in previous works on decay estimate of solutions to compressible navier stokes poisson equations finally asymptotic profile of the solution to the corresponding linear problem is also investigated

determination of configuration matrix element and outer synchronization among networks with different topologies abstract in this paper we research the outer synchronization among discrete networks with different topologies based on lyapunov theorem a novel synchronization technique is designed further the control inputs of the networks and the adaptive laws of configuration matrix element are obtained in the end a numerical example is given to illustrate the effectiveness of the synchronization technique it is found that the designed control input of the networks ensures the convergence of the errors among the networks to zero and the designed adaptive law of configuration matrix element can replace effectively configuration matrix element in networks

distributed consensus of second order multi agent systems with heterogeneous unknown inertias and control gains under a directed graph in this paper we study the consensus problem for second order multi agent systems with heterogeneous unknown inertias and control gains under a general directed graph unlike the existing consensus algorithms for second order multi agent systems in which all agents are assumed to have common unit inertias or share common control gains we allow the inertias and the control gains to be heterogeneous and time varying for each agent we propose fully distributed consensus algorithms over a general directed graph when there exist respectively absolute velocity damping and relative velocity damping novel integral type lyapunov functions are proposed to study the consensus convergence moreover the adaptive sigma modification schemes for the gain adaptation are proposed which renders smaller control gains and thus requires smaller amplitude on the control input without sacrificing consensus convergence furthermore we show that one proposed algorithm also works for consensus of agents with intrinsic lipschitz nonlinear dynamics the control gains are varying and updated by distributed adaptive laws as a result the proposed algorithms require no global information and thus can be implemented in a fully distributed manner

well posedness in critical spaces for the system of compressible navier stokes in larger spaces this paper is dedicated to the study of viscous compressible barotropic fluids in dimension n geq2 we address the question of well posedness for it large data having critical besov regularity our result improves the analysis of r danchin in cite dw of chen et al in cite c2 and of the author in cite h1 h2 inasmuch as we may take initial density in b nn p 1 with 1 leq p infty our result relies on a new a priori estimate for the velocity where we introduce a new unknown called textit effective velocity to weaken one the coupling between the density and the velocity in particular for the first time we obtain uniqueness without imposing hypothesis on the gradient of the density

sampled data based average consensus of second order integral multi agent systems switching topologies and communication noises a distributed sampled data based protocol is proposed for the average consensus of second order integral multi agent systems under switching topologies and communication noises under the proposed protocol it is proved that sufficient conditions for ensuring mean square average consensus are the consensus gain satisfies the stochastic approximation type condition and the communication topology graph at each sampling instant is a balanced graph with a spanning tree moreover if the consensus gain takes some particular forms the proposed protocol can solve the almost sure average consensus problem as well compared with the previous work the distinguished features of this paper lie in that 1 a sampled data based stochastic approximation type protocol is proposed for the consensus of second order integral multi agent systems 2 both communication noises and switching topologies are simultaneously considered and 3 average consensus can be reached not only in the mean square sense but also in the almost sure sense c 2013 elsevier ltd all rights reserved

adaptation and optimization of synchronization gains in the regulation control of networked distributed parameter systems this work is concerned with the design and effects of the synchronization gains on the synchronization problem for a class of networked distributed parameter systems the networked systems assumed to be described by the same evolution equation in a hilbert space differ in their initial conditions to address the synchronization problem a coupling term containing the pairwise state differences of all the networked systems weighted by the synchronization gains is included in the controller of each networked system by considering the aggregate closed loop systems an optimization scheme for the synchronization gains is proposed by minimizing an appropriate measure of synchronization the integrated control and synchronization design is subsequently cast as an optimal control problem the solution of which is found via the solution of parameterized operator lyapunov equations an alternative to the optimization of the synchronization gains is also proposed in which the adaptation of synchronization gains is derived from lyapunov redesign methods both choices of the proposed synchronization controllers aim at achieving both the control and the synchronization objectives an extensive numerical study examines the various aspects of the optimization and adaptation of the gains on the control and synchronization of networked 1d parabolic differential equations

