reach a nonlinear consensus for mas via doubly stochastic quadratic operators abstractthis technical note addresses the new nonlinear protocol class of doubly stochastic quadratic operators dsqos for coordination of consensus problem in multi agent systems mas we derive the conditions for ensuring that every agent reaches consensus on a desired rate of the group s decision where the group decision value in its agent s initial statuses varies besides that we investigate a nonlinear protocol sub class of extreme dsqo edsqo to reach a consensus for mas to a common value with nonlinear low complexity rules and fast time convergence if the interactions for each agent are not selfish in addition to extend the results to reach a consensus and to avoid the selfish case we specify a general class of dsqo for reaching a consensus under any given case of initial states the case that mas reach a consensus by dsqo is if each member of the agent group has positive interactions of dsqo pdsqo with the others the convergence of both edsqo and pdsqo classes is found to be directed tow

construction and analysis of fourth order finite difference schemes for the acoustic wave equation in nonhomogeneous media in this article we construct and analyse a family of finite difference schemes for the acoustic wave equation with variable coefficients these schemes are fourth order accurate in space and time in the case of smooth media and are designed to remain stable and optimal for reflection transmission phenomena in the case of discontinuous coefficients together with a detailed mathematical study various numerical results are presented

a note on the numerical solution of the wave equation with piecewise smooth coefficients the numerical solution of the initial value problem for the wave equation is considered for the case when the equation coefficients are piecewise smooth this problem models linear wave propagation in a medium in which the properties of the medium change discontinuously at interfaces convergent difference approximations can be found that do not require the explicit specification of the boundary conditions at interfaces in the medium and hence are simple to program although such difference approximations typically can only be expected to be first order accurate the numerical phase velocity has the same accuracy as the difference approximation would if the coefficients in the differential equation were smoooth this is proved for the one dimensional case and demonstrated numerically for an example in two space dimensions in which the interface is not aligned with the computational mesh

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

a new class of finite time nonlinear consensus protocols for multi agent systems this paper is devoted to investigating the finite time consensus problem for a multi agent system in networks with undirected topology a new class of global continuous time invariant consensus protocols is constructed for each single integrator agent dynamics with the aid of lyapunov functions in particular it is shown that the settling time of the proposed new class of finite time consensus protocols is upper bounded for arbitrary initial conditions this makes it possible for network consensus problems that the convergence time is designed and estimated offline for a given undirected information flow and a group volume of agents finally a numerical simulation example is presented as a proof of concept

technical communique sufficient conditions for the convergence of a class of nonlinear distributed consensus algorithms this paper is concerned with the convergence of a class of continuous time nonlinear consensus algorithms for single integrator agents in the consensus algorithms studied here the control input of each agent is assumed to be a state dependent combination of the relative positions of its neighbors in the information flow graph using a novel approach based on the smallest order of the nonzero derivative it is shown that under some mild conditions the convex hull of the agents has a contracting property a set valued lasalle like approach is subsequently employed to show the convergence of the agents to a common point the results are shown to be more general than the ones reported in the literature in some cases an illustrative example demonstrates how the proposed convergence conditions can be verified

identification of weakly singular relaxation kernels in three dimensional viscoelasticity existence and uniqueness theorems for solutions of inverse problems for determining weakly relaxation kernels in three dimensional isotropic viscoelasticity are proved

high order finite differences and the pseudospectral method on staggered grids finite difference approximations for the first derivative valid halfway between equidistant gridpoints are in general much more accurate than the corresponding approximations which are valid at gridpoints the pseudospectral fourier method can be viewed as the limit of finite difference approximations when the order of accuracy tends to infinity a fundamentally different and more accurate pseudospectral method is obtained from the halfway approximations this study derives these and related methods and discusses their accuracies

