convergence of consensus models with stochastic disturbances we consider consensus algorithms in their most general setting and provide conditions under which such algorithms are guaranteed to converge almost surely to a consensus let a t b t rn n be possibly stochastic nonstationary matrices and x t m t 6 rn 1 be state and perturbation vectors respectively for any consensus algorithm of the form x t 1 a t x t b t m t we provide conditions under which consensus is achieved almost surely i e pr limt x t c1 1 for some c r moreover we show that this general result subsumes recently reported results for specific consensus algorithms classes including sum preserving nonsum preserving quantized and noisy gossip algorithms also provided are the e converging time for any such converging iterative algorithm i e the earliest time at which the vector x t is e close to consensus and sufficient conditions for convergence in expectation to the average of the initial node measurements finally mean square error bounds of any consensus algorithm of the form discussed above are presented

stationary consensus of heterogeneous multi agent systems with bounded communication delays consensus seeking is investigated for the discrete time heterogeneous multi agent systems composed of first order agents and second order agents and two stationary consensus algorithms are constructed for the first order agents and the second order agents respectively based on the properties of nonnegative matrices sufficient consensus criteria are obtained for the agents with bounded communication delays under fixed topology and switching topologies respectively with some prerequisites on the coupling weights and the sampling interval the asymptotic consensus achievement of the dynamic agents is independent of the communication delay but strictly depends on the connectedness of the interconnection topology simulation results illustrate the correctness of the results

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

suppression and stabilisation of noise in this article we investigate the stochastic suppression and stabilisation of nonlinear systems given an unstable differential equation in which f satisfies the one sided polynomial growth condition we introduce two brownian noise feedbacks and therefore stochastically perturb this system into the nonlinear stochastic differential equation this article shows that appropriate may guarantee that this stochastic system exists as a unique global solution although the corresponding deterministic may explode in a finite time then sufficiently large q may ensure that this stochastic system is almost surely exponentially stable

state consensus for multi agent systems with switching topologies and time varying delays in this paper we investigate state consensus problems for discrete time multi agent systems with changing communications topologies and bounded time varying communication delays the analysis in this paper is based on the properties of non negative matrices we first extend the model of networks of dynamic agents to the case with multiple time delays and prove that if the communication topology time delays and weighting factors are time invariant then the necessary and sufficient condition that the multi agent system solves a consensus problem is that the communication topology represented by a directed graph has spanning trees then we allow for dynamically changing communication topologies and bounded time varying communication delays and present some sufficient conditions for state consensus of system finally as a special case of our model the problem of asynchronous information exchange is also discussed

controllability of heterogeneous multi agent systems under directed and weighted topology abstractthis paper considers the controllability problem for both continuous and discrete time linear heterogeneous multi agent systems with directed and weighted communication topology first two kinds of neighbour based control protocols based on the distributed protocol of first order and second order multi agent systems are proposed under which it is shown that a heterogeneous multi agent system is controllable if the underlying communication topology is controllable then under special leader selection the result shows that the controllability of a heterogeneous multi agent system is solely decided by its communication topology graph furthermore some necessary and or sufficient conditions are derived for controllability of communication topology from algebraic and graphical perspectives finally simulation examples are presented to demonstrate the effectiveness of the theoretical results

avoiding collisions in flocks among the many models for flocking systems of interacting particles the one introduced by cucker and smale has attracted attention due to the fact that a convergence to flocking i e to a common velocity could be established depending on conditions on the initial state of the system in this note we extend this model by adding to it a repelling force between particles we show that for this modified model convergence to flocking is established along the same lines while in addition avoidance of collisions i e the respect of a minimal distance between particles is ensured

consensus of multi agent systems based on sampled data control this article studies the consensus problem in directed networks assuming that each agent is with double integrator dynamics and only obtains the measurements of its positions relative to its neighbours at sampling instants we propose a protocol based on sampled data control and derive an equivalent characterisation of the solvability of the consensus problem under this protocol in virtue of this equivalent characterisation we further consider two cases fixed topology and switching topology for the first case we present a set of sampling periods and feedback coefficients which ensure that the protocol can solve a consensus problem for the second case we derive sufficient conditions for the protocol to solve a consensus problem under arbitrary switching signals and under a class of switching signals respectively finally simulations are provided to illustrate the effectiveness of the theoretical results