distributed nonlinear control of mobile autonomous multi agents abstract this paper studies the distributed nonlinear control of mobile autonomous agents with variable and directed topology a new distributed nonlinear design scheme is presented for multi agent systems modeled by double integrators with the new design the outputs of the controlled agents asymptotically converge to each other as long as a mild connectivity condition is satisfied moreover the velocity derivative of the output of each agent can be restricted to be within any specified neighborhood of the origin which is of practical interest for systems under such physical constraint the new design is still valid if one of the agents is a leader and the control objective is to achieve leader following as an illustration of the generality and effectiveness of the presented methodology the formation control of a group of unicycle mobile robots with nonholonomic constraints is revisited instead of assuming the point robot model the unicycle model is transformed into two double integrators by dynamic feedback linearization and the proposed distributed nonlinear design method is used to overcome the singularity problem caused by the nonholonomic constraint by properly restricting the velocities simulation results are included to illustrate the theoretical results

homoclinic orbits in a parametrized saddle focus system abstract we consider a parametrized dynamical system with a saddle focus equilibrium point and which for one value of the parameter has a homoclinic orbit conditions on the eigenvalues for the equilibrium point together with transversality conditions imply the existence of an infinite discrete set of parameter values for which the system has a homoclinic orbit such systems arise in the study of nerve axon equations where a homoclinic orbit corresponds to a finite train of nerve impulses traveling at a velocity identified by the associated parameter value

a global existence result for the compressible navier stokes equations in the critical l p framework the present paper is dedicated to the global well posedness issue for the barotropic compressible navier stokes system in the whole space mathbb r d with d 2 we aim at extending the work by danchin inventiones mathematicae 141 3 579 614 2000 to a critical framework which is not related to the energy space for small perturbations of a stable equilibrium state in the sense of suitable lp type besov norms we establish the global existence as a consequence like for incompressible flows one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true in passing we obtain new estimates for the linearized and the paralinearized systems which may be of interest for future works on compressible flows

global existence for compressible navier stokes poisson equations in three and higher dimensions the compressible navier stokes poisson system is concerned in the present paper and the global existence and uniqueness of the strong solution is shown in the framework of hybrid besov spaces in three and higher dimensions

stability of dynamical networks with non identical nodes a multiple v lyapunov function method global asymptotic stability of general dynamical networks with non identical nodes is studied by introducing multiple v lyapunov functions in such a network the coupling strength inner coupling matrix and outer coupling matrix are all allowed to be state dependent and nonlinear a stability criterion is proposed in terms of matrix norms and eigenvalues of some lower dimensional matrices based on this criterion an optimization problem is formed whose solution can be used to test global asymptotic stability we also study the problem of how to achieve global asymptotic stability by design of controllers under the scheme of multiple v lyapunov functions the control action is regarded as a re shape of outer coupling topology and the associated controllers are designed in particular a method of adding or removing a certain number of links is proposed stability analysis of coupled non identical lorenz systems and a design example are also given to illustrate the proposed method

state estimation of heterogeneous oscillators by means of proximity measurements in this paper we aim at estimating the state of an ensemble of mobile agents specifically each agent is an oscillator which moves along a circle at a given time varying angular velocity we assume that an agent can measure the distance from the other oscillators only when they are in its proximity we propose a recursive algorithm which based on these intermittent and uncertain measurements is capable of estimating in real time the relative angular position of the agents the algorithm combines the information coming from the collected measures with the information on the agents dynamics and its convergence is proved by means of interval analysis the theoretical analysis is complemented with extensive numerical simulations

distributed consensus tracking for multiple uncertain nonlinear strict feedback systems under a directed graph in this brief we study the distributed consensus tracking control problem for multiple strict feedback systems with unknown nonlinearities under a directed graph topology it is assumed that the leader s output is time varying and has been accessed by only a small fraction of followers in a group the distributed dynamic surface design approach is proposed to design local consensus controllers in order to guarantee the consensus tracking between the followers and the leader the function approximation technique using neural networks is employed to compensate unknown nonlinear terms induced from the controller design procedure from the lyapunov stability theorem it is shown that the consensus errors are cooperatively semiglobally uniformly ultimately bounded and converge to an adjustable neighborhood of the origin

