sampled data consensus over random networks this paper considers the consensus problem for a network of nodes with random interactions and sampled data control actions we first show that consensus in expectation in mean square and almost surely are equivalent for a general random network model when the inter sampling interval and maximum node degree satisfy a simple relation the three types of consensus are shown to be simultaneously achieved over an independent or a markovian random network defined on an underlying graph with a directed spanning tree for both independent and markovian random network models necessary and sufficient conditions for mean square consensus are derived in terms of the spectral radius of the corresponding state transition matrix these conditions are then interpreted as the existence of critical value on the intersampling interval below which a global mean square consensus is achieved and above which the system diverges in a mean square sense for some initial states finally we establish an upper bound on the intersampling interval below which almost sure consensus is reached and a lower bound on the intersampling interval above which almost sure divergence is reached some numerical simulations are given to validate the theoretical results and some discussions on the critical value of the inter sampling intervals for the mean square consensus are provided

couple group consensus for second order multi agent systems with fixed and stochastic switching topologies abstract this paper deals with the couple group consensus problem for second order discrete time multi agent systems both the fixed topology case and the stochastic switching topology case are considered the couple group consensus problem is converted into the stability problem of the error system by a linear transformation for the fixed topology case we obtain two different conditions of couple group consensus for the stochastic switching topology case we obtain a necessary and sufficient condition of mean square couple group consensus algorithms are provided to design the allowable control gains finally simulation examples are given to show the usefulness of the theoretical results

stability analysis and a priori error estimates of the third order explicit runge kutta discontinuous galerkin method for scalar conservation laws in this paper we present an analysis of the runge kutta discontinuous galerkin method for solving scalar conservation laws where the time discretization is the third order explicit total variation diminishing runge kutta method we use an energy technique to prove the mathrm l 2 norm stability for scalar linear conservation laws and to obtain a priori error estimates for smooth solutions of scalar nonlinear conservation laws quasi optimal order is obtained for general numerical fluxes and optimal order is given for upwind fluxes the theoretical results are obtained for piecewise polynomials with any degree k geq1 under the standard temporal spatial cfl condition tau leq gamma h where h and tau are the element length and time step respectively and the positive constant gamma is independent of h and tau

weighted consensus protocols design based on network centrality for multi agent systems with sampled data this technical note aims at constructing and analyzing an efficient framework for the leader following consensus protocol in multi agent systems mass we propose two novel consensus protocols weighted by calculating the betweenness and eigenvector centralities for agent and link which are determined by the interconnection structure of mass the concepts of centrality were introduced in the field of social science ultimately the use of the proposed protocols can be described with regard to not only the number of each agent s neighbors which was utilized in the existing works but also more information about agents through considering two such centralities by utilizing the lyapunov method and some mathematical techniques the leader following guaranteed cost consensus conditions for mass with the proposed protocols and sampled data will be established in terms of linear matrix inequalities lmis based on the result of consensus criteria two new protocol design methods which utilize the betweenness and eigenvector centralities will be proposed finally some simulation results are given to illustrate the advantages of the proposed protocols in point of the robustness on sampling interval and the transient consensus performance

on iterative learning algorithms for the formation control of nonlinear multi agent systems this paper deals with formation control problems for multi agent systems with nonlinear dynamics and switching network topologies using the nearest neighbor knowledge a distributed algorithm is constructed by employing the iterative learning control approach sufficient conditions are given to obtain the desired relative formations of agents which benefits from the strict positiveness of products of stochastic matrices it is shown that the derived results can effectively work although the network topologies dynamically change along both time and iteration axes and the corresponding directed graphs may not have spanning trees such result is also illustrated via numerical simulations

observer design for tracking consensus in second order multi agent systems fractional order less than two this technical note studies the leader following tracking consensus problem of a class of multi agent systems where the dynamics of the leader is described by second order systems in order to track the states of the leader observers for the followers are designed by fractional order multi agent systems where the relative velocity information is unavailable it is interestingly found that the followers can track the leader with second order dynamics even if the fractional order is less than two by only using the position information of the local neighbors which is different from the existing results a novel fractional order observer is first proposed whose order is surprisingly less than the original leader system it is also shown that leader following consensus can be ensured if some carefully selected followers are informed and the relative position based protocols are appropriately designed with fractional order being between one and two a necessary and sufficient condition for the leader following consensus in multi agent systems without control input delay is proposed the results are then extended to the case with constant control input delay it is found that in both cases the real and imaginary parts of the eigenvalues of the augmented laplacian matrix of the topology play an important role in achieving consensus

