control problems in fuzzy systems abstract this paper deals with some problems of the control of fuzzy systems described by means of a relational equation of the type x 1 u x r the basic aspects such as mutual identification and control stabilization control control with constraints generation of control rules of a fuzzy logic controller important from the theoretical and applicational point of view are discussed and illustrated by means of numerical examples

the reduction of binary fuzzy relations and its applications this paper introduces the concept of t reduction of binary fuzzy relations and establishes its properties it presents an approach to providing the one valued restoration of any boundary transitive and t asymmetric binary fuzzy relation by its t reduction a theoretical basis for this approach is established showing that t reduction is the smallest fuzzy relation whose t transitive closure coincides with the given binary fuzzy relation and where an nxn fuzzy relation on a finite universe with cardinality n can be represented by n 1 values this approach opens up an original way for constructing the membership functions of certain binary fuzzy relations important examples for the application of this concept are given

on identification of multidimensional fuzzy systems abstract the paper is concerned with identification of multidimensional fuzzy systems the authors introduce the fuzzy implication operator which ensures in systems with normal fuzzy sets as inputs the minimal value of the average relative hamming distance between calculated and actual fuzzy output a corresponding theorem is proved the approach is illustrated by a catalyst properties catalytic activity model

fuzzy n cell numbers and the differential of fuzzy n cell number value mappings in this paper we give the definition of a special kind of n dimension fuzzy numbers fuzzy n cell numbers discuss their operations and representation theorems define a complete metric on the fuzzy n cell number space and prove that the metric is equivalent to the supremum metric derived by the hausdorff metric between the level sets of the n dimension fuzzy numbers and obtain an embedding theorem of the fuzzy n cell number space isometrically embeds it into a concrete banach space we also consider the differential of the fuzzy mappings from an interval into the fuzzy n cell number space by using the embedding theorem

fuzzy learning control for a flexible link robot there are two main drawbacks in fuzzy control 1 the design of fuzzy controllers is usually performed in an ad hoc manner where it is often difficult to choose some of the controller parameters and 2 the fuzzy controller constructed for the nominal plant may later perform inadequately if significant and unpredictable plant parameter variations occur in this paper we illustrate these two problems on a two link flexible robot testbed by 1 developing implementing and evaluating a fuzzy controller for the robotic mechanism and 2 illustrating that payload variations can have negative effects on the performance of a well designed fuzzy control system next we show how to develop and implement a fuzzy model reference learning controller for the flexible robot and illustrate that it can automatically synthesize a rule base for a fuzzy controller that will achieve comparable performance to the case where it was manually constructed and automatically tune the fuzzy controller so that it can adapt to variations in the payload

a fuzzy dynamic model based state estimator systems containing uncertainty are traditionally analyzed with probabilistic methods however for non linear non gaussian systems solutions can sometimes be very difficult to obtain the focus of this work is to determine if in such cases fuzzy dynamic system models may provide an alternative approach that more easily leads us to a good solution in this paper we present a fuzzy estimator whose system model is a fuzzy dynamic system we show that for the linear gaussian case the fuzzy estimator produces the same result as the kalman filter more importantly we show that the fuzzy estimator can succeed for some non gaussian nonlinear systems finally we illustrate the application of the fuzzy estimator on a non linear non gaussian time varying rocket launch problem where we show that it performs better than the extended kalman filter from a broad perspective this paper essentially shows how to build on zadeh s seminal ideas in fuzzy sets logic and systems and use kalman s seminal ideas on optimal estimators to construct a novel fuzzy estimator for non linear estimation problems while this seems to reconcile some of the fundamental ideas of zadeh and kalman it is unfortunate that the fuzzy estimator can be very computationally complex to implement for practical applications

numerical and applicational aspects of fuzzy relational equations we discuss numerical methods leading to a resolution of fuzzy relational equations which create a formal description of ill defined systems an applicability of the numerical approach is shown in solving some problems in fuzzy systems such as identification and control an idea of fuzzy discretization fuzzy chopping as a meaningful tool for handling various problems is also investigated

transitivity of generalized fuzzy matrices generalized fuzzy matrices are considered as matrices over a special type of semiring which is called a path algebra transitivity of generalized fuzzy matrices is defined and some properties of transitivity are shown especially properties of the composition of transitive fuzzy matrices representing transitive fuzzy relations are examined by introducing a third operation on the semiring with two operations the transitivity is closely related to metrics distances ultrametrics and so on