stochastic stability of continuous time consensus protocols a unified approach to studying convergence and stochastic stability of continuous time consensus protocols cps is presented in this work our method applies to networks with directed information flow both cooperative and noncooperative interactions networks under weak stochastic forcing and those whose topology and strength of connections may vary in time the graph theoretic interpretation of the analytical results is emphasized we show how the spectral properties such as algebraic connectivity and total effective resistance as well as the geometric properties such as the dimension and the structure of the cycle subspace of the underlying graph shape stability of the corresponding cps in addition we explore certain implications of spectral graph theory to cp design in particular we point out that expanders sparse highly connected graphs generate cps whose performance remains uniformly high when the size of the network grows unboundedly similarly we highlight the benefits of using random

distributed algorithm for solving convex inequalities in this note a distributed subgradient based algorithm is proposed for continuous time multi agent systems to search a feasible solution to convex inequalities the algorithm involves each agent achieving a state constrained by its own inequalities while exchanging local information with other agents under a time varying directed communication graph with the validity of a mild connectivity condition associated with the communication graph it is shown that all agents will reach agreement asymptotically and the consensus state is in the solution set of the inequalities furthermore the method is also extended to solving the distributed optimization problem of minimizing the sum of local objective functions subject to convex inequalities simulation examples are presented to demonstrate the effectiveness of the theoretical results

consensus conditions of continuous time multi agent systems with time delays and measurement noises this work is concerned with stochastic consensus conditions of multi agent systems with both time delays and measurement noises for the case of additive noises we develop some necessary conditions and sufficient conditions for stochastic weak consensus by estimating the differential resolvent function for delay equations by the martingale convergence theorem we obtain necessary conditions and sufficient conditions for stochastic strong consensus for the case of multiplicative noises we consider two kinds of time delays appeared in the measurement term and the noise term respectively we first show that stochastic weak consensus with the exponential convergence rate implies stochastic strong consensus then by constructing degenerate lyapunov functional we find the sufficient consensus conditions and show that stochastic consensus can be achieved by carefully choosing the control gain according to the noise intensities and the time delay in the measurement term

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

topology selection for multi agent systems with opposite leaders abstract for the multi agent system with a navigational leader and its opponent the followers cannot converge to the state of the navigational leader in this paper we consider the topology selection problem to minimize the opponent s influence which is measured by the tracking error of the system firstly two combinatorial optimization problems are formulated one is to minimize the tracking error by selecting guided informed agents the followers who can obtain the navigational leader s information the other is to choose minimal number of guided informed agents under an upper bound constraint of the tracking error secondly for the scenario where the guided informed agents are preset we consider the problem of assigning the weights of edges to minimize the tracking error three convex optimization problems are proposed to evaluate the upper and lower bounds of the tracking error finally numerical examples are provided to illustrate the effectiveness of the theoretical results

consensus of heterogeneous multi agent systems without velocity measurements this article considers the consensus problem of heterogeneous multi agent system composed of first order and second order agents in which the second order integrator agents cannot obtain the velocity second state measurements for feedback two different consensus protocols are proposed first we propose a consensus protocol and discuss the consensus problem of heterogeneous multi agent system by applying the graph theory and the lyapunov direct method some sufficient conditions for consensus are established when the communication topologies are undirected connected graphs and leader following networks second due to actuator saturation we propose another consensus protocol with input constraint and obtain the consensus criterions for heterogeneous multi agent system finally some examples are presented to illustrate the effectiveness of the obtained criterions

a necessary and sufficient condition for consensus of continuous time agents over undirected time varying networks the average consensus problem of continuous time agents in undirected time varying networks is studied the network is allowed to be disconnected a notion called infinite integral connectivity is proposed based on the notion a necessary and sufficient condition for achieving consensus is given that is when the network topology is described by an undirected time varying graph g t the agents achieve consensus if and only if the infinite integral graph of g t over 0 is connected this criterion does not hold for directed networks