formation tracking of the second order multi agent systems using position only information via impulsive control with input delays in this paper the formation tracking problem for the second order multi agent system with and without input delay are investigated respectively the objective is to design the formation tracking algorithm such that a certain follower follows the trajectory of the leader while also maintains a certain desired geometric formation with other agents simultaneously the impulsive algorithms are designed by using only the relative position information of the neighbors for both the cases with and without the input delay by using properties of the laplacian matrix and combining the stability theory of impulsive systems necessary and sufficient conditions are derived to achieve the formation tracking of the second order multi agent system with and without the input delay respectively the numerical examples are given to illustrate the effectiveness of our theoretical results

distributed leader follower flocking control for multi agent dynamical systems with time varying velocities abstract using tools from algebraic graph theory and nonsmooth analysis in combination with ideas of collective potential functions velocity consensus and navigation feedback a distributed leader follower flocking algorithm for multi agent dynamical systems with time varying velocities is developed where each agent is governed by second order dynamics the distributed leader follower algorithm considers the case in which the group has one virtual leader with time varying velocity for each agent i this algorithm consists of four terms the first term is the self nonlinear dynamics which determines the final time varying velocity the second term is determined by the gradient of the collective potential between agent i and all of its neighbors the third term is the velocity consensus term and the fourth term is the navigation feedback from the leader to avoid an impractical assumption that the informed agents sense all the states of the leader the new designed distributed algorithm is developed by making use of observer based pinning navigation feedback in this case each informed agent only has partial information about the leader yet the velocity of the whole group can still converge to that of the leader and the centroid of those informed agents having the leader s position information follows the trajectory of the leader asymptotically finally simulation results are presented to demonstrate the validity and effectiveness of the theoretical analysis surprisingly it is found that the local minimum of the potential function may not form a commonly believed lattice

impulsive multiconsensus of second order multiagent networks using sampled position data a multiconsensus problem of multiagent networks is solved in this paper where multiconsensus refers to that the states of multiple agents in each subnetwork asymptotically converge to an individual consistent value when there exist information exchanges among subnetworks a distributed impulsive protocol is proposed to achieve multiconsensus of second order multiagent networks in terms of three categories 1 stationary multiconsensus 2 the first dynamic multiconsensus and 3 the second dynamic multiconsensus this impulsive protocol utilizes only sampled position data and is implemented at sampling instants for those three categories of multiconsensus the control parameters in the impulsive protocol are designed respectively moreover necessary and sufficient conditions are derived under which each multiconsensus can be reached asymptotically several simulations are finally provided to demonstrate the effectiveness of the obtained theoretical results

high order discontinuous galerkin methods with lagrange multiplier for hyperbolic systems of conservation laws in this work we present novel high order discontinuous galerkin methods with lagrange multiplier dglm for hyperbolic systems of conservation laws lagrange multipliers are introduced on the inter element boundaries via the concept of weak divergence static condensation on element unknowns considerably reduces globally coupled degrees of freedom resulting in the stiffness equations in the lagrange multipliers only we first establish stability results and provide conditions on the stabilization parameter which plays an important role in resolving discontinuities as well accuracy tests are then performed which shows optimal convergence in the l2 norm extensive numerical results indicate that the dglm has potentials in delivering high order accurate information for various problems in hyperbolic conservation laws numerical examples include inviscid burgers equations shallow water equations subcritical flow and supercritical upstream subcritical downstream flow and 2d circular dam break and compressible euler equations intersection of mach 3 and sods shock tube

disconnected synchronized regions of complex dynamical networks this technical note addresses the synchronized region problem which is converted to a more convenient matrix stability problem for complex dynamical networks for any natural number n the existence of a network with n disconnected synchronized regions is theoretically proved and numerically demonstrated this shows the intrinsic complexity of the network synchronization problem convexity characteristic of stability for relevant matrix pencils is further discussed a smooth chua s circuit network is finally discussed as an example for illustration

high order dg dglm method for hyperbolic conservation laws abstract a high order discontinuous galerkin method in time combined with discontinuous galerkin method with lagrange multiplier dglm kim 2015 4 in space is proposed to approximate the solution to hyperbolic conservation laws with boundary conditions stability of the approximate solution is proved in a broken l 2 l 2 norm and also in an l l 2 norm error estimates of o h r 1 2 k n q 1 2 with p r e and p q j n elements r q d 1 2 are derived in a broken l 2 l 2 norm where h and k n are the maximum diameters of the elements and the time step of j n respectively j n is the time interval and d is the dimension of the spatial domain an explanation on algorithmic aspects is given