synchronizing nonlinear complex networks via switching disconnected topology the current theoretical study on the synchronization mechanism of complex networks mainly focuses on fixed connected topology or switching balanced topology which is heavily based on constructing common smooth lyapunov functions however for complex networks with nonlinear node dynamics it is still unknown whether such kind of networks can synchronize under the condition of switching directed and disconnected topology by employing the ideas of sequential connectivity and joint connectivity this paper finds that complex networks with one sided lipschitz node dynamics can realize synchronization even if the network topology is not connected at any time instant by iteratively estimating the maximal distance between different nodes this paper gives several sufficient conditions on synchronization of nonlinear complex networks under switching disconnected topology finally simulation examples validate the main results

sufficient conditions on observability grammian for synchronization in arrays of coupled linear time varying systems synchronizability of stable output coupled identical linear time varying systems is studied it is shown that if the observability grammian satisfies a persistence of excitation condition then there exists a bounded linear time varying feedback law that yields exponential synchronization for all fixed asymmetrical interconnections with connected graphs also a weaker condition on the grammian is given for asymptotic synchronization no assumption is made on the strength of coupling between the systems

global existence of small solutions to a class of nonlinear evolution equations on etudie le comportement global des solutions d une classe d equations d evolution non lineaires on considere le probleme aux valeurs initiales pour des equations quasilineaires qui sont des perturbations d equations lineaires dissipatives

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

some estimates of solutions for the equations of motion of compressible viscous fluid in the three dimensional exterior domain abstract we consider the equations of motion of compressible viscous fluid in an exterior domain in r 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem in particular we shall give l 1 estimates which implies the diffusion wave of compressible navier stokes flow

existence and stability of multiple impulse solutions of a nerve equation a piecewise linear partial differential equation which models the propagation of a nerve impulse along an axon is studied for the equation parameters used there are two solutions which represent solitary impulses traveling with fixed form one with a slower velocity c s1 than the velocity c f1 of the other we show that near these velocities there exist multiple impulse solutions and exhibit four such solutions each of which has two pulses the local stability of these solutions is analyzed the two solutions whose velocities are near c s1 demonstrate instabilities which indicate growth or decay of the separate pulses for one of the multiple impulse solutions with velocity near c s1 and for one of those with velocity near c f1 the second pulse deomonstrates an instability which indicates a change in the spacing between the two pulses the other solution with velocity near c f1 is stable

distributed consensus algorithms in sensor networks quantized data and random link failures the paper studies the problem of distributed average consensus in sensor networks with quantized data and random link failures to achieve consensus dither small noise is added to the sensor states before quantization when the quantizer range is unbounded countable number of quantizer levels stochastic approximation shows that consensus is asymptotically achieved with probability one and in mean square to a finite random variable we show that the mean squared error mse can be made arbitrarily small by tuning the link weight sequence at a cost of the convergence rate of the algorithm to study dithered consensus with random links when the range of the quantizer is bounded we establish uniform boundedness of the sample paths of the unbounded quantizer this requires characterization of the statistical properties of the supremum taken over the sample paths of the state of the quantizer this is accomplished by splitting the state vector of the quantizer in two components one along the consensus subspace and the other along the subspace orthogonal to the consensus subspace the proofs use maximal inequalities for submartingale and supermartingale sequences from these we derive probability bounds on the excursions of the two subsequences from which probability bounds on the excursions of the quantizer state vector follow the paper shows how to use these probability bounds to design the quantizer parameters and to explore tradeoffs among the number of quantizer levels the size of the quantization steps the desired probability of saturation and the desired level of accuracy away from consensus finally the paper illustrates the quantizer design with a numerical study

