sampled data consensus of linear multi agent systems with packet losses in this paper the consensus problem is studied for a class of multi agent systems with sampled data and packet losses where random and deterministic packet losses are considered respectively for random packet losses a bernoulli distributed white sequence is used to describe packet dropouts among agents in a stochastic way for deterministic packet losses a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way the purpose of this paper is to derive consensus criteria such that linear multi agent systems with sampled data and packet losses can reach consensus by means of the lyapunov function approach and the decomposition method the design problem of a distributed controller is solved in terms of convex optimization the interplay among the allowable bound of the sampling interval the probability of random packet losses and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions the obtained criteria are closely related to the maximum eigenvalue of the laplacian matrix versus the second minimum eigenvalue of the laplacian matrix which reveals the intrinsic effect of communication topologies on consensus performance finally simulations are given to show the effectiveness of the proposed results

experimental evidence of stochastic resonance without tuning due to non gaussian noises in order to test theoretical predictions we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non gaussian noise in agreement with the theoretical predictions our main findings are an enhancement of the sensibility of the system together with a remarkable widening of the response robustness this implies that even a single resonant unit can reach a marked reduction in the need for noise tuning

technical communique forced consensus in networks of double integrator systems with delayed input this communique presents forced second order consensus protocols with communication time delays for the network of agents with double integrator dynamics and gives a measure of the robustness of the protocols to the communication time delays by employing a frequency domain method it is proven that the forced consensus is achieved asymptotically for appropriate time delay if the network is connected particularly the maximum fixed time delay that can be tolerated by the network is found the forced consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents which reduces the complexity of connections between agents significantly numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results

pinning dynamic systems of networks with markovian switching couplings and controller node set in this paper we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller node set here the coupling matrices and the controller node sets change with time induced by a continuous time markov chain by constructing lyapunov functions we establish tractable sufficient conditions for exponential stability of the coupled system two scenarios are considered here first we prove that if each subsystem in the switching system i e with the fixed coupling can be stabilized by the fixed pinning controller node set and in addition the markovian switching is sufficiently slow then the time varying dynamical system is stabilized second we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast the time varying system is stabilized two numerical examples are provided to demonstrate the validity of these theoretical results including a switching dynamical system between several stable subsystems and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre designed region

stochastic bounded consensus tracking of second order multi agent systems with measurement noises based on sampled data with general sampling delay this paper is devoted to the stochastic bounded consensus tracking problems of second order multi agent systems where the control input of each agent can only use the information measured at the sampling instants from its neighbors or the virtual leader with a time varying reference state the measurements are corrupted by random noises and the signal sampling process induces the small sampling delay the augmented matrix method the probability limit theory and some other techniques are employed to derive the necessary and sufficient conditions guaranteeing the mean square bounded consensus tracking we show that the convergence of the proposed protocol simultaneously depends on the constant feedback gains the network topology the sampled period and the sampling delay and that the static consensus tracking error depends on not only the above mentioned factors but also the noise intensity and the upper bound of the velocity and the acceleration of the virtual leader the obtained results cover no sampling delay as its one special case simulations are provided to demonstrate the effectiveness of the theoretical results

distributed formation control of multi agent systems using complex laplacian the paper concentrates on the fundamental coordination problem that requires a network of agents to achieve a specific but arbitrary formation shape a new technique based on complex laplacian is introduced to address the problems of which formation shapes specified by inter agent relative positions can be formed and how they can be achieved with distributed control ensuring global stability concerning the first question we show that all similar formations subject to only shape constraints are those that lie in the null space of a complex laplacian satisfying certain rank condition and that a formation shape can be realized almost surely if and only if the graph modeling the inter agent specification of the formation shape is 2 rooted concerning the second question a distributed and linear control law is developed based on the complex laplacian specifying the target formation shape and provable existence conditions of stabilizing gains to assign the eigenvalues of the closed loop system at desired locations are given moreover we show how the formation shape control law is extended to achieve a rigid formation if a subset of knowledgable agents knowing the desired formation size scales the formation while the rest agents do not need to re design and change their control laws