designing fully distributed consensus protocols for linear multi agent systems with directed graphs this technical note addresses the distributed consensus protocol design problem for multi agent systems with general linear dynamics and directed communication graphs existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the laplacian matrix associated with the communication graph which however is global information in this technical note based on only the agent dynamics and the relative states of neighboring agents a distributed adaptive consensus protocol is designed to achieve leader follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node the proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed extensions to the case with multiple leaders are further studied

doubly stochastic quadratic operators and birkhoff s problem abstract in the present we introduce a concept of doubly stochastic quadratic operator we study necessary and sufficient conditions for doubly stochasticity of operator moreover we study analogue of birkhoff s theorem for the class of doubly stochastic operators

compact structure preserving approach to solitary wave in shallow water modeled by the rosenau rlw equation abstract a mass preserving scheme a nonlinear algorithm based on modification of a finite difference method to the rosenau rlw equation is proposed subject to homogeneous boundary conditions the key feature of the method for improving the accuracy of approximate solutions is to develop a compact higher order scheme together with an iterative algorithm for solving the nonlinear implicit scheme the derivatives for space discretization are approximated by using the algorithm dealing with a five point stencil in addition a three level average difference technique is used to perform time discretization the conservation of mass and both the existence and uniqueness of the numerical solution are proved the stability and convergence of the numerical solution with order o 4 2 h 2 h 4 are also confirmed for efficiency analysis numerical results show that the computational efficiency of the compact scheme is much higher than that of non compact schemes moreover long time behavior is also used to validate the capability of the present method

a necessary and sufficient condition for reaching a consensus using degroot s method abstract degroot 1974 proposed a model in which a group of k individuals might reach a consensus on a common subjective probability distribution for an unknown parameter this paper presents a necessary and sufficient condition under which a consensus will be reached by using degroot s method this work corrects an incorrect statement in the original paper about the conditions needed for a consensus to be reached the condition for a consensus to be reached is straightforward to check and yields the value of the consensus if one is reached

majorization doubly stochastic matrices and comparison of eigenvalues abstract 1 basic properties of majorization 2 isotone maps and algebraic operations 3 double sub and superstochasticity 4 doubly stochastic matrices 5 doubly stochastic matrices with minimum permanent 6 comparison of eigenvalues 7 doubly stochastic maps

distributed consensus of heterogeneous multi agent systems with fixed and switching topologies in this article we study distributed consensus of heterogeneous multi agent systems with fixed and switching topologies the analysis is based on graph theory and nonnegative matrix theory we propose two kinds of consensus protocols based on the consensus protocol of first order and second order multi agent systems some necessary and sufficient conditions that the heterogeneous multi agent system solves the consensus problems under different consensus protocols are presented with fixed topology we also give some sufficient conditions for consensus of the heterogeneous multi agent system with switching topology simulation examples are provided to demonstrate the effectiveness of the theoretical results

consensus in directed networks of agents with nonlinear dynamics this technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network both local and global consensus are defined and investigated techniques for studying the synchronization in such complex networks are exploited to establish various sufficient conditions for reaching consensus the local consensus problem is first studied via a combination of the tools of complex analysis local consensus manifold approach and lyapunov methods a generalized algebraic connectivity is then proposed to study the global consensus problem in strongly connected networks and also in a broad class of networks containing spanning trees for which ideas from algebraic graph theory matrix theory and lyapunov methods are utilized

stability of the method of lines it is well known that a necessary condition for the lax stability of the method of lines is that the eigenvalues of the spatial discretization operator scaled by the time stepk lie within a distanceo k of the stability region of the time integration formula ask 0 in this paper we show that a necessary and sufficient condition for stability except for an algebraic factor is that the pseudo eigenvalues of the same operator lie within a distanceo o k of the stability region ask 0 our results generalize those of an earlier paper by considering a runge kutta and other one step formulas b implicit as well as explicit linear multistep formulas c weighted norms d algebraic stability e finite and infinite time intervals and f stability regions with cusps in summary the theory presented in this paper amounts to a transplantation of the kreiss matrix theorem from the unit disk for simple power iterations to an arbitrary stability region for method of lines calculations

time compact high order difference methods for wave propagation we construct one step explicit difference methods for solution of wave propagation problems with fourth order accuracy in both space and time by using a principle that can be generalized to arbitrary order we use the first order system form and a staggered grid the fourth order accuracy in time is obtained by transferring time derivatives in the truncation error to space derivatives discontinuous coefficients corresponding to interfaces between different materials are considered as a special case of variable coefficients and the method is applied across the discontinuities the accuracy is much improved compared to second order methods even for this type of problem a certain norm is shown to be conserved ensuring good accuracy even for long time integration