observer based distributed consensus for general nonlinear multi agent systems with interval control inputs in this paper observer based distributed consensus for general nonlinear multi agent systems with interval control inputs under strongly connected balanced topology is encountered when the relative states of agents are unavailable or undesirable theoretical analysis method is further extended to the case of general nonlinear multi agent systems under switching setting moreover tracking problem on the leader follower scenario is also explicitly investigated under a mutual assumption that the communication graph which represents the interaction among agents contains a directed spanning tree with the leader as its root it is shown that the consensus for underlying considered multi agent systems can be desirable as long as the data missing rate does not exceed a certain threshold finally simulation examples are presented to effectively corroborate the analytical findings

distributed velocity constrained consensus of discrete time multi agent systems with nonconvex constraints switching topologies and delays in this technical note a distributed velocity constrained consensus problem is studied for discrete time multi agent systems where each agent s velocity is constrained to lie in a nonconvex set a distributed constrained control algorithm is proposed to enable all agents to converge to a common point using only local information the gains of the algorithm for all agents need not to be the same or predesigned and can be adjusted by each agent itself based on its own and neighbors information it is shown that the algorithm is robust to arbitrarily bounded communication delays and arbitrarily switching communication graphs provided that the union of the graphs has directed spanning trees among each certain time interval the analysis approach is based on multiple novel model transformations proper control parameter selections boundedness analysis of state dependent stochastic matrices1 exploitation of the convexity of stochastic matrices and the joint connectivity of the communication graphs numerical examples are included to illustrate the theoretical results

synchronization of complex dynamical networks with switching topology a switched system point of view in this paper we study the synchronization problem for complex dynamical networks with switching topology from a switched system point of view the synchronization problem is transformed into the stability problem for time varying switched systems we address two basic problems synchronization under arbitrary switching topology and synchronization via design of switching within a pre given collection of topologies when synchronization cannot be achieved by using any topology alone in this collection for the both problems we first establish synchronization criteria for general connection topology then under the condition of simultaneous triangularization of the connection matrices a common lyapunov function for the first problem and a single lyapunov and multiple lyapunov functions for the second problem are systematically constructed respectively by those of several lower dimensional dynamic systems in order to achieve synchronization using multiple lyapunov functions a stability condition and switching law design method for time varying switched systems are also presented which avoid the usual non increasing condition

bifurcations of systems with structurally unstable homoclinic orbits and moduli of ω equivalence abstract bifurcations of both two dimensional diffeomorphisms with a homoclinic tangency and three dimensional flows with a homoclinic loop of an equilibrium state of saddle focus type are studied in one and two parameter families due to the well known impossibility of a complete study of such bifurcations the problem is restricted to the study of the bifurcations of the so called low round periodic orbits in this connection the idea of taking moduli continuous invariants of the topological conjugacy on the nonwandering set as the main control parameters together with the standard splitting parameter is proposed on this way new bifurcational effects are found which do not occur at a one parameter analysis in particular the density of cusp bifurcations is revealed

synchronization in the kuramoto model a dynamical gradient network approach we propose a dynamical gradient network approach to consider the synchronization in the kuramoto model our scheme to adaptively adjust couplings is based on the dynamical gradient networks where the number of links in each time interval is the same as the number of oscillators but the links in different time intervals are also different the gradient network in the n 1 th time interval is decided by the oscillator dynamics in the nth time interval according to the gradient network in the n 1 th time interval only one inlink s coupling for each oscillator is adjusted by a small incremental coupling during the transition to synchronization the intensities for all oscillators are identical direct numerical simulations fully verify that the synchronization in the kuramoto model is realized effectively even if there exist delayed couplings and external noise

distributed h constrained consensus problem abstract this paper is concerned with the distributed h constrained consensus problem for multi agent systems the objective is to use local information to make all agents reach a consensus in a given convex set while satisfying a desired h performance index in the presence of external disturbances a nonlinear distributed algorithm is adopted to solve this constrained consensus problem to measure the effects of the disturbance on the consensus of all agents and the convergence of all agents to the convex set a nonlinear function is constructed as the h output function by analyzing the convexity of the convex set a sufficient condition is given to solve the constrained consensus problem with the desired h performance finally a numerical simulation example is provided to show the effectiveness of our theoretical results