adaptive finite time consensus in multi agent networks abstract this paper is concerned with the finite time consensus problem of distributed agents having non identical unknown nonlinear dynamics to a leader agent that also has unknown nonlinear control input signal by parameterization of unknown nonlinear dynamics a lyapunov technique in conjunction with homogeneity technique is presented for designing a decentralized adaptive finite time consensus control protocol in undirected networks homogeneous lyapunov functions and homogeneous vector fields are introduced in the stability analysis although the whole system is not homogeneous theoretical analysis shows that leader following consensus can be achieved in finite time meanwhile finite time parameter convergence can be also guaranteed under the proposed control scheme an example is given to validate the theoretical results

consensus and its ℒ 2 gain performance of multi agent systems with intermittent information transmissions this article addresses the consensus problem for cooperative multiple agents with nonlinear dynamics on a fixed directed information network where each agent can only communicate with its neighbours intermittently a class of control algorithms is first introduced using only intermittent relative local information by combining tools from switching systems and lyapunov stability theory some sufficient conditions are established for consensus of multi agent systems without any external disturbances under a fixed strongly connected topology theoretical analyses are further provided for consensus of multi agent systems in the presence of external disturbances it is shown that a finite 2 gain performance index for the closed loop multi agent systems can be guaranteed if the coupling strength of the network is larger than a threshold value determined by the average communication rate and the generalised algebraic connectivity of the strongly connected topology the results are then extended to consensus

adaptive consensus of multi agents in networks with jointly connected topologies in this paper the consensus problem of multi agent following a leader is studied an adaptive design method is presented for multi agent systems with non identical unknown nonlinear dynamics and for a leader to be followed that is also nonlinear and unknown by parameterizations of unknown nonlinear dynamics of all agents a decentralized adaptive consensus algorithm is proposed in networks with jointly connected topologies by incorporating local consensus errors in addition to relative position feedback analysis of stability and parameter convergence of the proposed algorithm are conducted based on algebraic graph theory and lyapunov theory finally examples are provided to validate the theoretical results

small gaps between primes we introduce a renement of the gpy sieve method for studying prime k tuples and small gaps between primes this renement avoids previous limitations of the method and allows us to show that for each k the prime k tuples conjecture holds for a positive proportion of admissible k tuples in particular lim infn pn m pn 1 for every integer m we also show that lim inf pn 1 pn 600 and if we assume the elliott halberstam conjecture that lim infn pn 1 pn 12 and lim infn pn 2 pn 600

mean field lqg control in leader follower stochastic multi agent systems likelihood ratio based adaptation we study large population leader follower stochastic multi agent systems where the agents have linear stochastic dynamics and are coupled via their quadratic cost functions the cost of each leader is based on a trade off between moving toward a certain reference trajectory which is unknown to the followers and staying near their own centroid on the other hand followers react by tracking a convex combination of their own centroid and the centroid of the leaders we approach this large population dynamic game problem by use of so called mean field mf linear quadratic gaussian lqg stochastic control theory in this model followers are adaptive in the sense that they use a likelihood ratio estimator on a sample population of the leaders trajectories to identify the member of a given finite class of models which is generating the reference trajectory of the leaders under appropriate conditions it is shown that the true reference trajectory model is identified by each follower in finite time with probability one as the leaders population goes to infinity furthermore we show that the resulting sets of mean field control laws for both leaders and adaptive followers possess an almost sure en nash equilibrium property for a system with population n where en goes to zero as n goes to infinity numerical experiments are presented illustrating the results

consensus control of a class of lipschitz nonlinear systems this paper deals with consensus control of a class of nonlinear systems with lipschitz nonlinearities certain features of the laplacian matrix are explored in the real jordan form to identify conditions for global consensus control under the identified conditions consensus control and stability of the proposed control are analysed in time domain through lyapunov functions in real domain the proposed control uses relative state information of the system a simulation study is included to demonstrate the proposed control designs with some simulation results shown

kinetics of self induced aggregation of brownian particles non markovian and non gaussian features in this paper we have explored a model for self induced aggregation of brownian particles incorporating non markovian and non gaussian character of the associated random noise processes the time evolution of each individual is guided by an overdamped langevin equation of motion with a nonlocal drift arising out of the imbalance in the local distribution of the other individuals our simulation results show that colored noise enhances the tendency of cluster formation another observation is that the critical noise variance decreases at first with increase in noise correlation time followed by an increase after exhibiting a minimum furthermore in the long time limit the cluster number in the aggregation process exhibits depletion with time following a power law with an exponent which increases remarkably with non markovian character of the noise processes

