global synchronization for a class of dynamical complex networks abstract this paper is concerned with the problem of global synchronization for a class of dynamical complex networks composed of general lur e systems based on the absolute stability theory and the kalman yakubovich popov kyp lemma sufficient conditions are established to guarantee global synchronization of dynamical networks with complex topology directed and weighted couplings several global synchronization criteria formulated in the form of linear matrix inequalities lmis or frequency domain inequalities are also proposed for undirected dynamical networks in order to obtain global results no linearization technique is involved through derivation of the synchronization criteria numerical examples are provided to demonstrate the effectiveness of the proposed results

construction of aggregation operators with noble reinforcement this paper examines disjunctive aggregation operators used in various recommender systems a specific requirement in these systems is the property of noble reinforcement allowing a collection of high valued arguments to reinforce each other while avoiding reinforcement of low valued arguments we present a new construction of lipschitz continuous aggregation operators with noble reinforcement property and its refinements

three dimensional circular formations via set stabilization the paper addresses distributed stabilization of a class of circular formations for steered kinematic particles in three dimensional euclidean space information exchange between the particles is modeled by a bidirectional graph which is assumed to have a spanning tree distributed control design is based on a hierarchical approach that relies on set stabilization and a reduction principle for asymptotic stability of closed sets the approach allows to solve for different formation specifications in a decoupled manner

variety and generality of clustering in globally coupled oscillators abstract clustering behavior in globally coupled identical oscillators is studied by using the phase model any pair of oscillators is assumed to interact through their phase difference without specifying the coupling function the stability of symmetric cluster states in analyzed where symmetric means that the clusters contain the same number of oscillators it is found that higher harmonics in the coupling function are essential to clustering examples show that various cluster states appear depending on the coupling form including those with oscillating intervals anti phase states and chaotic long transient apart from the phase model we also study a general model for globally coupled limit cycle oscillators in the vicinity of the hopf bifurcation and find that such a system does not exhibit clustering within the lowest order approximation

a recursive algorithm for linear system identification this paper deals with the pole zero identification of a linear system from a measured input output record it is shown that the minimization of a modified version of the squared kalman equation error can be implemented by an order recursive algorithm in the time domain the algorithm is based on the gram schmidt orthogonalization of intertwined krylov sequences involving a skew self adjoint linear operator

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

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

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

brief paper decentralized coordination of autonomous swarms using parallel gibbs sampling in this paper we present analysis of a discrete time decentralized stochastic coordination algorithm for a group of mobile nodes called an autonomous swarm on a finite spatial lattice all nodes take their moves by sampling in parallel their locally perceived gibbs distributions corresponding to a pairwise nearest neighbor potential the algorithm has no explicit requirements on the connectedness of the underlying information graph which varies with the swarm configuration it is established that with an appropriate annealing schedule the algorithm results in swarm configurations converging to the global minimizers of a modified potential energy function the extent of discrepancy between the modified and original potential energy functions is determined by the maximum node travel between time steps and when such distance is small the ultimate swarm configurations are close to the global minimizers of the original potential energy simulation results are further presented to illustrate the capability of the sampling algorithm in approximate global optimization for swarms

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

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

a discussion of various approaches to the linear system identification problem this paper deals with the pole zero identification of a linear system from a measured input output record one objective is to show that the pencil of function method minimizes a weighted version of the kalman equation error it follows that the pencil of function method is capable of yielding robust estimates for poles located in a given region of the complex s plane the second objective of this paper is to illustrate that identical sets of equations arise in three supposedly different analytical techniques for obtaining the impulse response of a system the techniques investigated are 1 the least squares technique based on the discrete wiener hopf equation 2 pisarenko s eigenvalue method and 3 jain s pencil of function method the proof of equivalence is valid only for the noise free case when the system order is known instead of using the conventional differential equation formulation equivalence is shown with the integral form utilized in the pencil of function method

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

stability properties of the collective stationary motion of self propelling particles with conservative kinematic constraints in our previous papers we proposed a continuum model for the dynamics of the systems of self propelling particles with conservative kinematic constraints on the velocities we have determined a class of stationary solutions of this hydrodynamic model and have shown that two types of stationary flow linear and axially symmetric vortical flow are possible in this paper we consider the stability properties of these stationary flows we show using a linear stability analysis that the linear solutions are neutrally stable with respect to the imposed velocity and density perturbations a similar analysis of the stability of the vortical solution is found to be not conclusive

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

hierarchical clustering of dynamical networks using a saddle point analysis this paper studies cluster synchronization in dynamical networks a class of cooperative dynamical networks that exhibit clustering in their asymptotic behavior is analyzed the network nodes are equipped with heterogeneous dynamics and interact with a nonlinear and saturated interaction rule it is proven that cluster synchronization appears asymptotically independent of the initial conditions the clustering behavior of the dynamic network is shown to correspond to the solution of a static saddle point problem enabling a precise characterization of the clustering structure we show how the clustering structure depends on the relation between the underlying graph the node dynamics and the saturation level of the interactions this interpretation leads to deeper combinatorial insights related to clustering including a generalization of classical network partitioning problems such as the inhibiting bisection problem the min s t cut problem and hierarchical clustering analysis the theoretical results are applied for the analysis of a test case network inspired by the ieee 30 bus system

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

fuzzy logic methods in recommender systems here we consider methodologies for constructing recommender systems the approaches studied here differ from collaborative filtering they are based solely on the preferences of the single individual for whom we are providing the recommendation and make no use of the preferences of other collaborators we have called these reclusive methods another important feature distinguishing these reclusive methods from collaborative methods is that they require a representation of the objects considerable use is made of fuzzy set methods for the representation and subsequent construction of justifications and recommendation rules it is pointed out these reclusive methods rather than being competitive with collaborative methods are complementary

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

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

invariance principles allowing of non lyapunov functions for estimating attractor of discrete dynamical systems this technical note establishes several versions of invariance principles for describing the eventual dynamical behaviors of discrete dynamical systems instead of the requirement of the so called lyapunov functions in the classical lasalle invariance principle some more relaxed conditions are imported the established invariance principles thus can be applied to a more general class of discrete dynamical systems for classifying their orbits into two categories based on the eventual dynamical behaviors and the proposed classification scheme is suitable for theoretically and numerically estimating the local or global attractors produced by the discrete dynamical systems the practical usefulness of the analytical results is verified by systematically investigating several representative discrete systems

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

stabilization of a class of dynamical complex networks based on decentralized control abstract this paper deals with a stabilization problem for a class of dynamical complex networks with each node being a general lur e system based on a lur e postnikov function and a special decentralized control strategy the problem of designing a linear feedback controller such that states of all nodes are globally stabilized onto an expected homogeneous state is addressed a controller design method based on parameter dependent lur e postnikov function is proposed in order to reduce the conservativeness and the controller can be constructed via feasible solutions of a certain set of linear matrix inequalities lmis a dynamical network composed of identical chua s circuits is adopted as a numerical example to demonstrate the effectiveness of the proposed results

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

generalizing leximin to t norms and t conorms the lexit and lexis orderings the leximin procedure introduced by dubois and prade in 1996 provides a methodology for adjudicating ties in aggregated values when using the min t norm here with the introduction of the lexit procedure we generalize these ideas to provide a tool for adjudicating ties when aggregating data using any t norm we then provide the lexis procedure for adjudicating ties when aggregating arguments using t conorms

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

an order recursive algorithm for estimating pole zero models this paper deals with the pole zero estimation of a discrete time linear system from a measured input output record it is shown that the minimization of the squared equation error for a recursive n n 1 filter can be implemented by an order recursive algorithm using scalar products of records derived from the data the algorithm is based on the gram schmidt orthogonalization of an intertwined krylov sequence which consists of successively time shifted or circularly time shifted versions of the input and output records

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

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

phase and frequency shifts in a population of phase oscillators we investigate the synchronization behavior of a population of globally coupled phase oscillators with randomly distributed eigenfrequencies a variety of synchronized states is rigorously analyzed by means of the center manifold theorem combined with a nonlinear renormalization procedure this way the different synchronized states are determined explicitly we observe n cluster states where n 1 dots 4 in a synchronized state all oscillators have the same frequency synchronization frequency and mutual phase differences depend on model parameters as well as on the configuration of the synchronized state i e the number of oscillators within each cluster the synchronization frequency may decisively differ from the mean of the eigenfrequencies e g giving rise to frozen states which are synchronized states with vanishing synchronization frequency unstable cluster states are associated with transitions between different synchronization frequencies our approach can easily be extended to a population of oscillators with randomly distributed coupling strengths the different synchronized states are discussed in the context of neural coding

noble reinforcement in disjunctive aggregation operators we discuss the role of disjunctive aggregation operators in prototype based reasoning systems such as recommender systems we indicate a need for these aggregation operators to have the additional property of noble reinforcement allowing a collection of high valued arguments to reinforce each other to give complete satisfaction while avoiding the situation in which a collection of low valued arguments act in the same way we describe the difficulty that most t conorms have in realizing this feature of noble reinforcement we show that by relaxing the requirement of associativity we can provide disjunctive type aggregation operators that manifest noble reinforcement

a mathematical model for the dynamics of clustering abstract the formation of several clusters arising from attracting forces between nonidentical entities or agents is a phenomenon observed in diverse fields think of people gathered through a mutual interest swarm behaviour of animals or clustering of oscillators in brain cells we introduce a dynamic model of mutually attracting agents for which we prove that the long term behaviour consists of agents organized into several groups or clusters we have completely characterized the cluster structure i e the number of clusters and their composition by means of a set of inequalities in the parameters of the model and have identified the intensity of the attraction as a key parameter governing the transition between different cluster structures the versatility of the model will be illustrated by discussing its relation to the kuramoto model and by describing how it applies to a system of interconnected water basins

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

distributed network optimization with heuristic rational agents a network of distributed agents wants to minimize a global cost given by a sum of local terms involving nonlinear convex functions of self and neighboring variables agents update their variables at random times by observing the values of neighboring agents and applying a random heuristic rule intent on minimizing the local cost with respect to their own variables the heuristic rules are rational in that their average result is the actual optimal action with respect to the given values of neighboring variables by identifying heuristic rational optimization with stochastic coordinate descent it is shown that all agents visit a neighborhood of the optimal cost infinitely often with probability 1 an exponential probability bound on the worst deviation from optimality between visits to near optimal operating points is also derived commonly used models of consensus and opinion propagation in social networks markov random field estimation in wireless sensor networks and cohesive foraging of animal herds are cast in the language of heuristic rational optimization numerical simulations for these three examples are presented to corroborate analytical results

control of frictional dynamics of a one dimensional particle array control of frictional forces is required in many applications of tribology while the problem is approached by chemical means traditionally a recent approach was proposed to control the system mechanically to tune frictional responses we design feedback control laws for a one dimensional particle array sliding on a surface subject to friction the frenkel kontorova model describing the dynamics is a nonlinear interconnected system and the accessible control elements are average quantities only we prove local stability of equilibrium points of the un controlled system in the presence of linear and nonlinear particle interactions respectively we then formulate a tracking control problem whose control objective is for the average system to reach a designated targeted velocity using accessible elements sufficient stabilization conditions are explicitly derived for the closed loop error systems using the lyapunov theory based methods simulation results show satisfactory performances the results can be applied to other physical systems whose dynamics is described by the frenkel kontorova model

legendre series approach to identification and analysis of linear systems in this paper the legendre operational matrix of integration is introduced and it is subsequently used for the identification and analysis of linear systems the algorithms proposed are easily implementable in a digital computer and they are analogous to those already derived for other types of orthogonal functions

partial entrainment in the finite kuramoto sakaguchi model abstract although modifications of the kuramoto model have been the subject of extensive research the model itself is not yet fully understood we offer several results and observations some analytic others through simulations we derive a sufficient condition for the existence of a solution exhibiting partial entrainment with respect to a given subset of oscillators the result also implies persistence of the entrainment behavior under perturbations the critical values of the coupling strength defining the transitions between different forms of partial entrainment are predicted by an analytical approximation based on the fact that oscillators with large differences in their natural frequencies have little influence on each other s entrainment behavior the predictions agree with the actual values obtained by simulations we indicate by simulations that entrainment can disappear with increasing coupling strength and that in arrays of josephson junctions a similar phenomenon can be observed where it is also possible that a junction leaving one entrained subset joins another entrained subset

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