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

an implicit high order hybridizable discontinuous galerkin method for nonlinear convection diffusion equations in this paper we present hybridizable discontinuous galerkin methods for the numerical solution of steady and time dependent nonlinear convection diffusion equations the methods are devised by expressing the approximate scalar variable and corresponding flux in terms of an approximate trace of the scalar variable and then explicitly enforcing the jump condition of the numerical fluxes across the element boundary applying the newton raphson procedure and the hybridization technique we obtain a global equation system solely in terms of the approximate trace of the scalar variable at every newton iteration the high number of globally coupled degrees of freedom in the discontinuous galerkin approximation is therefore significantly reduced we then extend the method to time dependent problems by approximating the time derivative by means of backward difference formulae when the time marching method is p 1 th order accurate and when polynomials of degree p 0 are used to represent the scalar variable each component of the flux and the approximate trace we observe that the approximations for the scalar variable and the flux converge with the optimal order of p 1 in the l 2 norm finally we apply element by element postprocessing schemes to obtain new approximations of the flux and the scalar variable the new approximate flux which has a continuous interelement normal component is shown to converge with order p 1 in the l 2 norm the new approximate scalar variable is shown to converge with order p 2 in the l 2 norm the postprocessing is performed at the element level and is thus much less expensive than the solution procedure for the time dependent case the postprocessing does not need to be applied at each time step but only at the times for which an enhanced solution is required extensive numerical results are provided to demonstrate the performance of the present method

fully discrete finite element analysis of multiphase flow in groundwater hydrology this paper deals with the development and analysis of a fully discrete finite element method for a nonlinear differential system for describing an air water system in groundwater hydrology the nonlinear system is written in a fractional flow formulation i e in terms of a saturation and a global pressure the saturation equation is approximated by a finite element method while the pressure equation is treated by a mixed finite element method the analysis is carried out first for the case where the capillary diffusion coefficient is assumed to be uniformly positive and is then extended to a degenerate case where the diffusion coefficient can be zero it is shown that error estimates of optimal order in the l 2 norm and almost optimal order in the l infty norm can be obtained in the nondegenerate case in the degenerate case we consider a regularization of the saturation equation by perturbing the diffusion coefficient the norm of error estimates depends on the severity of the degeneracy in diffusivity with almost optimal order convergence for nonsevere degeneracy implementation of the fractional flow formulation with various nonhomogeneous boundary conditions is also discussed results of numerical experiments using the present approach for modeling groundwater flow in porous media are reported

a space time discontinuous galerkin method for the incompressible navier stokes equations we introduce a space time discontinuous galerkin dg finite element method for the incompressible navier stokes equations our formulation can be made arbitrarily high order accurate in both space and time and can be directly applied to deforming domains different stabilizing approaches are discussed which ensure stability of the method a numerical study is performed to compare the effect of the stabilizing approaches to show the method s robustness on deforming domains and to investigate the behavior of the convergence rates of the solution recently we introduced a space time hybridizable dg hdg method for incompressible flows s rhebergen b cockburn a space time hybridizable discontinuous galerkin method for incompressible flows on deforming domains j comput phys 231 2012 4185 4204 we will compare numerical results of the space time dg and space time hdg methods this constitutes the first comparison between dg and hdg methods

coupling discontinuous galerkin and mixed finite element discretizations using mortar finite elements discontinuous galerkin dg and mixed finite element mfe methods are two popular methods that possess local mass conservation in this paper we investigate dg dg and dg mfe domain decomposition couplings using mortar finite elements to impose weak continuity of fluxes and pressures on the interface the subdomain grids need not match and the mortar grid may be much coarser giving a two scale method convergence results in terms of the fine subdomain scale h and the coarse mortar scale h are established for both types of couplings in addition a nonoverlapping parallel domain decomposition algorithm is developed which reduces the coupled system to an interface mortar problem the properties of the interface operator are analyzed

a discontinuous galerkin method with lagrange multiplier for hyperbolic conservation laws with boundary conditions we introduce a discontinuous galerkin method with lagrange multiplier dglm to approximate the solution to the hyperbolic conservation laws with boundary conditions lagrange multipliers are introduced on the edge face of the element via weak divergence wang and ye 2014 the final global system has reduced numbers of unknowns of the standard dg methods numerical fluxes from finite volume difference method are not considered for the time discretization backward euler difference method is used stability of the approximate solution is proved in energy norm discontinuity of the solution is allowed in the error analysis local error estimates of o hr 12 t with pr e elements rd 12 are derived where h and t are the maximum diameter of the elements and time steps respectively and d is the dimension of the spatial domain the high order approximation is obtained under an appropriate condition on the stabilizing parameter it is shown that the method preserves the property of the local mass conservation an explanation on algorithmic aspects is given

