consensus in multi agent systems with random delays governed by a markov chain abstract this paper investigates the consensus problem in a multi agent system with random delays governed by a markov chain the communication topology is assumed to be directed and fixed with first order dynamics under the sampled data setting we first convert the original system into a reduced order one featuring the error dynamics accordingly the consensus problem is transformed into the stabilization of the error dynamic system thereafter based on the theory in stochastic stability for time delay systems a sufficient condition is established in terms of a set of linear matrix inequalities lmis the mean square stability of the error dynamics is shown to guarantee consensus of the multi agent system by explicitly incorporating the transition probability of the random delay into consideration the conservativeness in control design is reduced a delay dependent switching control scheme is developed by redesigning the adjacency matrix finally simulation results are provided to verify the effectiveness of the proposed approach

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

consensus of high order multi agent systems with large input and communication delays we study in this paper the consensus problem for multi agent systems with agents characterized by high order linear systems with time delays in both the communication network and inputs provided that the open loop dynamics of the agents is not exponentially unstable but may be polynomially unstable and the communication topology contains a directed spanning tree a truncated predictor feedback approach is established to solve the consensus problem it is shown that if the delays are constant and exactly known the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays if it is further assumed that the open loop dynamics of the agents only contains zero eigenvalues the delays are allowed to be time varying and unknown numerical examples are worked out to illustrate the effectiveness of the proposed approaches

three and higher dimensional autonomous formations rigidity persistence and structural persistence in this paper we generalize the notion of persistence which has been originally introduced for two dimensional formations to r d for d 3 seeking to provide a theoretical framework for real world applications which often are in three dimensional space as opposed to the plane persistence captures the desirable property that a formation moves as a cohesive whole when certain agents maintain their distances from certain other agents we verify that many of the properties of rigid and or persistent formations established in r 2 are also valid for higher dimensions analysing the closed subgraphs and directed paths in persistent graphs we derive some further properties of persistent formations we also provide an easily checkable necessary condition for persistence we then turn our attention to consider some practical issues raised in multi agent formation control in three dimensional space we display a new phenomenon not present in r 2 whereby subsets of agents can behave in a problematic way when this behaviour is precluded we say that the graph depicting the multi agent formation has structural persistence in real deployment of controlled multi agent systems formations with underlying structurally persistent graphs are of interest we analyse the characteristics of structurally persistent graphs and provide a streamlined test for structural persistence we study the connections between the allocation of degrees of freedom dofs across agents and the characteristics of persistence and or structural persistence of a directed graph we also show how to transfer dofs among agents when the formation changes with new agent s added to preserve persistence and or structural persistence

lp theory for the multidimensional aggregation equation we consider well posedness of the aggregation equation tu div uv 0 v k u with initial data in input amssym cal p 2 rm bbb r d rm cap l p bbb r d in dimensions 2 and higher we consider radially symmetric kernels where the singularity at the origin is of order x 2 d and prove local well posedness in input amssym cal p 2 bbb r d rm cap l p bbb r d for sufficiently large p ps in the special case of k x x the exponent ps d d 1 is sharp for local well posedness in that solutions can instantaneously concentrate mass for initial data in input amssym cal p 2 bbb r d rm cap l p bbb r d with p ps we also give an osgood condition on the potential k x that guarantees global existence and uniqueness in input amssym cal p 2 bbb r d rm cap l p bbb r d 2010 wiley periodicals inc