the effect of interference of coloured additive and multiplicative white noises on escape rate in this paper we have calculated the escape rate from a meta stable state for coloured and correlated noise driven open systems based on the fokker planck description of the stochastic process we consider the effect of two correlation times due to the additive coloured noise and the correlation between additive coloured and multiplicative white noises the effect of the noise correlation strength on the rate has also been investigated

a graph laplacian approach to coordinate free formation stabilization for directed networks this paper concentrates on coordinate free formation control for directed networks for which the dynamic motion of each agent is assumed to be governed only by a local control we develop a graph laplacian approach to solve the global and exponential formation stablization problem using merely relative position measurements between neighbors first to capture the sensing and control architectures that are needed to maintain the shape of a formation a necessary and sufficient topological condition is proposed second a laplacian based control law is developed for the stablization problem of a group of mobile agents to a desired formation shape under both fixed and switching topologies due to temporal node failures simulation results are provided to demonstrate that our laplacian based formation control strategy is inherently fault tolerant and robust to node failures

distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks in this paper we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies first when the leaders are stationary and all followers share an inertial coordinate frame we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is fixed we partition the nonsymmetric laplacian matrix and explore its properties to derive the convergence results when the directed network topology is switching the commonly adopted decoupling technique based on the kronecker product in a high dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results the proposed coordinate transformation technique also has potential applications in other high dimensional distributed control scenarios and might be used to simplify the analysis of a high dimensional system to that of a one dimensional system when the decoupling technique based on the kronecker product cannot be applied second when the leaders are dynamic and all followers share an inertial coordinate frame we propose a distributed tracking control algorithm without velocity measurements when the directed network topology is fixed we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is switching we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high dimensional space we also show via some counterexamples that it is in general impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high dimensional space simulation results are presented as a proof of concept

target point formation control in this paper a new distributed feedback strategy is proposed for controlling a rigid acyclic formation of kinematic point modeled mobile autonomous agents in the plane the strategy makes use of a new concept called a target point and is applicable to any two dimensional acyclic formation whose underlying directed graph can be generated by a sequence of henneberg vertex additions it is shown that the method can cause a group of agents starting in any given initial positions in the plane to move into a prescribed formation exponentially fast provided the formation s designated leader and first follower start in different positions

effect of adding edges to consensus networks with directed acyclic graphs consensus of a network with a directed acyclic graph a directed graph with no directed cycles is always guaranteed if it contains a spanning tree this paper studies the effect of adding edges to a directed acyclic graph that may result in a directed cycle it is shown that the effect on consensus performance of the whole network is only determined by a local subnetwork containing all the added edges more specifically both a one dimensional 1 d chain network and a 2 d grid network are investigated in this paper it is proved that when a reverse edge is added the consensus performance is degraded by the amount only determined by the edge range that is independent of the network size or the location of the added edge

kinetics of self induced aggregation in brownian particles we study a model of interacting random walkers that proposes a simple mechanism for the emergence of cooperation in a group of individuals each individual represented by a brownian particle experiences an interaction produced by the local unbalance in the spatial distribution of the other individuals this interaction results in a nonlinear velocity driving the particle trajectories in the direction of the nearest more crowded region the competition among different aggregating centers generates nontrivial dynamical regimes our simulations show that for sufficiently low randomness the system evolves through a coalescence behavior characterized by clusters of particles growing with a power law in time in addition the typical scaling properties of the general theory of stochastic aggregation processes are verified

decentralized control of vehicle formations this paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory the vehicles exchange information according to a pre specified communication digraph g a feedback control is designed using relative information between a vehicle and its in neighbors in g we prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that g has a rooted directed spanning tree we show the direct relationship between the rate of convergence to formation and the eigenvalues of the directed laplacian of g various special situations are discussed including symmetric communication graphs and formations with leaders several numerical simulations are used to illustrate the results