flocking of multi agent systems with multiple groups in this paper we consider the flocking problem of multi agent systems with multiple groups first some algorithms using local information are designed to divide the agents into any pre assigned number of groups in fixed and switching heterogeneous networks respectively based on algebraic graph theory and barbalat s lemma convergence criteria are established to ensure velocity alignment and cohesion of each subgroup as well as collision avoidance between any agents in the whole group second an algorithm for homogeneous networks is studied simulation examples are finally presented to verify the effectiveness of our theoretical results

finite time information consensus for multi agent systems with fixed and switching topologies in this paper we study the consensus problems for a group of interacting agents first we analytically establish the explicit expression of the consensus state for the entire group second we prove that the agents of the group under a particular type of nonlinear interaction can reach the consensus state in finite time in the scenarios with fixed and switching undirected topologies the results are also extended to the case where the topology of the group is directed and satisfies a detailed balance condition on coupling weights third some numerical examples are provided to analyze the influencing factors of the convergence time that is the parameter of the particular interaction function and the algebraic connectivity of graphs finally an application of the theoretical results in sensor networks is given namely computing the maximum likelihood estimate of unknown parameters

mitigation of complex behavior over networked systems analysis of spatially invariant structures in this paper we consider a simple distributed averaging system which incorporates various communication constraints including delays noise and link failures it has been shown in wang and elia 2012 that such networked system generates a collective levy flight behavior when part of the system loses mean square ms stability we focus on spatially invariant architectures to gain more insights into how model parameters affect emergence of this complex scale invariant behavior and to seek structures robust to communication constraints specifically we develop a computational expression for checking ms stability which is scalable with the number of unreliable links we derive the closed form formulas from this expression in the limiting case of zero and large delays and in the case of large number of nodes in the limit of large delays we derive various results that are independent of the network size and its specific interconnections we find that small inter agent coupling improves the robustness of the system networks with larger connectivity tend to be more fragile in the presence of fading connections for fixed inter agent coupling that gossiping improves the robustness and that the lattice is the most robust among the spatially invariant systems with generalized circulant interconnections

some sufficient optimality conditions in nonsmooth analysis in this paper we study some second order conditions that may be added to the first order nessessary optimality condition 0 in partial p f bar x with partial p f denoting the proximal subdifferential in order to obtain a sufficient condition for a strict local minimum for extended real valued nonsmooth functions three different types of second order conditions are investigated all based on a different second order subdifferential namely the subhessian the graphical derivative and the contingent coderivative to the proximal subdifferential

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

fuzzy observed based adaptive consensus tracking control for second order multiagent systems with heterogeneous nonlinear dynamics in this paper the consensus tracking control problem of second order multiagent systems with unknown nonlinear dynamics immeasurable states and disturbances is investigated the nonlinear dynamics in multiagent systems do not satisfy the matched condition in this paper fuzzy logic system is introduced to approximate the unknown nonlinear dynamics and adaptive high gain observer is designed to estimate the unmeasured states based on backstepping approach and lyapunov theory a new adaptive fuzzy distributed controller is proposed for each agent only using the information of itself and its neighbors then the consensus tracking is achieved under the designed distributed controller moreover it is proved that all the signals in the multiagent systems are semiglobally uniformly ultimately bounded and the consensus tracking error converges to a small neighborhood of the origin that can be designed as small as possible finally the simulation result illustrates the effectiveness of the designed controller

on the regularization of the kepler problem an intimate relationship between moser s regularization 1 and the ks regularization 3 of the 3 dimensional kepler problem is established explicit formulae linking moser s and the ks transformation are obtained in the case of negative as well as in the case of positive energies as a side result it is shown that the ks transformation owes its existence to the local isomorphism of so 2 4 and su 2 2