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

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

non linear protocols for optimal distributed consensus in networks of dynamic agents we consider stationary consensus protocols for networks of dynamic agents with fixed topologies at each time instant each agent knows only its and its neighbors state but must reach consensus on a group decision value that is function of all the agents initial state we show that the agents can reach consensus if the value of such a function is time invariant when computed over the agents state trajectories we use this basic result to introduce a non linear protocol design rule allowing consensus on a quite general set of values such a set includes e g any generalized mean of order p of the agents initial states as a second contribution we show that our protocol design is the solution of individual optimizations performed by the agents this notion suggests a game theoretic interpretation of consensus problems as mechanism design problems under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives we prove that such objectives can be chosen so that rational agents have a unique optimal protocol and asymptotically reach consensus on a desired group decision value we use a lyapunov approach to prove that the asymptotical consensus can be reached when the communication links between nearby agents define a time invariant undirected network finally we perform a simulation study concerning the vertical alignment maneuver of a team of unmanned air vehicles

the theoretical accuracy of runge kutta time discretizations for the initial boundary value problem a study of the boundary error the conventional method of imposing time dependent boundary conditions for runge kutta rk time advancement reduces the formal accuracy of the space time method to first order locally and second order globally independently of the spatial operator this counter intuitive result is analyzed in this paper two methods of eliminating this problem are proposed for the linear constant coefficient case 1 impose the exact boundary condition only at the end of the complete rk cycle 2 impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives the first method while retaining the rk accuracy in all cases results in a scheme with much reduced cfl condition rendering the rk scheme less attractive the second method retains the same allowable time step as the periodic problem however it is a general remedy only for the linear case for non linear hyperbolic equations the second method is effective only for for rk schemes of third order accuracy or less numerical studies are presented to verify the efficacy of each approach

event triggered consensus control for discrete time stochastic multi agent systems this paper is concerned with the event triggered consensus control problem for a class of discrete time stochastic multi agent systems with state dependent noises a novel definition of consensus in probability is proposed to better describe the dynamics of the consensus process of the addressed stochastic multi agent systems the measurement output available for the controller is not only from the individual agent but also from its neighboring ones according to the given topology an event triggered mechanism is adopted with hope to reduce the communication burden where the control input on each agent is updated only when a certain triggering condition is violated the purpose of the problem under consideration is to design both the output feedback controller and the threshold of the triggering condition such that the closed loop system achieves the desired consensus in probability first of all a theoretical framework is established for analyzing the so called input to state stability in probability issip for general discrete time nonlinear stochastic systems within such a theoretical framework some sufficient conditions on event triggered control protocol are derived under which the consensus in probability is reached furthermore both the controller parameter and the triggering threshold are obtained in terms of the solution to certain matrix inequalities involving the topology information and the desired consensus probability finally a simulation example is utilized to illustrate the usefulness of the proposed control protocol

time compact difference methods for wave propagation in discontinuous media in b gustafsson and e mossberg siam j sci comput 26 2004 pp 259 271 a fourth order one step method was constructed for the solution of wave propagation problems the method is based on the first order system form of the pde and uses a staggered grid both in space and time the method was also applied with good results to a problem with discontinuous coefficients without using any special procedure across the discontinuity in this paper we will analyze a model problem from acoustics and demonstrate the theoretical foundation for this behavior furthermore we shall present more detailed numerical experiments which confirm the theoretical results

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