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

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

leader follower formation via complex laplacian the paper introduces complex valued laplacians for graphs whose edges are attributed with complex weights and studies the leader follower formation problem based on complex laplacians the main goal is to control the shape of a planar formation of point agents in the plane using simple and linear interaction rules related to complex laplacians we present a characterization of complex laplacians that preserve a specific planar formation as an equilibrium solution for both single integrator kinematics and double integrator dynamics planar formations under study are subject to translation rotation and scaling in the plane but can be determined by two co leaders in leader follower networks furthermore when a complex laplacian does not result in an asymptotically stable behavior of the multi agent system we show that a stabilizing matrix which updates the complex weights exists to asymptotically stabilize the system while preserving the equilibrium formation also algorithms are provided to find stabilizing matrices finally simulations are presented to illustrate our results

computation of the target state and feedback controls for time optimal consensus in multi agent systems abstractn identical agents with bounded inputs aim to reach a common target state consensus in the minimum possible time algorithms for computing this time optimal consensus point the control l

enhancement of stochastic resonance the role of non gaussian noises abstract we have analyzed the phenomenon of stochastic resonance in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation that enables us to get through the two state theory analytical expressions for the signal to noise ratio finding an enhancement of this quantity when the system departs from gaussian behavior this finding is supported by extensive numerical simulations we discuss the relation of these results to some experiments in sensory systems

brief paper collective motions and formations under pursuit strategies on directed acyclic graphs a novel pursuit based approach is presented to investigate collective motions and formations of a large number of agents with both single integrator kinematics and double integrator dynamics on directed acyclic graphs dags each agent pursues its neighbors according to a directed acyclic graph in which the agents without neighbors are leaders based on signal flow graph analysis and mason s rule necessary and sufficient conditions are derived for bibo stability of resulting pursuit systems moreover achievable collective motions and formations are analyzed by adjusting a set of control parameters when leaders keep stationary perform uniform rectilinear motions and perform uniform circular motions finally simulations are provided for achieving a static formation and mimicking several complex collective behaviors observed in nature such as v formation vortex motions and tornado motions

influence of noise on the synchronization of the stochastic kuramoto model we consider the kuramoto model of globally coupled phase oscillators subject to ornstein uhlenbeck and non gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process we use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise and find that the threshold of synchronization strongly depends on the nature of the noise it is found to be lower for both the ornstein uhlenbeck and non gaussian processes compared to the case of white noise a finite correlation time also favors the achievement of the full synchronization of the system in contract to the white noise process which does not allow that finally we discuss possible applications of the stochastic kuramoto model to oscillations taking place in biochemical systems

a decentralized controller observer scheme for multi agent weighted centroid tracking in this technical note a decentralized controller observer scheme for a multi agent system is presented the key idea is to develop for each agent an observer of the collective system s state and a motion controller the observer is updated using only information from the agent itself and from its neighbors the motion controller is designed in order to allow the team s weighted centroid to track an assigned time varying reference convergence of the overall scheme is proven for directed and undirected communication graphs moreover the extensions to the case of switching communication topologies and to the presence of saturation in the control input are discussed finally numerical simulations are illustrated to validate the approach

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

role of phase difference and colored cross correlation on current in multiplicative and additive noises driven systems abstract we have investigated the transport properties of multiplicative and additive noise driven spatially periodic system the phase difference between periodic potential and periodic function in multiplicative noise term and the cross correlation between multiplicative and additive noise can break the detail balance of the system independently to produce directed motion the magnitude of current due to phase difference is smaller in comparison to cross correlation between the noises the phase difference can be used to control the direction of the cross correlation induced current another interesting observation is that there is a current inversion with increase of cross correlation time the current increases linearly with the strength of cross correlation

a new tabular form for determining root distribution of a complex polynomial with respect to the imaginary axis the original routh table dealing with real polynomials is further investigated for complex polynomials a tabular form for determining root distribution of a complex polynomial with respect to the imaginary axis is developed and modified procedures for directly treating singularities in the array are proposed also procedures are developed for determining the respective orders of simple and or repeated roots lying on the imaginary axis conditional stability and instability can be distinguished from each other by the criteria developed here

stability analysis of stochastic delayed systems with an application to multi agent systems this technical note is concerned with the stability problem of stochastic delayed systems by using a more general halanay type inequality with time varying coefficients a new comparison principle of the proposed halanay type inequality is developed to ensure the stability of stochastic delayed systems the p th moment stability p th moment asymptotic stability and p th moment exponential stability are investigated by means of the proposed general halanay type inequality two examples including one of the consensus of multi agent systems with time varying topologies and transmission delays are presented to demonstrate the effectiveness of the proposed results