perturbation of hamiltonian systems with keplerian potentials on considere l existence des solutions periodiques pour une classe de systemes hamiltoniens obtenus comme des perturbations de l hamiltonien keplerien k p q 1 2 p 2 q 0

consensus conditions of multi agent systems with time varying topologies and stochastic communication noises this paper investigates the average consensus problem of first order discrete time multi agent networks in uncertain communication environments each agent can only use its own and neighbors information to design its control input to attenuate the communication noises a distributed stochastic approximation type protocol is used by using probability limit theory and algebraic graph theory consensus conditions for this kind of protocols are obtained a for the case of fixed topologies a necessary and sufficient condition for mean square average consensus is given which is also sufficient for almost sure consensus b for the case of time varying topologies sufficient conditions for mean square average consensus and almost sure consensus are given respectively especially if the network switches between jointly containing spanning tree instantaneously balanced graphs then the designed protocol can guarantee that each individual state converges both almost surely and in mean square to a common random variable whose expectation is right the average of the initial states of the whole system and whose variance describes the static maximum mean square error between each individual state and the average of the initial states of the whole system

consensus of multiagent systems with distance dependent communication networks in this paper we study the consensus problem of discrete time and continuous time multiagent systems with distance dependent communication networks respectively the communication weight between any two agents is assumed to be a nonincreasing function of their distance first we consider the networks with fixed connectivity in this case the interaction between adjacent agents always exists but the influence could possibly become negligible if the distance is long enough we show that consensus can be reached under arbitrary initial states if the decay rate of the communication weight is less than a given bound second we study the networks with distance dependent connectivity it is assumed that any two agents interact with each other if and only if their distance does not exceed a fixed range with the validity of some conditions related to the property of the initial communication graph we prove that consensus can be achieved asymptotically third we present some applications of the main results to opinion consensus problems and formation control problems finally several simulation examples are presented to illustrate the effectiveness of the theoretical findings

coordination and consensus of networked agents with noisy measurements stochastic algorithms and asymptotic behavior this paper considers the coordination and consensus of networked agents where each agent has noisy measurements of its neighbors states for consensus seeking we propose stochastic approximation type algorithms with a decreasing step size and introduce the notions of mean square and strong consensus although the decreasing step size reduces the detrimental effect of the noise it also reduces the ability of the algorithm to drive the individual states towards each other the key technique is to ensure a trade off for the decreasing rate of the step size by following this strategy we first develop a stochastic double array analysis in a two agent model which leads to both mean square and strong consensus and extend the analysis to a class of well studied symmetric models subsequently we consider a general network topology and introduce stochastic lyapunov functions together with the so called direction of invariance to establish mean square consensus finally we apply the stochastic lyapunov analysis to a leader following scenario

stationary distribution for stochastic coupled systems with regime switching and feedback control abstract the existence of stationary distribution for stochastic coupled systems with regime switching and feedback control is investigated in terms of model feedback control is concerned in the existence of stationary distribution for stochastic coupled systems with regime switching in terms of method graph theory is employed to investigate the existence of stationary distribution for stochastic coupled systems with regime switching and some sufficient conditions are given based on lyapunov method connected with the graph theory and the m matrix method to ensure the existence of stationary distribution which reveals the influences that feedback control brings on stationary distribution and the existing area is related to stochastic disturbance feedback control and coupling strength furthermore the application to stochastic coupled oscillators with feedback control and regime switching can demonstrate the practicability of our theoretical results finally a numerical example is presented to verify the effectiveness and availability of our results as well as the superiority of influence that feedback control brings on stationary distribution