optimal decay rate for the compressible navier stokes poisson system in the critical l p framework abstract in this paper we consider the large time behavior of global solutions to the initial value problem for the compressible navier stokes poisson system in the l p critical framework and in any dimension n 3 we obtain the time decay rates not only for lebesgue spaces but also for a family of besov norms with negative or nonnegative regularity exponents which improves the decay results in high sobolev regularity the proof is mainly based on the littlewood paley theory and refined time weighted inequalities in fourier space

topology of vibro impact systems in the neighborhood of grazing abstract the grazing bifurcation is considered for the newtonian model of vibro impact systems a brief review on the conditions sufficient for the existence of a grazing family of periodic solutions is given the properties of these periodic solutions are discussed a plenty of results on the topological structure of attractors of vibro impact systems is known however since the considered system is strongly nonlinear these attractors must be very sensitive to changes of parameters of the system on the other hand they are observed in experiments and numerical simulations we offer theorem 2 an approach which allows to explain this contradiction and give a new robust mathematical model of the non hyperbolic dynamics in a neighborhood of grazing

synchronization of diffusively coupled systems on compact riemannian manifolds in the presence of drift abstract recently it has been shown that the synchronization manifold is an asymptotically stable invariant set of diffusively coupled systems on riemannian manifolds we regionally investigate the stability properties of the synchronization manifold when the systems are subject to drift when the drift vector field is quad i e satisfies a certain quadratic inequality and the underlying riemannian manifold is compact we prove that a sufficiently large algebraic connectivity of the underlying graph is sufficient for the synchronization manifold to remain asymptotically stable for drift vector fields which are quad or contracting we explicitly characterize the rate at which the solution converges to the synchronization manifold our main result is that the synchronization manifold is asymptotically stable even for drift vector fields which are only locally lipschitz continuous as long as the algebraic connectivity of the underlying graph is sufficiently large

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

parameter identification and synchronization for uncertain network group with different structures abstract we design a novel synchronization technique to research the synchronization of network group constituted of uncertain networks with different structures based on lyapunov theorem the selection principles of the control inputs and the parameter identification laws of the networks are determined and synchronization conditions of the network group are obtained some numerical simulations are provided to verify the correctness and effectiveness of the synchronization technique we find that the network number the number of network nodes and network connections indeed will not affect the stability of synchronization of network group

lyapunov based approach to multiagent systems with switching jointly connected interconnection this note addresses a coordination problem of a multiagent system with jointly connected interconnection topologies neighbor based rules are adopted to realize local control strategies for these continuous time autonomous agents described by double integrators although the interagent connection structures vary over time and related graphs may not be connected a sufficient condition to make all the agents converge to a common value is given for the problem by a proposed lyapunov based approach and related space decomposition technique

optimal decay rate for strong solutions in critical spaces to the compressible navier stokes equations abstract in this paper we are concerned with the convergence rates of the global strong solution to motionless state with constant density for the compressible navier stokes equations in the whole space r n for n 3 it is proved that the perturbations decay in critical spaces if the initial perturbations of density and velocity are small in b 2 1 n 2 r n b 1 0 r n and b 2 1 n 2 1 r n b 1 0 r n respectively

optimal time decay estimates for the compressible navier stokes equations in the critical l p framework the global existence issue for the isentropic compressible navier stokes equations in the critical regularity framework was addressed in danchin invent math 141 3 579 614 2000 more than 15 years ago however whether optimal time decay rates could be shown in critical spaces has remained an open question here we give a positive answer to that issue not only in the l2 critical framework of danchin invent math 141 3 579 614 2000 but also in the general lp critical framework of charve and danchin arch ration mech anal 198 1 233 271 2010 chen et al commun pure appl math 63 9 1173 1224 2010 haspot arch ration mech anal 202 2 427 460 2011 we show that under a mild additional decay assumption that is satisfied if for example the low frequencies of the initial data are in l p 2 mathbb r d the lp norm the slightly stronger dot b 0 p 1 norm in fact of the critical global solutions decays like t d frac 1p frac14 for t to infty exactly as firstly observed by matsumura and nishida in proc jpn acad ser a 55 337 342 1979 in the case p 2 and d 3 for solutions with high sobolev regularity