min max time consensus tracking with communication guarantee in this paper a collection of double integrator agents with bounded inputs is considered communication is possible between any two agents only if the inter agent distance is less than a fixed threshold a special node referred to as the leader generates an unknown reference trajectory to which all the other agents are required to converge in the shortest possible time assuming the initial communication graph to be connected a directed spanning tree rooted at the leader is identified using a local algorithm the dynamics of any two agents connected by an edge in the selected tree are modeled as a time optimal pursuit evasion game while maintaining the inter agent communication link using the corresponding feedback saddle point strategies local min max time control laws for each pair of agents are formulated for the selected tree the proposed collection of local min max time control strategies is shown to be the communication preserving global min max time strategy

leader following consensus problem with a varying velocity leader and time varying delays abstract in this paper we study a leader following consensus problem for a multi agent system with a varying velocity leader and time varying delays here the interaction graph among the followers is switching and balanced at first we propose a neighbor based rule for every agent to track a leader whose states may not be measured in addition we consider the convergence analysis of this multi agent system under two different conditions the connection between the followers and the leader is time invariant and time varying for the first case a novel decomposition method is introduced to facilitate the convergence analysis by utilizing a lyapunov krasovskii functional we obtain sufficient conditions for uniformly ultimately boundedness of the tracking errors finally two simulations are also presented to illustrate our theoretical results

effective markovian approximation for non gaussian noises a path integral approach abstract we have analyzed diffusion in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation to the initially non markovian problem such an approximation allows us to get analytical expressions for the mean first passage time that has been tested against extensive numerical simulations

stability measures in metastable states with gaussian colored noise we present a study of the escape time from a metastable state of an overdamped brownian particle in the presence of colored noise generated by ornstein uhlenbeck process we analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity we observe the noise enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau c investigated we can distinguish two dynamical regimes characterized by weak and strong correlated noises depending on the value of tau c with respect to the relaxation time of the system

bounded intervals containing many primes by combining a sieve method of harman with the work of maynard and tao we show that begin aligned liminf n rightarrow infty p n m p n ll exp 3 815m end aligned

multi vehicle consensus with a time varying reference state in this paper we study the consensus problem in multi vehicle systems where the information states of all vehicles approach a time varying reference state under the condition that only a portion of the vehicles e g the unique team leader have access to the reference state and the portion of the vehicles might not have a directed path to all of the other vehicles in the team we first analyze a consensus algorithm with a constant reference state using graph theoretical tools we then propose consensus algorithms with a time varying reference state and show necessary and sufficient conditions under which consensus is reached on the time varying reference state the time varying reference state can be an exogenous signal or evolve according to a nonlinear model these consensus algorithms are also extended to achieve relative state deviations among the vehicles an application example to multi vehicle formation control is given as a proof of concept

brief paper distributed discrete time coordinated tracking with a time varying reference state and limited communication this paper studies a distributed discrete time coordinated tracking problem where a team of vehicles communicating with their local neighbors at discrete time instants tracks a time varying reference state available to only a subset of the team members we propose a pd like discrete time consensus algorithm to address the problem under a fixed communication graph we then study the condition on the communication graph the sampling period and the control gain to ensure stability and give the quantitative bound of the tracking errors it is shown that the ultimate bound of the tracking errors is proportional to the sampling period the benefit of the proposed pd like discrete time consensus algorithm is also demonstrated through comparison with an existing p like discrete time consensus algorithm simulation results are presented as a proof of concept

event based model predictive tracking control of nonholonomic systems with coupled input constraint and bounded disturbances this paper studies the event based model predictive control empc for tracking of nonholonomic mobile robot with coupled input constraint and bounded disturbances first an event triggering mechanism is presented by designing a threshold for the error between the actual trajectory and the predicted one aiming at reducing the computational load second a model predictive control strategy is developed based on the event triggering mechanism recursive feasibility is guaranteed by designing a robust terminal region and the proper parameters we show that the tracking system is practically stable and also provides a convergence region for the tracking error the convergence region indicates that the tracking performance is negatively related to the minimal interevent time as well as the bound of the disturbances finally simulation results show that the computation load is significantly reduced and illustrate the efficiency of our proposed strategy