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

distributed control of networked dynamical systems static feedback integral action and consensus this paper analyzes distributed control protocols for first and second order networked dynamical systems we propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain and a sum of nonlinear interaction functions by using integral lyapunov functions we prove the stability of the proposed control protocols and explicitly characterize the equilibrium set we also propose a distributed proportional integral pi controller for networked dynamical systems the pi controllers successfully attenuate constant disturbances in the network we prove that agents with single integrator dynamics are stable for any integral gain and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double integrator dynamics throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites power systems and building temperature control

distributed consensus algorithms in sensor networks with imperfect communication link failures and channel noise the paper studies average consensus with random topologies intermittent links and noisy channels consensus with noise in the network links leads to the bias variance dilemma running consensus for long reduces the bias of the final average estimate but increases its variance we present two different compromises to this tradeoff the a nd algorithm modifies conventional consensus by forcing the weights to satisfy a persistence condition slowly decaying to zero and the a nc algorithm where the weights are constant but consensus is run for a fixed number of iterations iota then it is restarted and rerun for a total of p runs and at the end averages the final states of the p runs monte carlo averaging we use controlled markov processes and stochastic approximation arguments to prove almost sure convergence of a nd to a finite consensus limit and compute explicitly the mean square error mse variance of the consensus limit we show that a nd represents the best of both worlds zero bias and low variance at the cost of a slow convergence rate rescaling the weights balances the variance versus the rate of bias reduction convergence rate in contrast a nc because of its constant weights converges fast but presents a different bias variance tradeoff for the same number of iterations iota p shorter runs smaller iota lead to high bias but smaller variance larger number p of runs to average over for a static nonrandom network with gaussian noise we compute the optimal gain for a nc to reach in the shortest number of iterations iota p with high probability 1 delta epsiv delta consensus epsiv residual bias our results hold under fairly general assumptions on the random link failures and communication noise

a necessary and sufficient condition for consensus over random networks we consider the consensus problem for stochastic discrete time linear dynamical systems the underlying graph of such systems at a given time instance is derived from a random graph process independent of other time instances for such a framework we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments this easily verifiable condition uses the spectrum of the average weight matrix finally we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1

convergence of type symmetric and cut balanced consensus seeking systems we consider continuous time consensus seeking systems whose time dependent interactions are cut balanced in the following sense if a group of agents influences the remaining ones the former group is also influenced by the remaining ones by at least a proportional amount models involving symmetric interconnections and models in which a weighted average of the agent values is conserved are special cases we prove that such systems always converge we give a sufficient condition on the evolving interaction topology for the limit values of two agents to be the same conversely we show that if our condition is not satisfied then these limits are generically different these results allow treating systems where the agent interactions are a priori unknown being for example random or determined endogenously by the agent values

passivity as a design tool for group coordination we pursue a group coordination problem where the objective is to steer the differences between output variables of the group members to a prescribed compact set to stabilize this set we study a class of feedback rules that are implementable with local information available to each member when the information flow between neighboring members is bidirectional we show that the closed loop system exhibits a special interconnection structure which inherits the passivity properties of its components by exploiting this structure we develop a passivity based design framework which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature the passivity approach offers additional design flexibility compared to these special cases and systematically constructs a lurie type lyapunov function for the closed loop system we further study the robustness of these feedback laws in the presence of a time varying communication topology and present a persistency of excitation condition which allows the interconnection graph to lose connectivity pointwise in time as long as it is established in an integral sense

the multi agent rendezvous problem part 2 the asynchronous case this paper is concerned with the collective behavior of a group of n 1 mobile autonomous agents labelled 1 through n which can all move in the plane each agent is able to continuously track the positions of all other agents currently within its sensing region where by an agent s sensing region we mean a closed disk of positive radius r centered at the agent s current position the multi agent rendezvous problem is to devise local control strategies one for each agent which without any active communication between agents cause all members of the group to eventually rendezvous at a single unspecified location this paper describes a family of unsynchronized strategies for solving the problem correctness is established appealing to the concept of analytic synchronization

exponential synchronization of complex networks of linear systems and nonlinear oscillators a unified analysis a unified approach to the analysis of synchronization for complex dynamical networks i e networks of partial state coupled linear systems and networks of full state coupled nonlinear oscillators is introduced it is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks thus making it feasible to consider the error dynamics for the whole network system different from the other various methods given in the existing literature the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form but also explicitly specifying the convergence rate