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

reaching a consensus in a dynamically changing environment convergence rates measurement delays and asynchronous events this paper uses recently established properties of compositions of directed graphs together with results from the theory of nonhomogeneous markov chains to derive worst case convergence rates for the headings of a group of mobile autonomous agents which arise in connection with the widely studied vicsek consensus problem the paper also uses graph theoretic constructions to solve modified versions of the vicsek problem in which there are measurement delays asynchronous events or a group leader in all three cases the conditions under which consensus is achieved prove to be almost the same as the conditions under which consensus is achieved in the synchronous delay free leaderless case

gibbs sampler based coordination of autonomous swarms in this paper a novel gibbs sampler based algorithm is proposed for coordination of autonomous swarms the swarm is modeled as a markov random field mrf on a graph with a time varying neighborhood system determined by local interaction links the gibbs potential is designed to reflect global objectives and constraints it is established that with primarily local sensing communications the swarm configuration converges to the global minimizer s of the potential function the impact of the gibbs potential on the convergence speed is investigated finally a hybrid algorithm is developed to improve the efficiency of the stochastic scheme by integrating the gibbs sampler based method with the deterministic gradient flow method simulation results are presented to illustrate the proposed approach and verify the analyses

self organization in systems of self propelled particles we investigate a discrete model consisting of self propelled particles that obey simple interaction rules we show that this model can self organize and exhibit coherent localized solutions in one and in two dimensions in one dimension the self organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges in two dimensions we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions even in the absence of a confining boundary furthermore we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent

asymptotic swarm stability of fractional order swarm systems in the presence of uniform time delays abstractin this paper asymptotic swarm stability of fractional order swarm systems in the presence of uniform time delays is studied by using a frequency domain approach the necessary and sufficient condition on the values of time delay is derived to guarantee the asymptotic swarm stability under a directed undirected interaction graph numerical examples are given to confirm the obtained analytical results

spontaneously ordered motion of self propelled particles we study a biologically inspired inherently non equilibrium model consisting of self propelled particles in the model particles move on a plane with a velocity of constant magnitude they locally interact with their neighbours by choosing at each timestep a velocity direction equal to the average direction of their neighbours thus in the limit of vanishing velocities the model becomes analogous to a monte carlo realization of the classical xy ferromagnet we show by large scale numerical simulations that unlike in the equilibrium xy model a long range ordered phase characterized by non vanishing net flow emerges in this system in a phase space domain bordered by a critical line along which the fluctuations of the order parameter diverge the corresponding phase diagram as a function of two parameters the amplitude of noise and the average density of the particles is calculated and is found to have the form we also find that scales as a function of the external bias h field or wind according to a power law in the ordered phase the system shows long range correlated fluctuations and 1 f noise

lower bounds on the proportion of leaders needed for expected consensus of 3 d flocks this paper considers the consensus behavior of a spatially distributed 3 d dynamical network composed of heterogeneous agents leaders and followers in which the leaders have the preferred information about the destination while the followers do not have all followers move in a 3 d euclidean space with a given speed and with their headings updated according to the average velocity of the corresponding neighbors compared with the 2 d model a key point lies in how to analyze the dynamical behavior of a linear nonhomogeneous equation where the nonhomogeneous term strongly nonlinearly depends on the states of all agents using the network structure and the estimation of some characteristics for the initial states we present a proper decaying rate for the nonhomogeneous term and then establish lower bounds on the ratio of the number of leaders to the number of followers that is needed for the expected consensus by considering two cases 1 fixed speed and neighborhood radius and 2 variable speed and neighborhood radius with respect to the population size some simulation examples are given to justify the theoretical results

simple bounds for recovering low complexity models this note presents a unified analysis of the recovery of simple objects from random linear measurements when the linear functionals are gaussian we show that an s sparse vector in mathbb r n can be efficiently recovered from 2s log n measurements with high probability and a rank r n n matrix can be efficiently recovered from r 6n 5r measurements with high probability for sparse vectors this is within an additive factor of the best known nonasymptotic bounds for low rank matrices this matches the best known bounds we present a parallel analysis for block sparse vectors obtaining similarly tight bounds in the case of sparse and block sparse signals we additionally demonstrate that our bounds are only slightly weakened when the measurement map is a random sign matrix our results are based on analyzing a particular dual point which certifies optimality conditions of the respective convex programming problem our calculations rely only on standard large deviation inequalities and our analysis is self contained

