extending fuzzy logics with many hedges abstract fuzzy logic aims at modeling logical reasoning with vague or imprecise statements which may contain linguistic hedges in fact many hedges e g very highly rather and slightly can be used simultaneously to express different levels of emphasis moreover each hedge might have a dual one e g slightly can be seen as a dual hedge of very thus it is necessary to extend systems of fuzzy logic with multiple hedges this work proposes two axiomatizations for multiple hedges as an expansion of a core fuzzy logic in one axiomatization hedges do not have any dual one while in the other each hedge can have its own dual one it is shown that the proposed logics not only cover a large class of hedge functions but also have all completeness properties as the underlying logic w r t the class of their chains as well as distinguished subclasses of their chains including standard completeness the axiomatizations are also extended to the first order level furthermore we present a method to build linguistic fuzzy logics based on the axiomatizations and a hedge algebra whose corresponding algebras use a linguistic truth domain taken from the hedge algebra for representing and reasoning with linguistically expressed human knowledge where truth values of vague sentences are given in linguistic terms

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

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

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

algebraic and proof theoretic characterizations of truth stressers for mtl and its extensions extensions of monoidal t norm logic mtl and related fuzzy logics with truth stresser modalities such as globalization and very true are presented here both algebraically in the framework of residuated lattices and proof theoretically as hypersequent calculi completeness with respect to standard algebras based on t norms embeddings between logics decidability and the finite embedding property are then investigated for these logics

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

a class of attractions repulsion functions for stable swarm aggregations in this brief article we consider an m member individual based continuous time swarm model in an n dimensional space and extend the results in gazi and passino 2003 by specifying a general class of attraction repulsion functions that can be used to achieve swarm aggregation these functions are odd functions that have terms for attraction and repulsion acting in opposite directions in compliance with real biological swarms we present stability analysis for several cases of the functions considered to characterize swarm cohesiveness size and ultimate motions while in a cohesive group moreover we show how the model can be extended for achieving formation control furthermore we discuss how the attraction repulsion functions can be modified to incorporate the finite body size of the swarm members numerical simulations are also presented for illustration purposes

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

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

gaslike model of social motility we propose a model to represent the motility of social elements the model is completely deterministic possesses a small number of parameters and exhibits a series of properties that are reminiscent of the behavior of comunities in social ecological competition these are i similar individuals attract each other ii individuals can form stable groups iii a group of similar individuals breaks into subgroups if it reaches a critical size iv interaction between groups can modify the distribution of the elements as a result of fusion fission or pursuit v individuals can change their internal state by interaction with their neighbors the simplicity of the model and its richness of emergent behaviors such as for example pursuit between groups make it a useful toy model to explore a diversity of situations by changing the rule by which the internal state of individuals is modified by the interactions with the environment

on fuzzy type theory this paper is a generalization of classical simple type theory we have developed a formal system of fuzzy type theory which differs from the classical one essentially in extension of truth values from two to infinitely many the structure of truth values is assumed to be an imtl algebra residuated lattice with prelinearity and double negation extended by the baaz delta operation various properties of fuzzy type theory are proved including its completeness

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

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

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

singular patterns for an aggregation model with a confining potential abstract we consider the aggregation equation with an attractive repulsive force law recent studies kolokolnikov et al 2011 22 von brecht et al 2012 23 balague et al 2013 15 have demonstrated that this system exhibits a very rich solution structure including steady states consisting of rings spots annuli n fold symmetries soccer ball patterns etc we show that many of these patterns can be understood as singular perturbations off lower dimensional equilibrium states for example an annulus is a bifurcation from a ring soccer ball patterns bifurcate off solutions that consist of delta point concentrations we apply asymptotic methods to classify the form and stability of many of these patterns to characterize spot solutions a class of semi linear aggregation problems is derived where the repulsion is described by a nonlinear term and the attraction is linear but non symmetric for a special class of perturbations that consists of a newtonian repulsion the spot shape is shown to be an ellipse whose precise dimensions are determined via a complex variable method for annular shapes their width and radial density profile are described using perturbation techniques

resource bounded randomness and computational complexity the following is a survey of resource bounded randomness concepts and their relations to each other further we introduce several new resource bounded randomness concepts corresponding to the classical randomness concepts and show that the notion of polynomial time bounded ko randomness is independent of the notions of polynomial time bounded lutz schnorr and kurtz randomness lutz has conjectured that for a given time or space bound the corresponding resource bounded lutz randomness is a proper renement of resource bounded schnorr randomness this conjecture is answered for the case of polynomial time bound moreover we will show that polynomial time bounded schnorr randomness is a proper renement of polynomial time bounded kurtz randomness in contrast to this result we show that the notions of polynomial time bounded lutz schnorr and kurtz randomness coincide in the case of recursive sets thus it suces to study the notion of resource bounded lutz randomness in the context of complexity theory the stochastic properties of resource bounded random sequences will be discussed in detail schnorr has already shown that the law of large numbers holds for p random sequences we will show that another important law in probability theory the law of the iterated logarithm holds for p random sequences too hence almost all sets in the exponential time complexity class are hard from the viewpoint of statistics c 2000 elsevier science b v all rights reserved

a simple unpredictable pseudo random number generator two closely related pseudo random sequence generators are presented the 1 p generator with input p a prime outputs the quotient digits obtained on dividing 1 by p the x 2 bmod n generato

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

multiparticle random walks on a deformable medium multiparticle random walks on a deformable medium have been investigated in 2 1 dimensions the time evolution of the particle distribution is studied the results show that the randomly distributed particles in the beginning will be self organized into a cluster pattern in the intermediate stage and then return to the random distribution pattern in the late stage the dependence of the clustering degree on the stiffness parameter of medium ensuremath alpha stability parameter of systems ensuremath beta and average particle density ensuremath rho 0 is also investigated there exists an optimal clustering stability ensuremath beta p at which the system has the strongest clustering ability and corresponds to a maximum clustering coefficient ensuremath gamma p the dependence of the optimal clustering coefficient ensuremath gamma p on the stiffness ensuremath alpha and particle density ensuremath rho 0 is obtained and the landscape of the medium generated by particles is also investigated

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

self organized network of phase oscillators coupled by activity dependent interactions we investigate a network of coupled phase oscillators whose interactions evolve dynamically depending on the relative phases between the oscillators we found that this coevolving dynamical system robustly yields three basic states of collective behavior with their self organized interactions the first is the two cluster state in which the oscillators are organized into two synchronized groups the second is the coherent state in which the oscillators are arranged sequentially in time the third is the chaotic state in which the relative phases between oscillators and their coupling weights are chaotically shuffled furthermore we demonstrate that self assembled multiclusters can be designed by controlling the weight dynamics note that the phase patterns of the oscillators and the weighted network of interactions between them are simultaneously organized through this coevolving dynamics we expect that these results will provide new insight into self assembly mechanisms by which the collective behavior of a rhythmic system emerges as a result of the dynamics of adaptive interactions

a comparison of two approaches to pseudorandomness the concept of pseudorandomness plays an important role in cryptography in this note we contrast the notions of complexity theoretic pseudorandom strings from algorithmic information theory and pseudorandom strings from cryptography for example we show that we can easily distinguish a complexity theoretic pseudorandom ensemble from the uniform ensemble both notions of pseudorandom strings are uniformly unpredictable in contrast with pseudorandom strings complexity theoretic pseudorandom strings are not polynomial time unpredictable

new tools for characterizing swarming systems a comparison of minimal models abstract we compare three simple models that reproduce qualitatively the emergent swarming behavior of bird flocks fish schools and other groups of self propelled agents by using a new set of diagnosis tools related to the agents spatial distribution two of these correspond in fact to different implementations of the same model which had been previously confused in the literature all models appear to undergo a very similar order to disorder phase transition as the noise level is increased if we only compare the standard order parameter which measures the degree of agent alignment when considering our novel quantities however their properties are clearly distinguished unveiling previously unreported qualitative characteristics that help determine which model best captures the main features of realistic swarms additionally we analyze the agent clustering in space finding that the distribution of cluster sizes is typically exponential at high noise and approaches a power law as the noise level is reduced this trend is sometimes reversed at noise levels close to the phase transition suggesting a non trivial critical behavior that could be verified experimentally finally we study a bi stable regime that develops under certain conditions in large systems by computing the probability distributions of our new quantities we distinguish the properties of each of the coexisting metastable states our study suggests new experimental analyses that could be carried out to characterize real biological swarms

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

exactly conservative integrators traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of any nonlinear invariants in this work we present a general approach for developing explicit nontraditional algorithms that conserve such invariants exactly we illustrate the method by applying it to the three wave truncation of the euler equations the lotka volterra predator prey model and the kepler problem the ideas are discussed in the context of symplectic phase space conserving integration methods as well as nonsymplectic conservative methods we comment on the application of our method to general conservative systems

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

numerical methods for hamiltonian pdes the paper provides an introduction and survey of conservative discretization methods for hamiltonian partial differential equations the emphasis is on variational symplectic and multi symplectic methods the derivation of methods as well as some of their fundamental geometric properties are discussed basic principles are illustrated by means of examples from wave and fluid dynamics

hypersequent rules with restricted contexts for propositional modal logics as part of a general research programme into the expressive power of different generalisations of the sequent framework we investigate hypersequent calculi given by rules of the newly introduced format of hypersequent rules with context restrictions the introduced rule format is used to prove uniform syntactic cut elimination decidability and complexity results we also introduce transformations between hypersequent rules of this format and hilbert axioms entailing a result about the limits of such rules as case studies we apply our methods to several modal logics and obtain e g a complexity optimal decision procedure for the logic s5 and new calculi for the logic k4 2 as well as combinations of modal logics in the form of simply dependent bimodal logics

dynamic critical approach to self organized criticality a dynamic scaling ansatz for the approach to the self organized critical soc regime is proposed and tested by means of extensive simulations applied to the bak char21 sneppen model bs which exhibits robust soc behavior considering the short time scaling behavior of the density of sites ensuremath rho t below the critical value it is shown that i starting the dynamics with configurations such that ensuremath rho t 0 ensuremath rightarrow 0 one observes an initial increase of the density with exponent ensuremath theta 0 12 2 ii using initial configurations with ensuremath rho t 0 ensuremath rightarrow 1 the density decays with exponent ensuremath delta 0 47 2 it is also shown that the temporal autocorrelation decays with exponent c a 0 35 2 using these dynamically determined critical exponents and suitable scaling relationships all known exponents of the bs model can be obtained e g the dynamical exponent z 2 10 5 the mass dimension exponent d 2 42 5 and the exponent of all returns of the activity ensuremath tau text all 0 39 2 in excellent agreement with values already accepted and obtained within the soc regime

density elimination density elimination a close relative of cut elimination consists of removing applications of the takeuti titani density rule from derivations in gentzen style hypersequent calculi its most important use is as a crucial step in establishing standard completeness for syntactic presentations of fuzzy logics that is completeness with respect to algebras based on the real unit interval 0 1 this paper introduces the method of density elimination by substitutions for general classes of first order hypersequent calculi it is shown that density elimination by substitutions is guaranteed by known sufficient conditions for cut elimination these results provide the basis for uniform characterizations of calculi complete with respect to densely and linearly ordered algebras standard completeness follows for many first order fuzzy logics using a dedekind macneille style completion and embedding

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

space dimension and scaling in fish school size distributions a simple model of aggregation has been used in its mean field version to explain the observed scaling property of tuna fish school size distributions bonabeau e and dagorn l 1995 phys rev e 51 5220 this model makes additional predictions when the dimension of the space in which the fish move is taken into account in this letter we identify two cases where the mean field assumption which was justified for free swimming tuna fish is no longer valid in these two examples scaling is also observed and the exponent is modified from the mean field case in a way predicted by the model

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

phase transitions in self driven many particle systems and related non equilibrium models a network approach we investigate the conditions that produce a phase transition from an ordered to a disordered state in a family of models of two dimensional elements with a ferromagnetic like interaction this family is defined to contain under the same framework among others the xy model and the self driven particles model introduced by vicsek et al each model is distinguished only by the rules that determine the set of elements with which each element interacts we propose a new member of the family the vectorial network model in which a given fraction of the elements interact through direct random connections this model is analogous to an xy system on a network and as such can be of interest for a wide range of problems it captures the main aspects of the interaction dynamics that produce the phase transition in other models of the family the network approach allows us to show analytically the existence of a phase transition in this vectorial network model and to compute its relevant parameters for the case in which all elements are randomly connected finally we study numerically the conditions required for a phase transition to exist for different members of the family our results show that a qualitatively equivalent phase transition appears whenever even a small amount of long range interactions are present or built over time regardless of other equilibrium or non equilibrium properties of the system

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

expanding basic fuzzy logic with truth constants for component delimiters in this paper we investigate the propositional logic of standard algebras for hajek s basic fuzzy logic bl in a language expanded with propositional constants for the idempotent elements delimiting the l g and p components of the algebra we start from a fixed standard bl algebra introduce new propositional constants present a suitable set of axioms investigate completeness results and give some complexity results

modal mtl algebras a modal mtl algebra is an algebra in the variety generated by the modal mtl chains linearly ordered commutative bounded integral residuated lattices equipped with a unary order preserving operation reverse modal mtl algebras can be defined similarly by equipping a unary order reversing operation instead we axiomatize the variety of reverse modal mtl algebras two constructions are considered on reverse modal mtl chains the macneille completion of the underlying order and a finite embeddability construction in both cases we define a suitable extension of the unary order preserving reversing operation properties preserved via these constructions are investigated using approximations in particular a large class of identities preserved by each of the constructions is described syntactically

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

constrained consensus of asynchronous discrete time multi agent systems with time varying topology the union graph is assumed to be strongly connected over each finite interval an approach is proposed to transform the original network to a synchronous one we show that the linear part converges and the projection error vanishes over time in this paper the constrained consensus problem is studied for asynchronous discrete time multi agent system where each agent needs to lie in a closed convex constraint set while reaching consensus the communication graphs are assumed to be directed unbalanced dynamically changing in addition their union graph is assumed to be strongly connected among certain intervals of finite length to deal with the asynchronous communications among agents the original asynchronous system is equivalently transformed to the synchronous one by adding new agents by employing the properties of the projection on the convex sets the distance from the states of the agents in the newly constructed system to the intersection set of all agents constraint sets is estimated based on this estimation the original system is proven to reach consensus by showing that the linear parts of the newly constructed systems converge and the nonlinear parts vanish over time finally two numerical examples are provided to show the effectiveness of the theoretical results

on synchronous robotic networks part ii time complexity of rendezvous and deployment algorithms this paper analyzes a number of basic coordination algorithms running on synchronous robotic networks we provide upper and lower bounds on the time complexity of the move toward average and circumcenter laws both achieving rendezvous and of the centroid law achieving deployment over a region of interest the results are derived via novel analysis methods including a set of results on the convergence rates of linear dynamical systems defined by tridiagonal toeplitz and circulant matrices

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

how to generate cryptographically strong sequences of pseudo random bits we give a set of conditions that allow one to generate 50 50 unpredictable bits based on those conditions we present a general algorithmic scheme for constructing polynomial time deterministic algorithms that stretch a short secret random input into a long sequence of unpredictable pseudo random bits we give an implementation of our scheme and exhibit a pseudo random bit generator for which any efficient strategy for predicting the next output bit with better than 50 50 chance is easily transformable to an equally efficient algorithm for solving the discrete logarithm problem in particular if the discrete logarithm problem cannot be solved in probabilistic polynomial time no probabilistic polynomial time algorithm can guess the next output bit better than by flipping a coin if head guess 0 if tail guess 1

flocks herds and schools a quantitative theory of flocking we present a quantitative continuum theory of flocking the collective coherent motion of large numbers of self propelled organisms in agreement with everyday experience our model predicts the existence of an ordered phase of flocks in which all members of even an arbitrarily large flock move together with the same mean velocity stackrel ensuremath rightarrow v ensuremath ne 0 this coherent motion of the flock is an example of spontaneously broken symmetry no preferred direction for the motion is picked out a priori in the model rather each flock is allowed to and does spontaneously pick out some completely arbitrary direction to move in by analyzing our model we can make detailed quantitative predictions for the long distance long time behavior of this broken symmetry state the goldstone modes associated with this spontaneously broken rotational symmetry are fluctuations in the direction of motion of a large part of the flock away from the mean direction of motion of the flock as a whole these goldstone modes mix with modes associated with conservation of bird number to produce propagating sound modes these sound modes lead to enormous fluctuations of the density of the flock far larger at long wavelengths than those in e g an equilibrium gas our model is similar in many ways to the navier stokes equations for a simple compressible fluid in other ways it resembles a relaxational time dependent ginsburg landau theory for an n d component isotropic ferromagnet in spatial dimensions dg4 the long distance behavior is correctly described by a linearized theory and is equivalent to that of an unusual but nonetheless equilibrium model for spin systems for dl4 nonlinear fluctuation effects radically alter the long distance behavior making it different from that of any known equilibrium model in particular we find that in d 2 where we can calculate the scaling exponents exactly flocks exhibit a true long range ordered spontaneously broken symmetry state in contrast to equilibrium systems which cannot spontaneously break a continuous symmetry in d 2 the mermin wagner theorem we make detailed predictions for various correlation functions that could be measured either in simulations or by quantitative imaging of real flocks we also consider an anisotropic model in which the birds move preferentially in an easy e g horizontal plane and make analogous but quantitatively different predictions for that model as well for this anisotropic model we obtain exact scaling exponents for all spatial dimensions including the physically relevant case d 3

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

stochastic flocking dynamics of the cucker smale model with multiplicative white noises we present a strong asymptotic stochastic flocking estimate for the stochastically perturbed cucker smale model we characterize a form of multiplicative white noises and present sufficient conditions on the control parameters to guarantee the almost sure exponential convergence toward constant equilibrium states when the strength of multiplicative noises is sufficiently large we show that the strong stochastic flocking occurs even for negative communication weights

nonsmooth coordination and geometric optimization via distributed dynamical systems emerging applications for networked and cooperative robots motivate the study of motion coordination for groups of agents for example it is envisioned that groups of agents will perform a variety of useful tasks including surveillance exploration and environmental monitoring this paper deals with basic interactions among mobile agents such as move away from the closest other agent or move toward the furthest vertex of your own voronoi polygon these simple interactions amount to distributed dynamical systems because their implementation requires only minimal information about neighboring agents we characterize the close relationship between these distributed dynamical systems and the disk covering and sphere packing cost functions from geometric optimization our main results are as follows i we characterize the smoothness properties of these geometric cost functions ii we show that the interaction laws are variations of the nonsmooth gradient of the cost functions and iii we establish various asymptotic convergence properties of the laws the technical approach relies on concepts from computational geometry nonsmooth analysis and nonsmooth stability theory

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

interaction ruling animal collective behavior depends on topological rather than metric distance evidence from a field study numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals however very little is known about the nature of such interaction so that models and theories mostly rely on aprioristic assumptions by reconstructing the three dimensional positions of individual birds in airborne flocks of a few thousand members we show that the interaction does not depend on the metric distance as most current models and theories assume but rather on the topological distance in fact we discovered that each bird interacts on average with a fixed number of neighbors six to seven rather than with all neighbors within a fixed metric distance we argue that a topological interaction is indispensable to maintain a flock s cohesion against the large density changes caused by external perturbations typically predation we support this hypothesis by numerical simulations showing that a topological interaction grants significantly higher cohesion of the aggregation compared with a standard metric one

diffusive influence systems influence systems seek to model how influence broadly defined spreads across a dynamic network we build a general analytical framework which we then use to prove that while turing complete influence dynamics of the diffusive type is almost surely asymptotically periodic in addition to resolving the dynamics of a widely used family of multiagent systems we introduce a general renormalization method for the bifurcation analysis of multiagent systems

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

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 modified vicsek model for self propelled agents with exponential neighbor weight and restricted visual field abstract large flocks of wild beings can have coordinated motion with neither leading center nor global information the vicsek model and its new versions explained such collective behavior of self propelled agents with the mechanism of un weighted influence of neighbors and global visual field gvf which may not always fit the reality in the present work we take both exponential neighbor weight enw and restricted visual field rvf into account and investigate the combinatory effect of them based on this mechanism in most cases of our simulation stationary direction consensus v a exhibits a maximum or decreases with v f and a minimum convergence time t m i n appears in rvf which demonstrates that gvf is not necessary for coordinated motion while rvf matched enw would be reasonable moreover we simulated various recipes for optimizing v a and t in unfavorable cases and found critical points separating inverse dependent variations of t the present work may be useful in improving the efficiency of direction consensus of large flocks of artificial individuals besides the understanding of biological collective motion in nature

a logical approach to fuzzy truth hedges the starting point of this paper are the works of hajek and vychodil on the axiomatization of truth stressing and depressing hedges as expansions of hajek s bl logic by new unary connectives they showed that their logics are chain complete but standard completeness was only proved for the expansions over godel logic we propose weaker axiomatizations over an arbitrary core fuzzy logic which have two main advantages i they preserve the standard completeness properties of the original logic and ii any subdiagonal resp superdiagonal non decreasing function on 0 1 preserving 0 and 1 is a sound interpretation of the truth stresser resp depresser connectives hence these logics accommodate most of the truth hedge functions used in the literature about of fuzzy logic in a broader sense

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

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

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

geometric integrators for odes geometric integration is the numerical integration of a differential equation while preserving one or more of its geometric properties exactly i e to within round off error many of these geometric properties are of crucial importance in physical applications preservation of energy momentum angular momentum phase space volume symmetries time reversal symmetry symplectic structure and dissipation are examples in this paper we present a survey of geometric numerical integration methods for ordinary differential equations our aim has been to make the review of use for both the novice and the more experienced practitioner interested in the new developments and directions of the past decade to this end the reader who is interested in reading up on detailed technicalities will be provided with numerous signposts to the relevant literature

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

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

gas kinetic derivation of navier stokes like traffic equations macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies therefore this paper shows how to construct a logically consistent fluid dynamic traffic model from basic laws for the acceleration and interaction of vehicles these considerations lead to the gas kinetic traffic equation of paveri fontana its stationary and spatially homogeneous solution implies equilibrium relations for the fundamental diagram the variance density relation and other quantities which are partly difficult to determine empirically paveri fontana s traffic equation allows the derivation of macroscopic moment equations which build a system of non closed equations this system can be closed by the well proved method of chapman and enskog which leads to euler like traffic equations in zeroth order approximation and to navier stokes like traffic equations in first order approximation the latter are finally corrected for the finite space requirements of vehicles it is shown that the resulting model is able to withstand the above mentioned criticism

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