finite time consensus for stochastic multi agent systems in this article we study the finite time consensus in probability for stochastic multi agent systems first we give the nonlinear consensus protocol for multi agent systems with gaussian white noise and define the concept of finite time consensus in probability second we prove that multi agent systems can achieve the finite time consensus in probability under five different kinds of communication topologies by using graph theory stochastic lyapunov theory and probability theory finally some simulation examples are provided to illustrate the effectiveness of the theoretical results

fixed time synchronization of complex networks with impulsive effects via nonchattering control dealing with impulsive effects is one of the most challenging problems in the field of fixed time control in this paper we solve this challenging problem by considering fixed time synchronization of complex networks cns with impulsive effects by designing a new lyapunov function and constructing comparison systems a sufficient condition formulated by matrix inequalities is given to ensure that all the dynamical subsystems in the cns are synchronized with an isolated system in a settling time which is independent of the initial values of both the cns and the isolated system then by partitioning impulse interval and using the convex combination technique sufficient conditions in terms of linear matrix inequalities are provided our synchronization criteria unify synchronizing and desynchronizing impulses compared with the existing controllers for fixed time and finite time techniques the designed controller is continuous and does not include any sign function and hence the chattering phenomenon in most of the existing results is overcome an optimal algorithm is proposed for the estimation of the settling time numerical examples are given to show the effectiveness of our new results

consensus seeking of high order dynamic multi agent systems with fixed and switching topologies this article studies a consensus problem for a group of high order dynamic agents with fixed and switching topologies two linear consensus protocols which only depend on the agent s own information and its neighbours partial information are proposed respectively for the group with and without communication time delays for the case of fixed topology and zero communication time delay a necessary and sufficient condition for the consensus is established the parameter design of the protocol is also discussed under switching topology the consensus is investigated for two cases the case of zero communication time delay and the case of nonuniform communication time delays for each case a sufficient condition for the consensus is provided moreover for a group of double triple integrator agents with fixed topology and uniform constant time delay some necessary and sufficient conditions for the consensus are given finally numerical simulations are worked out to illustrate the effectiveness of the

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

on convergence rate of leader following consensus of linear multi agent systems with communication noises this note further studies the previously proposed consensus protocol for linear multi agent systems with communication noises each agent is allowed to have its own time varying gain to attenuate the effect of communication noises therefore the common assumption that all agents have the same noise attenuation gain is not necessary it has been proved that if all noise attenuation gains are infinitesimal of the same order then the mean square leader following consensus can be reached furthermore the convergence rate of the multi agent system has been investigated if the noise attenuation gains belong to a class of functions which are bounded above and below by t beta beta in 0 1 asymptotically then the second moment of the relative state between each follower agent and the leader agent is characterized by a function bounded above by t beta asymptotically

multi agent consensus with relative state dependent measurement noises in this note the distributed consensus corrupted by relative state dependent measurement noises is considered each agent can mea sure or receive its neighbors state information with random noises whose intensity is a vector function of agents relative states by investigating the structure of this interaction and the tools of stochastic differential equa tions we develop several small consensus gain theorems to give sufficient conditions in terms of the control gain the number of agents and the noise intensity function to ensure mean square m s and almost sure a s consensus and quantify the convergence rate and the steady state error especially for the case with homogeneous communication and control channels a necessary and sufficient condition to ensure m s consensus on the control gain is given and it is shown that the control gain is independent of the specific network topology but only depends on the number of nodes and the noise coefficient constant for symmetric measurement models the almost sure convergence rate is estimated by the iterated logarithm law of brownian motions index terms distributed consensus distributed coordination fading channel measurement noises multi agent system