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

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

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

adaptive estimation of a quadratic functional by model selection we consider the problem of estimating s 2 when s belongs to some separable hilbert space and one observes the gaussian process y t langles t rangle sigmal t for all t epsilon mathbb h where l is some gaussian isonormal process this framework allows us in particular to consider the classical gaussian sequence model for which mathbb h l 2 mathbb n and l t sum lambda geq1 t lambda varepsilon lambda where varepsilon lambda lambda geq1 is a sequence of i i d standard normal variables our approach consists in considering some at most countable families of finite dimensional linear subspaces of mathbb h the models and then using model selection via some conveniently penalized least squares criterion to build new estimators of s 2 we prove a general nonasymptotic risk bound which allows us to show that such penalized estimators are adaptive on a variety of collections of sets for the parameter s depending on the family of models from which they are built in particular in the context of the gaussian sequence model a convenient choice of the family of models allows defining estimators which are adaptive over collections of hyperrectangles ellipsoids l p bodies or besov bodies we take special care to describe the conditions under which the penalized estimator is efficient when the level of noise sigma tends to zero our construction is an alternative to the one by efroimovich and low for hyperrectangles and provides new results otherwise

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

finite size scaling analysis and dynamic study of the critical behavior of a model for the collective displacement of self driven individuals the vicsek model vm t vicsek et al phys rev lett 75 1226 1995 for the description of the collective behavior of self driven individuals assumes that each of them adopts the average direction of movement of its neighbors perturbed by an external noise a second order transition between a state of ordered collective displacement low noise limit and a disordered regime high noise limit was found early on however this scenario has recently been challenged by gr egory and chat e g gr egory and h chat e phys rev lett 92 025702 2004 who claim that the transition of the vm may be of first order by performing extensive simulations of the vm which are analyzed by means of both finite size scaling methods and a dynamic scaling approach we unambiguously demonstrate the critical nature of the transition furthermore the complete set of critical exponents of the vm in d 2 dimensions is determined by means of independent methods i e stationary and dynamic measurements we provide two tests showing that the standard hyperscaling relationship d ensuremath nu ensuremath 2 ensuremath beta ensuremath gamma holds where ensuremath beta ensuremath nu and ensuremath gamma are the order parameter correlation length and susceptibility critical exponents respectively furthermore we established that at criticality the correlation length grows according to ensuremath xi ensuremath sim t 1 z with z ensuremath simeq 1 27 3 independently of the degree of order of the initial configuration in marked contrast with the behavior of the xy model

robustness analysis of interval matrices based on kharitonov s theorem this paper deals with the robustness analysis problem of interval matrices expansion of det a b is used to get characteristic polynomials of two corresponding systems kharitonov s theorem is applied to test hurwitz properties of the two polynomials a new sufficient condition for all eigenvalues of the interval matrix to lie in a damping cone on complex plan is derived illustrative examples are given

technical communique on the robustness of linear systems with nonlinear uncertain parameters the present paper studies the stability robustness problem of an uncertain state space system we propose a new uncertain state space model which allows second order uncertain parameters the uncertainty in the model appears in the form of a combination of additive perturbation and multiplicative perturbation it is shown that the model has a strong practical background a robustness criterion based on the model is derived an example shows advantages of the proposed approach

stabilization of uncertain systems with norm bounded uncertainty a control a robust stabilization problem in a state space setting is treated it is assumed that the states are available for feedback using a fixed lyapunov function approach quadratic stability it is shown that an open loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear state feedback controller as a consequence it is shown that the existence of a quadratically stabilizing nonlinear time varying dynamic state feedback controller implies the existence of a quadratically stabilizing memoryless linear time invariant state feedback compensator