a space time hybridizable discontinuous galerkin method for incompressible flows on deforming domains we present the first space time hybridizable discontinuous galerkin hdg finite element method for the incompressible navier stokes and oseen equations major advantages of a space time formulation are its excellent capabilities of dealing with moving and deforming domains and grids and its ability to achieve higher order accurate approximations in both time and space by simply increasing the order of polynomial approximation in the space time elements our formulation is related to the hdg formulation for incompressible flows introduced recently in e g n c nguyen j peraire b cockburn a hybridizable discontinuous galerkin method for stokes flow comput methods appl mech eng 199 2010 582 597 however ours is inspired in typical dg formulations for compressible flows which allow for a more straightforward implementation another difference is the use of polynomials of fixed total degree with space time hexahedral and quadrilateral elements instead of simplicial elements we present numerical experiments in order to assess the quality of the performance of the methods on deforming domains and to experimentally investigate the behavior of the convergence rates of each component of the solution with respect to the polynomial degree of the approximations in both space and time

impulsive consensus algorithms for second order multi agent networks with sampled information in this paper the distributed consensus problem for second order continuous time multi agent networks with sampled data communication is investigated motivated by impulsive control strategy two kinds of impulsive distributed consensus algorithm are proposed these algorithms only utilize the sampled information and are implemented at sampled times by using the stability theory of impulsive systems and properties of the laplacian matrix necessary and sufficient conditions are obtained to ensure the consensus of the controlled networks it is shown that the control gains the sampling period and the eigenvalues of the laplacian matrix of the communication graph play key roles in achieving the consensus a numerical example is given to illustrate the results

global stabilization of rigid formations in the plane this paper considers the problem of distributed control of rigid formation shapes in the plane for multi agent systems a constructive perturbation method is proposed and combined with the conventional gradient control law the proposed control law stabilizes the desired rigid formation in a global sense for all initial conditions except the case when a pair of communicating agents happen to have the same initial location it also avoids collisions between any two communicating agents during the motion simulation results are provided to illustrate the effectiveness of the control algorithm

discontinuous galerkin methods for a model of population dynamics with unbounded mortality discontinuous galerkin finite element methods in age time domain are proposed to approximate a possibly nonsmooth solution to the model of population dynamics with unbounded mortality coefficient function the strong stability is established and a priori l 2 error estimates are obtained we show that the error estimates are optimal both in rate and in regularity away from the maximum age nonnegativity of the solution is also shown the scheme is explicit and the solution is computed strip by strip marching in time several numerical examples are presented

brief paper second order consensus in multi agent dynamical systems with sampled position data this paper studies second order consensus in multi agent dynamical systems with sampled position data a distributed linear consensus protocol with second order dynamics is designed where both the current and some sampled past position data are utilized it is found that second order consensus in such a multi agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period a necessary and sufficient condition for reaching consensus of the system in this setting is established based on which consensus regions are then characterized it is shown that if all the eigenvalues of the laplacian matrix are real then second order consensus in the multi agent system can be reached for any sampling period except at some critical points depending on the spectrum of the laplacian matrix however if there exists at least one eigenvalue of the laplacian matrix with a nonzero imaginary part second order consensus cannot be reached for sufficiently small or sufficiently large sampling periods in such cases one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods finally simulation examples are given to verify and illustrate the theoretical analysis

stability analysis of swarms in this note we specify an individual based continuous time model for swarm aggregation in n dimensional space and study its stability properties we show that the individuals autonomous agents or biological creatures will form a cohesive swarm in a finite time moreover we obtain an explicit bound on the swarm size which depends only on the parameters of the swarm model

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

analyzing and controlling the network synchronization regions abstract in this paper the commonly concerned issue of synchronization regions of complex dynamical networks is investigated for the case when the synchronous state is an equilibrium point some simple sufficient conditions for a network to have or have no unbounded synchronization regions of the form 1 are established where 1 is a constant in addition a sufficient condition for the existence of a bounded synchronization region of the form 2 3 is derived where 2 and 3 are constants by using the parameter dependent lyapunov function method furthermore some effective controller design methods are presented that can change the synchronization regions thereby managing the synchronizability of the network finally some numerical examples are given to show that a dynamical network may have disconnected synchronization regions particularly it may have the coexistence of unbounded and bounded synchronization regions in the form of 1 2 3