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

h consensus control with spectrum constraints for stochastic multi agent systems subject to x u v dependent noises abstract this paper is concerned with the problem of h consensus control with spectrum constraints for continuous time multi agent systems mass with x u v dependent noises by means of the spectrum technique the definition of stability is introduced and the relationship between the convergence rate of state responses and the stability is discussed for the closed loop system the aim of the addressed problem is to design a static output feedback controller such that the closed loop system is stable and the prescribed h performance requirement is satisfied in virtue of the stochastic analysis method and kronecker product sufficient conditions are obtained for the existence of h consensus controller two examples are provided to illustrate the availability of the proposed techniques

a study of tilt stable optimality and sufficient conditions abstract recent results by eberhard et al 2006 4 and eberhard and wenczel 2009 3 on the interaction of single and double envelope operations of nonsmooth functions and their interaction with second order derivations have been used to study tilt stability of local minima this continues the study begun by poliquin and rockafellar 1998 1 but now armed with new tools we are able to make some new observations we observe that tilt stability entails a local density within the graph of the proximal subderivative of strict local minima order two of the tilted function indeed it also entails the strict local minimality order two of the tilt stable local minimum itself for prox regular subdifferentially continuous functions this density property characterises tilt stability

consensus conditions of continuous time multi agent systems with additive and multiplicative measurement noises this work is concerned with the consensus problem of multi agent systems with additive and multiplicative measurement noises by developing general stochastic stability lemmas for nonautonomous stochastic differential equations stochastic weak and strong consensus conditions are investigated under fixed and time varying topologies respectively for the case with fixed topologies and additive noises the necessary and sufficient conditions for almost sure strong consensus are given it is revealed that almost sure strong consensus and mean square strong consensus are equivalent under general digraphs and almost sure weak consensus implies mean square weak consensus under undirected graphs if multiplicative noises appear then small noise intensities do not affect the control gain to guarantee stochastic strong consensus for the case with time varying topologies sufficient consensus conditions are given under the periodically connected condition of the topology flow

brief paper stability analysis for multi agent systems using the incidence matrix quantized communication and formation control the spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi agent control problems in particular we consider the problem of state agreement with quantized communication and the problem of distance based formation control in both cases stabilizing control laws are provided when the communication graph is a tree it is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi agent control problems

exponential stability of fractional order complex multi links networks with aperiodically intermittent control in this article the exponential stability problem for fractional order complex multi links networks with aperiodically intermittent control is considered using the graph theory and lyapunov method two theorems including a lyapunov type theorem and a coefficient type theorem are given to ensure the exponential stability of the underlying networks the theoretical results show that the exponential convergence rate is dependent on the control gain and the order of fractional derivative to be specific the larger control gain the higher the exponential convergence rate meanwhile when aperiodically intermittent control degenerates into periodically intermittent control a corollary is also provided to ensure the exponential stability of the underlying networks furthermore to show the practicality of theoretical results as an application the exponential stability of fractional order multi links competitive neural networks with aperiodically intermittent control is investigated and a stability criterion is established finally the effectiveness and feasibility of the theoretical results are demonstrated through a numerical example

time varying formation tracking for linear multiagent systems with multiple leaders time varying formation tracking problems for linear multiagent systems with multiple leaders are studied where the states of followers form a predefined time varying formation while tracking the convex combination of the states of multiple leaders followers are classified into well informed ones and uninformed ones where the neighbor set of the former contains all the leaders whereas the latter contains no leaders a formation tracking protocol is constructed using only neighboring relative information necessary and sufficient conditions for multiagent systems with multiple leaders to achieve time varying formation tracking are proposed by utilizing the properties of the laplacian matrix where the formation tracking feasibility constraints are also given an approach to design the formation tracking protocol is presented by solving an algebraic riccati equation the obtained results can be applied to deal with time varying formation tracking problems target enclosing problems and consensus tracking problems for linear multiagent systems with one or multiple targets leaders numerical simulations are provided to demonstrate the effectiveness of the theoretical results

necessary and sufficient conditions for isolated local minima of nonsmooth functions we consider the mathematical programming problem find inf f x mid x in c where f is an arbitrary extended real valued function and c a subset of a finite dimensional space we give necessary and sufficient optimality conditions for this problem generalizing previous results of a auslendex this journal 22 1984 pp 239 254

on partial smoothness tilt stability and the mathcal vu decomposition under the assumption of prox regularity and the presence of a tilt stable local minimum we are able to show that a mathcal vu like decomposition gives rise to the existence of a smooth manifold on which the function in question coincides locally with a smooth function