stabilization of an uncertain linear system in which uncertain parameters enter into the input matrix this paper presents a procedure for stabilizing a class of uncertain linear systems the uncertain systems under consideration are described by state equations in which the input matrix depends on a matrix of uncertain parameters this matrix of uncertain parameters may be time varying however it is constrained by a bound on its induced norm the stabilization procedure presented involves the repeated solution of an algebraic riccati equation when a positive definite solution to this riccati equation is obtained this solution is used to construct a stabilizing linear control law another important result contained in this paper can be stated roughly as follows for the class of uncertain systems under consideration if a system can be stabilized via nonlinear control then it is also possible to stabilize the system via linear control

optimal multi agent coordination under tree formation constraints this paper presents a framework for studying the centralized optimal multi agent coordination problem under tree formation constraints the geodesic equations characterizing the optimal coordinated motions are derived in a suitably chosen coordinate system for general tree formation constraints the solutions to these equations however may fail to be optimal once extended beyond certain points called the conjugate points due to the failure of the second order optimality condition for the particular class of star formations two methods for computing the conjugate points along a natural candidate solution are introduced using these methods we derive analytically the conjugate points as well as the better solutions once the candidate solution is extended beyond its first conjugate point the optimal centralized coordinated motions derived in this paper will yield a performance lower bound for those generated by decentralized algorithms

distributed consensus control for linear multi agent systems with discontinuous observations this article addresses the distributed consensus problem of linear multi agent systems with discontinuous observations over a time invariant undirected communication topology under the assumption that each agent can only intermittently share its outputs with the neighbours a class of distributed observer type of protocols are designed and utilised to achieve consensus by using appropriate matrix decomposition it is shown that consensus in the closed loop multi agent systems under a connected topology can be converted to the simultaneous asymptotic stability of a set of switching systems whose dimensions are the same as each agent from a multiple lyapunov functions approach it is proved that there exists a protocol to guarantee consensus if the communication time rate is larger than a threshold value furthermore a distributed pinning control method is employed to solve the consensus problem on an arbitrary given topology which needs not be connected particularly the questions of what kind of agen

asymptotically optimal decentralized control for large population stochastic multiagent systems the interaction of interest coupled decision makers and the uncertainty of individual behavior are prominent characteristics of multiagent systems mas how to break through the framework of conventional control theory which aims at single decision maker and single decision objective and to extend the methodology and tools in the stochastic adaptive control theory to analyze mas are of great significance in this paper a preliminary exploration is made in this direction and the decentralized control problem is considered for large population stochastic mas with coupled cost functions different from the deterministic discounted costs in the existing differential game models a time averaged stochastic cost function is adopted for each agent the decentralized control law is constructed based on the state aggregation method and tracking like quadratic optimal control by using probability limit theory the stability and optimality of the closed loop system are analyzed the main contributions of this paper include the following points 1 the concepts of asymptotic nash equilibrium in probability and almost surely respectively are introduced and the relationship between these concepts is illuminated which provide necessary tools for analyzing the optimality of the decentralized control laws 2 the closed loop system is shown to be almost surely uniformly stable and bounded independently of the number of agents n 3 the population state average psa is shown to converge to the infinite population mean ipm trajectory in the sense of both l2 norm and time average almost surely as n increases to infinity 4 the decentralized control law is designed and shown to be almost surely asymptotically optimal the cost of each agent based on local measurements converges to that based on global measurements almost surely as n increases to infinity

quantization effects on synchronized motion of teams of mobile agents with second order dynamics abstract for a team of mobile agents governed by second order dynamics this paper studies how different quantizers affect the performances of consensus type schemes to achieve synchronized collective motion it is shown that when different types of quantizers are used for the exchange of relative position and velocity information between neighboring agents different collective behaviors appear under the chosen logarithmic quantizers and with symmetric neighbor relationships we prove that the agents velocities and positions get synchronized asymptotically we show that under the chosen symmetric uniform quantizers and with symmetric neighbor relationships the agents velocities converge to the same value asymptotically while the differences of their positions converge to a bounded set we also show that when the uniform quantizers are not symmetric the agents velocities may grow unboundedly through simulations we present richer undesirable system behaviors when different logarithmic and uniform quantizers are used such different quantization effects underscore the necessity for a careful selection of quantization strategies especially for multi agent systems with higher order agent dynamics

clustering in a network of non identical and mutually interacting agents clustering is a phenomenon that may emerge in multi agent systems through self organization groups arise consisting of agents with similar dynamic behaviour it is observed in fields ranging from

existence properties and trajectory specification of generalised multi agent flocking a class of flocking algorithms for second order multi agent networks with single virtual leaders are developed by including more weighting and navigating matrices in this paper flocking existence