finite time distributed consensus via binary control protocols this paper investigates the finite time distributed consensus problem for multi agent systems using a binary consensus protocol and the pinning control scheme compared with other consensus algorithms which need the complete state or output information of neighbors the proposed algorithm only requires sign information of the relative state measurements that is the differences between a node s state and that of its neighbors this corresponds to only requiring a single bit quantization error relative to each neighbor this signum protocol is realistic in terms of observed behavior in animal groups where relative motion is determined not by full time signal measurements but by coarse estimates of relative heading differences between neighbors the signum protocol does not require explicit measurement of time signals from neighbors and hence has the potential to significantly reduce the requirements for both computation and sensing analysis of discontinuous dynamical systems is used including the filippov solutions and set valued lie derivative based on the second order information on the evolution of lyapunov functions the conditions that guarantee the finite time consensus for the systems are identified numerical examples are given to illustrate the theoretical results

escape through an unstable limit cycle driven by multiplicative colored non gaussian and additive white gaussian noises in a previous paper bag and hu phys rev e 73 061107 2006 we studied the mean lifetime mlt for the escape of a brownian particle through an unstable limit cycle driven by multiplicative colored gaussian and additive gaussian white noises and found resonant activation ra behavior in the present paper we switch from gaussian to non gaussian multiplicative colored noise we find that in the ra phenomenon the minimum appears at a smaller noise correlation time tau for non gaussian noises compared to gaussian noises in the plot of mlt vs tau for a fixed noise variance the same plot for a given noise strength increases linearly and the increasing rate is smaller for non gaussian noises than for the gaussian noises the plot of logarithm of inverse of mlt vs inverse of the strength of additive noise is arrhenius like for gaussian colored noise and it becomes similar to the quantum kramers rate if the multiplicative noise is non gaussian

distributed observer design for bounded tracking control of leader follower multi agent systems in a sampled data setting this paper studies the observer based bounded tracking control problem of second order multi agent systems in a disturbance environment via sampled data control two sampled data protocols are introduced under the assumption that the dynamic leader is only available to a portion of agents and distributed observers are designed to estimate the velocity of the active leader for the fixed communication topology case necessary and sufficient conditions of bounded consensus tracking are obtained by using the matrix analysis method for the switching communication topology case we prove that system can achieve bounded tracking by applying the common lyapunov function and perturbation theory simulation examples are given to illustrate the effectiveness of our results

bounded gaps between primes it is proved that lim inf n 8 p n 1 p n 7 10 7 where p n is the n th prime our method is a refinement of the recent work of goldston pintz and yildirim on the small gaps between consecutive primes a major ingredient of the proof is a stronger version of the bombieri vinogradov theorem that is applicable when the moduli are free from large prime divisors only but it is adequate for our purpose

containment control of continuous time linear multi agent systems with aperiodic sampling in this paper the containment control problem of continuous time linear multi agent systems is investigated an aperiodic sampled data based protocol is induced by using neighboring information with uncertainly time varying sampling intervals by utilizing the proposed protocol and properties of laplacian matrix the containment control problem of continuous time linear multi agent systems is equivalently transformed into a stability problem of discrete time linear systems the stability analysis is based on the robustness of related discrete time systems against perturbation caused by the variation of sampling intervals by using small gain theorem sufficient conditions are obtained to guarantee the stability of uncertain discrete time systems furthermore two special cases are given to illustrate the method proposed in this paper the theoretical results are verified by some simulations

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

rate laws of the self induced aggregation kinetics of brownian particles abstract in this paper we have studied the self induced aggregation kinetics of brownian particles in the presence of both multiplicative and additive noises in addition to the drift due to the self aggregation process the environment may induce a drift term in the presence of a multiplicative noise then there would be an interplay between the two drift terms it may account qualitatively the appearance of the different laws of aggregation process at low strength of white multiplicative noise the cluster number decreases as a gaussian function of time if the noise strength becomes appreciably large then the variation of cluster number with time is fitted well by the mono exponentially decaying function of time for additive noise driven case the decrease of cluster number can be described by the power law but in case of multiplicative colored driven process cluster number decays multi exponentially however we have explored how the rate constant in the mono exponentially cluster number decaying case depends on strength of interference of the noises and their intensity we have also explored how the structure factor at long time depends on the strength of the cross correlation cc between the additive and the multiplicative noises

distributed adaptive containment control of uncertain nonlinear multi agent systems in strict feedback form abstract this paper presents a distributed containment control approach for uncertain nonlinear strict feedback systems with multiple dynamic leaders under a directed graph topology where the leaders are neighbors of only a subset of the followers the strict feedback followers with nonparametric uncertainties are considered and the local adaptive dynamic surface controller for each follower is designed using only neighbors information to guarantee that all followers converge to the dynamic convex hull spanned by the dynamic leaders where the derivatives of leader signals are not available to implement controllers i e the position information of leaders is only required the function approximation technique using neural networks is employed to estimate nonlinear uncertainty terms derived from the controller design procedure for the followers it is shown that the containment control errors converge to an adjustable neighborhood of the origin

second order consensus for multi agent systems with switching topology and communication delay in this paper two kinds of consensus problems for second order agents under directed and arbitrarily switching topologies are investigated that is the cases without and with communication delay for the former by constructing a new kind of digraph and employing a new graphic method we can specify the least convergence rate for all the agents to reach consensus for the latter in virtue of a matrix inequality method a sufficient condition in the form of feasible matrix inequalities is presented for all the agents to reach consensus this on the other hand shows that consensus can be reached if the delay is small enough finally two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results

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

distributed adaptive asymptotically consensus tracking control of nonlinear multi agent systems with unknown parameters and uncertain disturbances abstract different from traditional centralized control one major challenge of distributed consensus tracking control lies in the constraint that the desired reference trajectory is only accessible by part of the subsystems currently most existing schemes require the availability of partial knowledge of the reference trajectories to all of the subsystems or information exchange of local control inputs in this paper we investigate distributed adaptive consensus tracking control without such requirements for nonlinear high order multi agent systems subjected to mismatched unknown parameters and uncertain external disturbances by introducing compensating terms in a smooth function form of consensus errors and certain positive integrable functions in each step of virtual control design a new backstepping based distributed adaptive control protocol is proposed an extra estimator is designed in each subsystem to handle the parametric uncertainties involved in its neighbors dynamics which avoids information exchange of local neighborhood consensus errors among connected subsystems it is shown that global uniform boundedness of all the closed loop signals and asymptotically output consensus tracking can be achieved simulation results are provided to verify the effectiveness of our scheme

consensus of multiple nonholonomic chained form systems abstract consensus problems of multiple nonholonomic systems are considered in this paper this problem is simplified into consensus problems of two subsystems based on the cascaded structure of nonholonomic chained form systems continuous and hybrid distributed controllers have been constructed for these two subsystems respectively based on the theory of cascaded systems consensus of multiple nonholonomic chained form systems can be realized using the methodology proposed in this paper no matter whether the group reference signal is persistently exciting or not different to previous assumptions on group reference such as persistent excitation or converging to nonzero constant the condition on the group reference signal have been further relaxed in this paper simulation results using matlab have illustrated the effectiveness of the results presented in this paper

the geometric convexity on se 3 and its application to the formation tracking in multi vehicle systems abstractthis paper considers the problem of geometric convexity on special euclidean group se 3 and its application to the formation tracking in multi vehicle systems motivated by the convex hull on euclidean space the specific expression of geodesic connecting two points on se 3 is obtained based on the pontryagin s minimum principle then it is extended to the geometric convex combination for multiple points based on which the virtual systems on se 3 is given to be used in the application of formation tracking problem in light of the geometric convex combination and virtual systems on se 3 a consensus based tracking protocol is proposed to guarantee that the formation is achieved under the directed acyclic graphs finally two numerical examples are provided to demonstrate the validity of the theoretical results

leader following formation control of multi agent systems under fixed and switching topologies in this article two kinds of leader following formation control problems for second order nonlinear multi agent systems are investigated that is the cases with fixed topology and with switching topology for the former by constructing an appropriate lyapunov functional and utilising linear matrix inequality lmi method we propose a formation control algorithm which makes the nonlinear multi agent systems converge to a desired formation in addition a formation control algorithm is also developed for coupled double integrators with a constant reference velocity then we extend these results to the case when the interaction topology is switching numerical simulations are presented finally to demonstrate the effectiveness of the proposed 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