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

reaching a consensus in a dynamically changing environment a graphical approach this paper presents new graph theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments the concepts of rooted strongly rooted and neighbor shared are defined and conditions are derived for compositions of sequences of directed graphs to be of these types the graph of a stochastic matrix is defined and it is shown that under certain conditions the graph of a sarymsakov matrix and a rooted graph are one and the same as an illustration of the use of the concepts developed in this paper graph theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied vicsek consensus problem

further remarks on the cayley hamilton theorem and leverrier s method for the matrix pencil se a some results for matrix pencils are extended to the singular case se a a singular leverrier s relation cayley hamilton theorem and newton s formula are given a finite series expansion for se a 1 is given in terms of the generalized tschirnhausen polynomials

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

brief paper some necessary and sufficient conditions for second order consensus in multi agent dynamical systems this paper studies some necessary and sufficient conditions for second order consensus in multi agent dynamical systems first basic theoretical analysis is carried out for the case where for each agent the second order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant a necessary and sufficient condition is given to ensure second order consensus and it is found that both the real and imaginary parts of the eigenvalues of the laplacian matrix of the corresponding network play key roles in reaching consensus based on this result a second order consensus algorithm is derived for the multi agent system facing communication delays a necessary and sufficient condition is provided which shows that consensus can be achieved in a multi agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value finally simulation examples are given to verify the theoretical analysis

fully discrete mixed finite element approximations for non darcy flows in porous media a numerical approximation procedure is proposed to solve equations describing non darcy flow of a single phase fluid in a porous medium in two or three spacial dimensions including the generalized forchheimer equation fully discrete mixed finite element methods are considered and analyzed for the approximation existence and uniqueness of the approximation are discussed and optimal order error estimates in l2 are derived for the three relevant functions

formation control of mobile agents based on distributed position estimation we propose a formation control strategy based on distributed position estimation for single integrator modeled agents by using relative position measurements under the proposed strategy the estimated and the actual formations globally exponentially converge to the actual and the desired formations respectively up to translation if and only if the interaction graph for the agents has a spanning tree a sufficient condition is provided for the case that the edge weights of the interaction graph are time varying further the proposed strategy is applied to formation control of unicycle like agents

a generalized cayley hamilton theorem abstract let f be a solvable lie subalgebra of the lie algebra gl n c c n n as a vector space let f k x 1 x 2 x p k 1 2 r be polynomials in the commuting variables x 1 x 2 x p with coefficients in c for n n matrices m 1 m 2 m r let f x 1 x 2 x p k 1 r m k f k x 1 x 2 x p and let f x 1 x 2 x p det f x 1 x 2 x p in this paper we prove that for a 1 a 2 a p m 1 m 2 m r f if one value of the matrix valued function f a 1 a 2 a p the value depends on the product order of the variables is nilpotent then a all values of f a 1 a 2 a p are nilpotent b all values of f a 1 a 2 a p again depends on the product order of the variables are nilpotent and one value is 0 this generalizes the recent result in 7 and makes his result accurate the main tool we use in this paper is the representation theory of solvable lie algebras

the generalized cayley hamilton theorem for standard pencils abstract the cayley hamilton theorem is extended from the case of one matrix to that of two matrices the developed theorem is suitable for the standard form pencil se a let s det se a r 0 n a r s r then we show that r 0 n a r a r e n r 0 such a neat result which is very similar to the original theorem also is due to some nice properties of the standard pair e a for example e and a commute and share the same eigenspaces

a generalized cayley hamilton theorem for polynomials with matrix coefficients abstract a family f of square matrices of the same order is called a quasi commuting family if ab ba c c ab ba for all a b c f where a b c need not be distinct let f k x 1 x 2 x p k 1 2 r be polynomials in the indeterminates x 1 x 2 x p with coefficients in the complex field c and let m 1 m 2 m r be n n matrices over c which are not necessarily distinct let f x 1 x 2 x p k 1 r m k f k x 1 x 2 x p and let f x 1 x 2 x p det f x 1 x 2 x p in this paper we prove that for n n matrices a 1 a 2 a p over c if a 1 a 2 a p m 1 m 2 m r is a quasi commuting family then f a 1 a 2 a p o implies that f a 1 a 2 a p o

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