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

the phase transition of matrix recovery from gaussian measurements matches the minimax mse of matrix denoising let be an unknown m by n matrix in matrix recovery one takes linear measurements of where and each is an m by n matrix a popular approach for matrix recovery is nuclear norm minimization nnm solving the convex optimization problem for all where denotes the nuclear norm namely the sum of singular values empirical work reveals a phase transition curve stated in terms of the undersampling fraction rank fraction and aspect ratio specifically when the measurement matrices ai have independent standard gaussian random entries a curve exists such that if nnm typically succeeds for large m n whereas if it typically fails an apparently quite different problem is matrix denoising in gaussian noise in which an unknown m by n matrix is to be estimated based on direct noisy measurements where the matrix z has independent and identically distributed gaussian entries a popular matrix denoising scheme solves the unconstrained optimization problem when optimally tuned this scheme achieves the asymptotic minimax mean squared error where we report extensive experiments showing that the phase transition in the first problem matrix recovery from gaussian measurements coincides with the minimax risk curve in the second problem matrix denoising in gaussian noise for any rank fraction at each common aspect ratio our experiments considered matrices belonging to two constraint classes real m by n matrices of various ranks and aspect ratios and real symmetric positive semidefinite n by n matrices of various ranks

double hopf bifurcation and quasi periodic attractors in delay coupled limit cycle oscillators abstract we investigate the double hopf bifurcation at zero equilibrium point firstly we give the critical values of hopf and double hopf bifurcations secondly we implement the normal form method and the center manifold theory for delay coupled limit cycle oscillators and derive the universal unfolding and a complete bifurcation diagram of the system thirdly many interesting phenomena such as attractive periodic motion and three dimensional invariant torus are observed using numerical simulation finally the normal forms of several strong resonant cases are listed

distributed circular formation stabilization for dynamic unicycles this paper investigates the problem of designing distributed control laws making a group of dynamic unicycles converge to a common circle of prespecified radius whose center is stationary but dependent on the initial conditions and travel around the circle in a desired direction the vehicles are required to converge to a formation on the circle expressed by desired separations and ordering of the unicycles the information exchange between unicycles is modelled by a directed graph which is assumed to have a spanning tree a hierarchical approach is proposed which simplifies the control design by decoupling the problem of making the unicycles converge to a common circle from the problem of stabilizing the formation

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

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

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

on the error in phase transition computations for compressed sensing evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with gaussian ensemble unfortunately the exact evaluation of the statistical dimension is very difficult and it has become standard to replace it with an upper bound to ensure that this technique is suitable 1 has introduced an upper bound on the gap between the statistical dimension and its approximation in this work we first show that the error bound in 1 in some low dimensional models such as total variation and ell 1 analysis minimization becomes poorly large next we develop a new error bound which significantly improves the estimation gap compared to 1 in particular unlike the bound in 1 that fails in some settings with overcomplete dictionaries our bound exhibits a decaying behavior in such cases

model consistency of partly smooth regularizers this paper studies least square regression penalized with partly smooth convex regularizers this class of penalty functions is very large and versatile and allows to promote solutions conforming to some notion of low complexity indeed such penalties regularizers force the corresponding solutions to belong to a low dimensional manifold the so called model which remains stable when the argument of the penalty function undergoes small perturbations such a good sensitivity property is crucial to make the underlying low complexity manifold model robust to small noise in a deterministic setting we show that a generalized irrepresentable condition implies stable model selection under small noise perturbations in the observations and the design matrix when the regularization parameter is tuned proportionally to the noise level as an algorithmic implication we also prove that this condition is almost necessary for stable model recovery we then turn to the random setting where the design matrix and the noise are random and the number of observations grows large we show that under our generalized irrepresentable condition and a proper scaling of the regularization parameter the regularized estimator is model consistent in plain words with a probability tending to one as the number of measurements tends to infinity the regularized estimator belongs to the correct low dimensional model manifold this paper unifies and generalizes a large body of literature where model consistency was known to hold for instance for the lasso group lasso total variation fused lasso and nuclear trace norm regularizers as an algorithmic implication we show that under the deterministic model selection conditions the forward backward proximal splitting algorithm used to solve the penalized least square regression problem is guaranteed to identify the model manifold after a finite number of iterations finally we detail how our results extend from the quadratic loss to an arbitrary smooth and strictly convex loss function we illustrate the usefulness of our results on the problem of low rank matrix recovery from random measurements using nuclear norm minimization

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

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

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

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

hierarchical cluster structures in a one dimensional swarm oscillator model swarm oscillator model derived by one of the authors tanaka where interacting motile elements form various kinds of patterns is investigated we particularly focus on the cluster patterns in one dimensional space we mathematically derive all static and stable configurations in final states for a particular but a large set of parameters in the derivation we introduce renormalized expression of this model we find that the static final states are hierarchical cluster structures in which a cluster consists of smaller clusters in a nesting manner

a note on robust stability bounds the authors comment on stability robustness bounds for linear systems with multiple uncertain parameters which were obtained by means of lyapunov functions results obtained with quadratic and with vector lyapunov functions are compared simple examples are used to illustrate the effects of the choice of functions corresponding majorizations and system decompositions

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

a novel alignment repulsion algorithm for flocking of multi agent systems based on the number of neighbours per agent in this paper an energy based control methodology is proposed to satisfy the reynolds three rules in a flock of multiple agents first a control law is provided that is directly derived from the passivity theorem in the next step the number of neighbours alignment repulsion algorithm is introduced for a flock of agents which loses the cohesion ability and uniformly joint connectivity condition with this method each agent tries to follow the agents which escape its neighbourhood by considering the velocity of escape time and number of neighbours it is mathematically proved that the motion of multiple agents converges to a rigid and uncrowded flock if the group is jointly connected just for an instant moreover the conditions for collision avoidance are guaranteed during the entire process finally simulation results are presented to show the effectiveness of the proposed methodology

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

robust stabilizability for linear systems with both parameter variation and unstructured uncertainty the authors consider the problem of finding a single compensator which stabilizes a plant having both parameter variation and high frequency unstructured uncertainty an uncertain system model is proposed to characterize plants containing those two different uncertainties closed loop stability criteria are then proposed for the model robust stabilizability for single input single output siso systems is studied a number of assumptions describing the set of admissable siso plants are imposed the satisfaction of these assumptions guarantees the existence of a proper stable compensator c s achieving robust stabilization the algorithm used for controller design is recursive in nature and allows the designer to select one compensator coefficient at a time also the minimum order of the desired stabilizer c s depends only on the largest relative degree of the nominal plants which often leads to a lower order compensator

a robust stability bound of linear systems with structured uncertainty the robust stability of linear uncertain systems with multiple uncertain parameters is considered a sphere norm bound condition on the uncertainties which assures stability of the systems is derived this bound is shown to be less conservative than existing ones a necessary condition to maximize this bound is also given

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

state transitions and the continuum limit for a 2d interacting self propelled particle system we study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism we find that the swarming system undergoes various changes of state as a function of the self propulsion and interaction potential parameters in this paper we utilize a procedure which connects a class of individual based models to their continuum formulations and determine criteria for the validity of the latter h stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions we perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual based one c 2007 elsevier b v all rights reserved

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

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