reaching an optimal consensus dynamical systems that compute intersections of convex sets in this paper multi agent systems minimizing a sum of objective functions where each component is only known to a particular node is considered for continuous time dynamics with time varying interconnection topologies assuming that each node can observe a convex solution set of its optimization component and the intersection of all such sets is nonempty the considered optimization problem is converted to an intersection computation problem by a simple distributed control rule the considered multi agent system with continuous time dynamics achieves not only a consensus but also an optimal agreement within the optimal solution set of the overall optimization objective directed and bidirectional communications are studied respectively and connectivity conditions are given to ensure a global optimal consensus in this way the corresponding intersection computation problem is solved by the proposed decentralized continuous time algorithm we establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non smooth analysis

emergent behavior in flocks we provide a model for both continuous and discrete time describing the evolution of a flock our model is parameterized by a constant beta capturing the rate of decay which in our model is polynomial of the influence between birds in the flock as they separate in space our main result shows that when beta 1 2 convergence of the flock to a common velocity is guaranteed while for betages1 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only

extensions of weak invariance principle for nonlinear switched systems with time invariant and time varying subsystems abstract this paper addresses the stability problem for nonlinear switched systems with both time invariant and time varying subsystems given that lyapunov like functions are difficult to construct for nonlinear switched systems generalized invariance principles are established based on observer functions for nonlinear switched systems where the subsystems share lyapunov like functions the generalized invariance principles can be specialized to lyapunov based invariance principles where accurate convergent region can be obtained in addition to the above efforts the definitions of p limit system and limit system set are presented under which the proposed invariance principles are extended to nonlinear switched systems with time varying subsystems illustrative examples show the effectiveness of the theoretical results

measure the structure similarity of nodes in complex networks based on relative entropy abstract similarity of nodes is a basic structure quantification in complex networks lots of methods in research on complex networks are based on nodes similarity such as node s classification network s community structure detection network s link prediction and so on therefore how to measure nodes similarity is an important problem in complex networks in this paper a new method is proposed to measure nodes structure similarity based on relative entropy and each node s local structure in the new method each node s structure feature can be quantified as a special kind of information the quantification of similarity between different pair of nodes can be replaced as the quantification of similarity in structural information then relative entropy is used to measure the difference between each pair of nodes structural information at last the value of relative entropy between each pair of nodes is used to measure nodes structure similarity in complex networks comparing with existing methods the new method is more accuracy to measure nodes structure similarity

on models with non rough poincare homoclinic curves abstract the possibility of an a priori complete description of finite parameter models including systems with structurally unstable poincare homoclinic curves is studied the main result reported here is that systems having a countable set of moduli of equivalence and systems having infinitely many degenerate periodic and homoclinic orbits are dense in the newhouse regions of non stability we discuss the question of correctly setting a problem for the analysis of models of such type

practical synchronization with diffusive couplings we investigate the problem of synchronizing nonidentical or perturbed nonlinear systems in the considered setup the systems are incapable to synchronize under diffusive couplings instead assuming the quad property for each system we derive conditions under which the synchronization error can be kept arbitrarily small by a proper choice of the interconnection structure this motivates the definition of practical synchronization as an alternative synchronization notion for nonidentical or perturbed dynamical systems the presented results are intimately related to synchronization of passive systems but it is shown that the stronger quad assumption is essential in our framework the proposed concept of practical synchronization translates directly into a notion of robust synchronization beyond that the results open the way for an investigation of synchronization phenomena on unbalanced graphs leading to the concept of cluster synchronization

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper