are grades of membership probabilities abstract a small sample is given of the difficulties with present day fuzzy set theory with respect to the requirements of a scientific theory and a summary of some probabilistic interpretations of grades of membership to be found in the literature the tee model for grades of membership is then suggested instead of starting out from mathematical postulates such as the assumed max and min operations for or and and the tee model uses a semantic physio logical psycho logical starting point by investigating the possibilities which a person has for assigning linguistic labels and partial grades of membership in a meaningful way the assignment of partial grades of membership is explained by the assumption that humans have the ability to take errors of observation and intersubject differences into consideration a membership value uex is identified with the subject s estimate of the probability that the label e g tall would be assigned to an object of exact attribute value uex in a natural language situation this situation being a labeling or a yes no one in which at least one of three possible sources of uncertainty is present almost all the accepted formulas of fuzzy set theory as well as the shapes of the grade of membership curves are then derived instead of having to be postulated however the derived formulas for or and and reduce to the max and min operations only in a number of special cases in another special case they reduce to the summation and the zero operation respectively the generally valid formulas are presented

brief paper distributed h consensus filtering in sensor networks with multiple missing measurements the finite horizon case this paper is concerned with a new distributed h consensus filtering problem over a finite horizon for sensor networks with multiple missing measurements the so called h consensus performance requirement is defined to quantify bounded consensus regarding the filtering errors agreements over a finite horizon a set of random variables are utilized to model the probabilistic information missing phenomena occurring in the channels from the system to the sensors a sufficient condition is first established in terms of a set of difference linear matrix inequalities dlmis under which the expected h consensus performance constraint is guaranteed given the measurements and estimates of the system state and its neighbors the filter parameters are then explicitly parameterized by means of the solutions to a certain set of dlmis that can be computed recursively subsequently two kinds of robust distributed h consensus filters are designed for the system with norm bounded uncertainties and polytopic uncertainties finally two numerical simulation examples are used to demonstrate the effectiveness of the proposed distributed filters design scheme

inferences from multinomial data learning about a bag of marbles a new method is proposed for making inferences from multinomial data in cases where there is no prior information a paradigm is the problem of predicting the colour of the next marble to be drawn from a bag whose contents are initially completely unknown in such problems we may be unable to formulate a sample space because we do not know what outcomes are possible this suggests an invariance principle inferences based on observations should not depend on the sample space in which the observations and future events of interest are represented objective bayesian methods do not satisfy this principle this paper describes a statistical model called the imprecise dirichlet model for drawing coherent inferences from multinomial data inferences are expressed in terms of posterior upper and lower probabilities the probabilities are initially vacuous reflecting prior ignorance but they become more precise as the number of observations increases this model does satisfy the invariance principle two sets of data are analysed in detail in the first example one red marble is observed in six drawings from a bag inferences from the imprecise dirichlet model are compared with objective bayesian and frequentist inferences the second example is an analysis of data from medical trials which compared two treatments for cardiorespiratory failure in newborn babies there are two problems to draw conclusions about which treatment is more effective and to decide when the randomized trials should be terminated this example shows how the imprecise dirichlet model can be used to analyse data in the form of a contingency table

a convenient technique for evaluating angular frequency in some nonlinear oscillations in this paper a convenient technique for evaluating angular frequency in some nonlinear oscillations is proposed it is well known that once the restoring force function is given beforehand the period of motion can be determined by an integral the angular frequency has a relation with the period of motion as well as the integral one makes a little modification for the integrand in the integral and a change of variable it is found that if the three divisions are chosen on the integration interval and the trapezoid quadrature rule is used a higher accurate result for the angular frequency can be achieved for the restoring force being an odd function three numerical examples are presented the eardrum type oscillation is studied as well higher accurate results for the angular frequency are obtained in all those examples

distributed average tracking of networked euler lagrange systems under an extended proportional integral pi control scheme a new class of distributed average tracking dat algorithms has been developed for three different kinds of references references with steady states references with bounded derivatives and references with a common derivative the class of dat algorithms are further applied to solve the dat problem for euler lagrange el systems

the concept of grade of membership abstract the concept of grade of membership is bound up with the general problem of fuzzy reasoning in this paper an approach to the latter problem is outlined and the consequences for the notion of grade of membership are described particular care is taken from the beginning to base the theory on concepts which have an immediate practical meaning for this reason assertions rather than sentences are taken as fundamental an assertion being characterized in terms of utility and decision theory fuzzy sentences and degrees of truth and then fuzzy sets and grades of membership are defined in terms of assertions the definitions being illustrated with examples the problem of defining unary and binary operations connectives for assertions sentences and fuzzy sets is discussed finally some other aspects of the logic of assertions are outlined and the extent to which the concepts of fuzzy set and grade of membership can be incorporated into the theory is discussed

comments on the method of harmonic balance the advantages and limitations of the harmonic balance or describing function approximation scheme for solving nonlinear ordinary differential equations of oscillatory motion are discussed advantages include appicability to equations of any order and with large degrees of nonlinearity ease of determining limit cycle behavior and its stability and overall speed and efficiency the limitation rules are essentially those described by mickens 1983 it is pointed out that perturbation procedures provide better results when the degree of nonlinearity is small

brief paper leader following consensus of second order agents with multiple time varying delays in this paper a leader following consensus problem of second order multi agent systems with fixed and switching topologies as well as non uniform time varying delays is considered for the case of fixed topology a necessary and sufficient condition is obtained for the case of switching topology a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large we not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate an example with simulation is presented to illustrate the theoretical results

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

supremum preserving upper probabilities abstract we study the relation between possibility measures and the theory of imprecise probabilities and argue that possibility measures have an important part in this theory it is shown that a possibility measure is a coherent upper probability if and only if it is normal a detailed comparison is given between the possibilistic and natural extension of an upper probability both in the general case and for upper probabilities defined on a class of nested sets we prove in particular that a possibility measure is the restriction to events of the natural extension of a special kind of upper probability defined on a class of nested sets we show that possibilistic extension can be interpreted in terms of natural extension we also prove that when either the upper or the lower cumulative distribution function of a random quantity is specified possibility measures very naturally emerge as the corresponding natural extensions next we go from upper probabilities to upper previsions we show that if a coherent upper prevision defined on the convex cone of all non negative gambles is supremum preserving then it must take the form of a shilkret integral associated with a possibility measure but at the same time we show that such a supremum preserving upper prevision is never coherent unless it is the vacuous upper prevision with respect to a non empty subset of the universe of discourse

a framework for linguistic modelling a new framework for linguistic reasoning is proposed based on a random set model of the degree of appropriateness of a label labels are assumed to be chosen from a finite predefined set of labels and the set of appropriate labels for a value is defined as a random set valued function from a population of individuals into the set of subsets of labels appropriateness degrees are then evaluated relative to the distribution on this random set where the appropriateness degree of a label corresponds to the probability that it is contained in the set of appropriate labels this interpretation is referred to as label semantics a natural calculus for appropriateness degrees is described which is weakly functional while taking into account the logical structure of expressions given this framework it is shown that a bayesian approach can be adopted in order to infer probability distributions on the underlying variable given constraints both in the form of linguistic expressions and mass assignments in addition two conditional measures are introduced for evaluating the appropriateness of a linguistic expression given other linguistic information

a behavioral model for linguistic uncertainty abstract the paper discusses the problem of modelling linguistic uncertainty which is the uncertainty produced by statements in natural language for example the vague statement mary is young produces uncertainty about mary s age we concentrate on simple affirmative statements of the type subject is predicate where the predicate satisfies a special condition called monotonicity for this case we model linguistic uncertainty in terms of upper probabilities which are given a behavioural interpretation as betting rates possibility measures and probability measures are special types of upper probability measure we evaluate zadeh s suggestion that possibility measures should be used to model linguistic uncertainty and the bayesian claim that probability measures should be used our main conclusion is that when the predicate is monotonic possibility measures are appropriate models for linguistic uncertainty we also discuss several assessment strategies for constructing a numerical model

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

consensusability of multi agent systems with time varying communication delay abstract this paper studies the consensusability problem of continuous time multi agent systems with time varying communication delay in undirected network we design a consensus protocol based on the low gain solution of a parametric algebraic riccati equation are and not use the precise information of the amount of time varying delay by studying the joint effect of agent dynamic and network topology sufficient conditions are given for consensus when all poles of the system matrix are on the closed left half plane in case of non zero poles on the imaginary axis maximal admissible upper bound of the time varying delay is given in terms of both the agent dynamic and network topology otherwise consensus can be achieved for the time varying delay with arbitrarily large upper bound finally simulation results are presented to demonstrate the effectiveness of the theoretical results

decentralized stabilizability of multi agent systems under fixed and switching topologies abstract the paper studies decentralized stabilizability for multi agent systems with general linear dynamics the stabilizability problem is formulated in a way that the protocol performance can be evaluated by means of the stabilizability region and the feedback gain for fixed topology it is proved that the system is stabilizable if and only if external control inputs are exerted on some indicated agents the result is further shown to be a prerequisite for subsequent design of the corresponding decentralized external self feedback control which is also necessary and sufficient based on this two methods are presented to find the agents under which stabilizability can be reached and the region of stabilizability is given to evaluate the protocol performance for switching interaction topology it is shown that the system is stabilizable even if each of its subsystems is not finally the results are employed to cope with the decentralized set point formation control problem for which some necessary and or sufficient conditions are developed numerical simulations are presented to demonstrate the effectiveness of the proposed results

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

consensus problem of second order multi agent systems with communication delay and input delay in this paper asynchronously coupled algorithm is used to solve the consensus problem of second order multi agent systems with both communication delay and input delay by constructing lyapunov krasovskii functional sufficient consensus conditions are obtained for second order systems under invariant input delays accompanied with time invariant and time varying communication delays respectively the conditions are all in the forms of linear matrix inequality lmi simulation illustrates the correctness of the results

on the determination of approximate periodic solutions of some non linear ode abstract we propose a numerical symbolic method for the approximation of periodic solutions of a type of non linear ode the efficiency of our method is contrasted with the harmonic balance method and with another one which combines the differential transformation method with pade approximants on a non trivial example the relativistic oscillator it is shown that our method is computationally more reliable

avoiding congestion in cluster consensus of the second order nonlinear multiagent systems in order to avoid congestion in the second order nonlinear leader following multiagent systems over capacity limited paths an approach called cluster lag consensus is proposed which means that the agents in different clusters will pass through the same positions with the same velocities but lag behind the leader at different times lyapunov functionals and matrix theory are applied to analyze such cluster lag consensus it is shown that when the graphic roots of clusters are influenced by the leader and the intracoupling of cluster agents is larger than a threshold the cluster lag consensus can be achieved furthermore the cluster lag consensus with a time varying communication topology is investigated finally an illustrative example is presented to demonstrate the effectiveness of the theoretical results in particular when the physical sizes of the agents are taken into consideration it is shown that with a rearrangement and a position transformation the multiagent system will reach cluster lag consensus in the new coordinate system this means that all agents in the same cluster will reach consensus on the velocity but their positions may be different and yet their relative positions converge to a constant asymptotically

interpretative versus prescriptive fuzzy set theory both traditional fuzzy set theory and the theory of subjective probabilities postulate their formulas the former because it does not accept a probabilistic interpretation of grades of membership the latter because it makes no connection between subjective probabilities and relative frequencies the interpretational theory of the tee model ascribes a well defined meaning to a membership value spl mu sub spl lambda in terms of probabilities which are limits of frequencies spl mu sub spl lambda is interpreted as the estimate by the subject of the probability that a given object would be assigned the label x in an everyday situation of uncertainty in contrast to the max min formulas used in many applications of fuzzy sets the postulated summation to 1 formula of all fuzzy clustering algorithms follows from the interpretative tee model this agrees with the author s view that fuzzy set theory should be defined as a theory which allows partial membership values of an object in a class or cluster not as a theory which uses specific mathematical operators the operators must be derived from the well defined interpretation of partial membership values

h consensus of second order multi agent systems with asymmetric delays abstract this paper is concerned with the problem of consensus in the h sense for second order continuous time multi agent systems with multiple asymmetric time varying delays by using a model transformation approach and matrix theory we establish several conditions in terms of linear matrix inequalities such that consensus of multi agent systems can be achieved in the h sense the feasibility of the consensus conditions is also analyzed as an application we consider the case of intermittent measurement between agents numerical examples are presented to illustrate the theoretical results which can be applied to the case of negative information weights

solutions of a quadratic nonlinear oscillator iteration procedure a modified iteration procedure is applied to a quadratic nonlinear oscillator qno when the solutions of the two auxiliary equations are available we obtain the first and second analytical approximate solutions to the qno our second approximation result significantly improves on the accuracy of the approximate solution obtained by using the first order harmonic balance method

a successive integration technique for the solution of the duffing oscillator equation with damping and excitation abstract in this paper a successive integration technique is suggested for solving the duffing oscillator equation with damping and excitation in the technique one performs integrations from some initial values over a wider range some of them may even be divergent however some of them will give a convergent result such that the periodic condition of motion is satisfied in fact the convergent result represents a stable periodic solution for the motion if a convergent result or a stable periodic solution is obtained the stability test is passed a harmonic balance method in conjunction with the successive integration technique abbreviated as hbmsit is also suggested in the method the initial values are obtained from the harmonic balance method therefore the hbmsit belongs to the successive integration techniques many examples with calculated results are presented

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

iterative solution of some nonlinear differential equations we propose an iterative method to solve some non linear ordinary differential equations comparing on the mathieu van der pol and hill equation of fourth order we see that this method is much more efficient than the well known methods by lyapunov or picard

the efficacy of fuzzy representations of uncertainty advocates of the theory of fuzzy sets as a system for representing uncertainty have based their case on five basic arguments these are 1 the reality hypothesis which holds that imprecision is an inherent property of the world external to an observer 2 the subjectivity hypothesis which holds that probability is an exclusively objective measure of uncertainty and that therefore subjective uncertainty can only be represented with fuzzy sets 3 the behaviorist hypothesis which claims that uncertainty systems should emulate rather than prescribe human behavior in the face of uncertainty 4 the probability as fiction hypothesis which claims that probability does not comprise a field of study in its own right and 5 the superset hypothesis which holds that fuzzy set theory includes probability as a special case and thus provides a richer uncertainty modeling environment we discuss and criticize all five we then criticize the argument that fuzziness represents a type of uncertainty distinct from probability and also the inordinate complexity of fuzzy methods we present a method for assessing the efficacy of fuzzy representations of uncertainty and apply this method in three examples

vagueness and bayesian probability this paper is a response to michael laviolette and john w seaman jr s ibid vol 2 no 1 p 4 1994 position paper the efficacy of fuzzy representations of uncertainty which criticizes fuzzy representations of uncertainty and suggests that bayesian probability can do better the commenter argues that the author s make some misleading comments about bayesian probability and he briefly discusses the problem of giving a satisfactory interpretation of membership functions

l 1 group consensus of multi agent systems with stochastic inputs under directed interaction topology we address l 1 group consensus problems of networked multi agent systems with fixed directed information exchange in this article a discrete time protocol is designed to solve the l 1 group consensus problems via general stochastic inputs under some mild assumptions we derive sufficient conditions to guarantee the l 1 group consensus based on algebraic graph theory and ergodicity theory for finite markov chains moreover the boundedness of the expected infinite sum of the inputs ensures the boundedness of the expected trajectory numerical simulations instantiating the inputs as varied independent and identically distributed random processes as well as autoregressive processes are presented to demonstrate the effectiveness of our theoretical results

several numerical solution techniques for nonlinear eardrum type oscillations three numerical solution techniques for nonlinear eardrum type oscillations with an even function in the restoring force are studied the first suggested technique is named the target function technique in the technique the second zeros of the target function is the circular frequency of motion the second suggested technique is named the multiple parameter technique and the involved parameters are evaluated from the governing equation the initial conditions and properties of motion the third suggested technique is named the direct integration technique all techniques depend on the computer computation significantly and provide very accurate numerical results finally numerical examples are given

fuzzy sets spl minus a convenient fiction for modeling vagueness and possibility this paper is a reply to laviolette and seaman s critical discussion of fuzzy set theory rather than questioning the interest of the bayesian approach to uncertainty some reasons why bayesian find the idea of a fuzzy set not palatable are laid bare some links between fuzzy sets and probability that laviolette and seaman seem not to be aware of are pointed out these links suggest that contrary to the claim sometimes found in the literature probability theory is not a special case of fuzzy set theory the major objection to laviolette and seaman is that they found their critique on as very limited view of fuzzy sets including debatable papers while they fail to account for significant works pertaining to axiomatic derivation of fuzzy set connectives possibility theory fuzzy random variables among others

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

an artificial parameter decomposition method for nonlinear oscillators applications to oscillators with odd nonlinearities abstract a method for obtaining series solutions of nonlinear second order ordinary differential equations based on the introduction of an artificial parameter is presented and shown to be identical to the well known adomian s decomposition technique the method is formulated in both integral and differential forms for the determination of the limit cycle of oscillators with odd nonlinearities two differential forms and one integral form of the artificial parameter method are presented these versions are based on introducing a linear stiffness term with an unknown frequency and the use of either the original independent variable or a new independent variable that depends linearly on the unknown frequency of the oscillator the three formulations provide identical results and their application to eight oscillators with odd nonlinearities shows that the artificial parameter technique presented in this paper predicts the same frequency of oscillation as the harmonic balance and iterative techniques as well as modified linstedt poincare methods however the method presented here is based on the introduction of an artificial parameter and does not require the presence of small perturbation parameters in the ordinary differential equation it is also shown that two and three level iterative methods yield the same frequency of oscillation as the artificial parameter technique presented in this paper provided that the initial iterate of the former coincides with the leading order solution of the latter and only one iteration of iterative techniques and only the second approximation of the artificial parameter method are determined

a modified mickens iteration procedure for nonlinear oscillators based on the mickens procedure a new iteration scheme is proposed for nonlinear oscillators different from the existing mickens procedures in the proposed procedure the algebraic equation governing the frequency of oscillation deduced at each iteration stage is always linear taking the duffing equation as an illustrative example excellent approximations can be easily obtained furthermore the proposed procedure is extended to obtain the limit cycle of the van der pol equation additionally a computational disadvantage of the mickens procedure is eliminated

a semantics for possibility theory based on likelihoods abstract in this paper a semantic basis for possibility theory based on likelihood functions is presented in some cases possibilities have been considered as approximations of shafer plausibility measures this approximation exchanges exactness of plausibility values for the simplicity of use of possibility values in this paper a different direction is followed possibility measures are considered as the supremum of a family of likelihood functions this is an exact interpretation not an approximation the minimum rule to combine possibility distributions is justified in this framework under general conditions conditions under which other rules can be applied are also studied

fuzzy logic based generalized decision theory with imperfect information the existing decision models have been successfully applied to solving many decision problems in management business economics and other fields but nowadays arises a need to develop more realistic decision models the main drawback of the existing utility theories starting from von neumann moregnstern expected utility to the advanced non expected models is that they are designed for laboratory examples with simple well defined gambles which do not adequately enough reflect real decision situations in real life decision making problems preferences are vague and decision relevant information is imperfect as described in natural language nl vagueness of preferences and imperfect decision relevant information require using suitable utility model which would be fundamentally different to the existing precise utility models precise utility models cannot reflect vagueness of preferences vagueness of objective conditions and outcomes imprecise beliefs etc the time has come for a new generation of decision theories in this study we propose a decision theory which is capable to deal with vague preferences and imperfect information the theory discussed here is based on a fuzzy valued non expected utility model representing linguistic preference relations and imprecise beliefs

a generalized iteration procedure for calculating approximations to periodic solutions of truly nonlinear oscillators abstract an extended iteration method for calculating the periodic solutions of nonlinear oscillator equations is given the procedure is illustrated by applying it to two truly nonlinear oscillator differential equations

analytic upper and lower bounds for the period of nonlinear oscillators we show that analytic expressions for the frequency of second order nonlinear oscillations can be obtained from dual variational principles at each amplitude two analytic expressions can be constructed which constitute upper and lower bounds to the exact value of the frequency the results are accurate at small and large amplitude and compare well with the perturbative approach

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

on the variational iteration method and other iterative techniques for nonlinear differential equations abstract a variety of iterative methods for the solution of initial and or boundary value problems in ordinary and partial differential equations is presented these iterative procedures provide the solution or an approximation to it as a sequence of iterates for initial value problems it is shown that these iterative procedures can be written in either an integral or differential form the integral form is governed by a volterra integral equation whereas the differential one can be obtained from the volterra representation by simply differentiation it is also shown that integration by parts variation of parameters adjoint operators green s functions and the method of weighted residuals provide the same volterra integral equation and that this equation in turn can be written as that of the variational iteration method it is therefore shown that the variational iteration method is nothing else by the picard lindelof theory for initial value problems in ordinary differential equations and banach s fixed point theory for initial value problems in partial differential equations and the convergence of these iterative procedures is ensured provided that the resulting mapping is lipschitz continuous and contractive it is also shown that some of the iterative methods for initial value problems presented here are special cases of the bellman kalaba quasilinearization technique provided that the nonlinearities are differentiable with respect to the dependent variable and its derivatives but such a condition is not required by the techniques presented in this paper for boundary value problems it is shown that one may use the iterative procedures developed for initial value problems but the resulting iterates may not satisfy the boundary conditions and two new iterative methods governed by fredholm integral equations are proposed it is shown that the resulting iterates satisfy the boundary conditions if the first one does so the iterative integral formulation presented here is applied to ten nonlinear oscillators with odd nonlinearities and it is shown that its results coincide with those of differential two and three level iterative techniques harmonic balance procedures and standard and modified linstedt poincare techniques the method is also applied to two boundary value problems

constrained optimization problems under uncertainty with coherent lower previsions we investigate a constrained optimization problem with uncertainty about constraint parameters our aim is to reformulate it as a constrained optimization problem without uncertainty this is done by recasting the original problem as a decision problem under uncertainty we give results for a number of different types of uncertainty models linear and vacuous previsions and possibility distributions and for two common but different optimality criteria for such decision problems maximinity and maximality we compare our approach with other approaches that have appeared in the literature

on the alleged superiority of probabilistic representation of uncertainty the author identifies some points of his agreement or disagreement with the position taken by laviolette and seaman 1994 in their debate paper in particular the author argues that some statements regarding the superiority of probabilistic representation of uncertainty which are made by laviolette and seaman in their paper are untenable

investigation of the properties of the period for the nonlinear oscillator x 1 x 2 x 0 abstract the mathematical properties of a nonlinear oscillator having the square of the angular frequency depend quadratically on the velocity is presented the major conclusion is that the exact period t a is well defined for all values of the amplitude where the initial conditions are taken to be x 0 a and x 0 0 an approximate expression is derived for t a

on modeling of linguistic information using random sets this paper discusses the formal connection between possibility distributions zadeh 21 and the theory of random sets via choquet s theorem based upon these relationships it is suggested that plausible inferences and modeling of common sense can be derived from the statistics of random sets the analysis of subjectivity in meaning representation of natural languages can be carried out by taking account of covariates of individuals as in the statistical analysis of survival data

solutions of nonlinear oscillators with fractional powers by an iteration procedure a modified iteration procedure is applied to nonlinear oscillations with fractional powers with the procedure the excellent approximate frequencies and the corresponding periodic solutions can be easily obtained

a classical iteration procedure valid for certain strongly nonlinear oscillators a classical iteration procedure is applied to nonlinear oscillations of conservative single degree of freedom systems with odd nonlinearity with the procedure the analytical approximate frequency and the corresponding periodic solution valid for small as well as large amplitudes of oscillation can be obtained two examples are given to illustrate the accuracy and effectiveness of the method another advantage of this classical iteration approach is that it also works if the linear part of restoring force is zero

synchronization of complex dynamical networks with switching topology a switched system point of view in this paper we study the synchronization problem for complex dynamical networks with switching topology from a switched system point of view the synchronization problem is transformed into the stability problem for time varying switched systems we address two basic problems synchronization under arbitrary switching topology and synchronization via design of switching within a pre given collection of topologies when synchronization cannot be achieved by using any topology alone in this collection for the both problems we first establish synchronization criteria for general connection topology then under the condition of simultaneous triangularization of the connection matrices a common lyapunov function for the first problem and a single lyapunov and multiple lyapunov functions for the second problem are systematically constructed respectively by those of several lower dimensional dynamic systems in order to achieve synchronization using multiple lyapunov functions a stability condition and switching law design method for time varying switched systems are also presented which avoid the usual non increasing condition

solutions of the duffing harmonic oscillator by an iteration procedure a modified iteration procedure is applied to the duffing harmonic oscillator with the procedure the excellent approximate frequencies and the corresponding periodic solutions can be easily obtained

on the picard lindelof method for nonlinear second order differential equations we consider a second order nonlinear ordinary differential equation which satisfies a lipschitz continuity condition and show that the method of variation of parameters allows us to write the solution as a volterra integral equation that includes the initial values of the solution and its first order derivative we also show that this integral formulation can be written as an iterative method which converges uniformly to the unique solution of the problem by making use of an integral identity the initial conditions can be eliminated from the integral equation and a new integral formulation that depends on the second order derivative of the solution is obtained it is shown that this integral formulation is exactly the same as that of the variational iteration method but does not require a variational principle neither does it require constrained variations for nonlinear terms we also show that the two integral formulations can be written in differential form and correspond to a two level iterative method by writing the second order ordinary differential equation as a two equation system of first order ordinary differential equations three different iterative procedures are developed but only one of them coincides with that derived from the two integral equations for the solution

the three semantics of fuzzy sets abstract three main semantics for membership functions seem to exist in the literature similarity preference and uncertainty each semantics underlies a particular class of applications similarity notions are exploited in clustering analysis and fuzzy controllers uncertainty is captured by fuzzy sets in the framework of possibility theory the membership function of a fuzzy set is also sometimes a kind of utility function that represents flexible constraints in decision problems this paper advocates the claim that progress in operational semantics of membership functions presupposes that these distinct semantics be acknowledged and related to more basic measurement issues in terms of distance cost and frequency on which scientific traditions exist

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

discussion further thoughts on possibilistic previsions a rejoinder this is a rejoinder to the comments moral scozzafava utkin zadeh fuzzy sets and systems 2005 by a number of authors on my paper about possibilistic previsions

a behavioural model for vague probability assessments i present an hierarchical uncertainty model that is able to represent vague probability assessments and to make inferences based on them this model can be given an interpretation in terms of the behaviour of a modeller in the face of uncertainty and is based on walley s theory of imprecise probabilities it is formally closely related to zadeh s fuzzy probabilities but it has a different interpretation and a different calculus through rationality coherence arguments the hierarchical model is shown to lead to an imprecise first order uncertainty model that can be used in decision making and as a prior in statistical reasoning

measures of uncertainty in expert systems abstract this paper compares four measures that have been advocated as models for uncertainty in expert systems the measures are additive probabilities used in the bayesian theory coherent lower or upper previsions belief functions used in the dempster shafer theory and possibility measures fuzzy logic special emphasis is given to the theory of coherent lower previsions in which upper and lower probabilities expectations and conditional probabilities are constructed from initial assessments through a technique of natural extension mathematically all the measures can be regarded as types of coherent lower or upper previsions and this perspective gives some insight into the properties of belief functions and possibility measures the measures are evaluated according to six criteria clarity of interpretation ability to model partial information and imprecise assessments especially judgements expressed in natural language rules for combining and updating uncertainty and their justification consistency of models and inferences feasibility of assessment and feasibility of computations each of the four measures seems to be useful in special kinds of problems but only lower and upper previsions appear to be sufficiently general to model the most common types of uncertainty

on linstedt poincare techniques for the quintic duffing equation abstract an artificial parameter method for the quintic duffing equation is presented the method is based on the introduction of a linear stiffness term and a new dependent variable both of which are proportional to the unknown frequency of oscillation the introduction of an artificial parameter and the expansion of both the solution and the unknown frequency of oscillation in series of the artificial parameter and results in linear ordinary differential equations at each order in the parameter by imposing the nonsecularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation the method does not require that a small parameter be present in the governing equation and its results are compared with those of linstedt poincare modified linstedt poincare harmonic balance and galerkin techniques it is shown that these four techniques predict the same first order approximation to the frequency of oscillation as the artificial parameter method presented in this paper and the latter introduces higher order corrections at second order whereas similar corrections are introduced by the linstedt poincare and modified linstedt poincare methods at orders equal to and higher than three

a split frequency harmonic balance method for nonlinear oscillators with multi harmonic forcing abstract a new harmonic balance method hbm is presented for accurately computing the periodic responses of a nonlinear sdof oscillator with multi harmonic forcing and non expansible nonlinearities the presence of multi harmonic forcing requires a large number of solution harmonics with a substantial increase in computational demand for either the conventional or the incremental hbm in this method the oscillator equation error is first defined in terms of two functions originally proposed for obtaining free vibration periods in r e mickens iteration procedure for determining approximate solutions to nonlinear oscillator equations journal of sound and vibration 116 1987 185 187 and more recently r e mickens a generalised iteration procedure for calculating approximations to periodic solutions of truly nonlinear oscillations journal of sound and vibration 287 2005 1045 1051 a fourier series solution is assumed in which the total number of harmonics is fixed by the chosen discrete time interval this series is split into two partial sums nominally associated with either low frequency or high frequency harmonics by exploiting a convergence property of the equation error functions the total solution is obtained in a new iterative scheme in which the low frequency components are computed via a conventional hbm using a small number of algebraic equations whereas the high frequency components are obtained in a separate step by updating by gradually increasing the number of harmonics in the low frequency group the equation error can be progressively reduced efficient use is made of fft based algebraic equation generation which allows an important class of non expansible nonlinearities to be handled the proposed method is tested on a duffing type oscillator and an oscillator with a non expansible 7th power stiffness term where in both cases up to 24 component multi harmonic forcing is applied as a comparison a conventional hbm is also used on the duffing model in which the algebraic equations are generated in symbolic form to totally avoid errors from entering the formulation through complicated expansion of the cubic stiffness term as in i senjanovic harmonic analysis of nonlinear oscillations of cubic dynamical systems journal of ship research 38 3 1994 225 238 and in a raghothama s narayanan periodic response and chaos in nonlinear systems with parametric excitation and time delay nonlinear dynamics 27 2002 341 365 the paper shows that in obtaining period 1 solutions the computational accuracy and efficiency of the proposed method is very good

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