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

random walk on random infinite looptrees looptrees have recently arisen in the study of critical percolation on the uniform infinite planar triangulation here we consider random infinite looptrees defined as the local limit of the looptree associated with a critical galton watson tree conditioned to be large we study simple random walk on these infinite looptrees by means of providing estimates on volume and resistance growth we prove that if the offspring distribution of the galton watson process is in the domain of attraction of a stable distribution with index alpha in 1 2 then the spectral dimension of the looptree is 2 alpha alpha 1

fuzzy relational equations with generalized connectives and their applications the idea of fuzzy relational equation with generalized connectives is introduced and algorithms of resolution of this class equations are presented in details it is clearly shown that some types of well known fuzzy relational equations sup min inf max can be treated as special cases of a wise class of equations under discussion applicational aspects are carefully investigated presenting the advantages of the proposed approach

adaptive output feedback control for nonlinear time delay systems by fuzzy approximation approach in this paper the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems with unknown time delay functions is investigated dynamic surface control technique is used to avoid the problem of explosion of complexity which is caused by repeated differentiation of certain nonlinear functions in the backstepping design process in addition the fuzzy logic systems are utilized to approximate the unknown and desired control input signals directly instead of the unknown nonlinear functions the designed controller can guarantee all the signals in the closed loop system to be semiglobally uniformly ultimately bounded and the tracking error to converge to a small neighborhood of the origin simulations results are provided to demonstrate the effectiveness of the proposed methods

communication delay distribution dependent networked control for a class of t s fuzzy systems this paper investigates a robust networked control for a class of takagi sugeno t s fuzzy systems the controller design specifically takes probabilistic interval distribution of the communication delay into account a general framework of networked control is first proposed the two main features are 1 the zero order hold can choose the latest control input signal when the packets received are out of order and 2 as the result of 1 the models of the all kinds of uncertainties in networked signal transfer including network induced delay and data packet dropout are under a unified framework next if the probability distribution of communication delay is known or specified in a design process sufficient stability conditions for networked t s fuzzy systems are derived which are based on the lyapunov theory following this a stabilizing controller design method is developed which shows that the solvability of the design depends not only on the upper and lower bounds of the delay but on its probability distribution as well finally a numerical example is used to show the application of the theoretical results obtained in this paper

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

an approach to systematic design of the fuzzy control system abstract this paper presents a new design method of fuzzy control system fcs the concept from the sliding mode control is adopted to construct fuzzy control scheme if the original control rules are inappropriate the adaptive mechanism will modify these rules according to the proposed algorithms in particular the structure of sliding surface provides a reasonable estimation to the universes of discourse on which the fuzzy control rules are based finally an inverted pendulum system is used to demonstrate the availability of the proposed approaches

the multiplicative coalescent inhomogeneous continuum random trees and new universality classes for critical random graphs one major open conjecture in the area of critical random graphs formulated by statistical physicists and supported by a large amount of numerical evidence over the last decade braunstein et al in phys rev lett 91 16 168701 2003 wu et al in phys rev lett 96 14 148702 2006 braunstein et al int j bifurc chaos 17 07 2215 2255 2007 chen et al in phys rev lett 96 6 068702 2006 is as follows for a wide array of random graph models with degree exponent tau in 3 4 distances between typical points both within maximal components in the critical regime as well as on the minimal spanning tree on the giant component in the supercritical regime scale like n tau 3 tau 1 in this paper we study the metric space structure of maximal components of the multiplicative coalescent in the regime where the sizes converge to excursions of levy processes without replacement aldous and limic electron in j probab 3 3 59 1998 yielding a completely new class of limiting random metric spaces a by product of the analysis yields the continuum scaling limit of one fundamental class of random graph models with degree exponent tau in 3 4 where edges are rescaled by n tau 3 tau 1 yielding the first rigorous proof of the above conjecture the limits in this case are compact tree like random fractals with a dense collection of hubs infinite degree vertices a finite number of which are identified with leaves to form shortcuts in a special case we show that the minkowski dimension of the limiting spaces equal tau 2 tau 3 a s in stark contrast to the erd s renyi scaling limit whose minkowski dimension is 2 a s it is generally believed that dynamic versions of a number of fundamental random graph models as one moves from the barely subcritical to the critical regime can be approximated by the multiplicative coalescent in work in progress the general theory developed in this paper is used to prove analogous limit results for other random graph models with degree exponent tau in 3 4 our proof makes crucial use of inhomogeneous continuum random trees icrt which have previously arisen in the study of the entrance boundary of the additive coalescent we show that tilted versions of the same objects using the associated mass measure describe connectivity properties of the multiplicative coalescent since convergence of height processes of corresponding approximating mathbf p trees is not known we use general methodology in athreya et al 2014 and develop novel techniques relying on first showing convergence in the gromov weak topology and then extending this to gromov hausdorff prokhorov convergence by proving a global lower mass bound

most trees are short and fat this work proves new probability bounds relating to the height width and size of galton watson trees for example if t is any galton watson tree and h w and t are the height width and size of t respectively then h w has sub exponential tails and h t 1 2 has sub gaussian tails although our methods apply without any assumptions on the offspring distribution when information is provided about the distribution the method can be adapted accordingly and always seems to yield tight bounds

new results on h_ infty tracking control based on the t s fuzzy model for sampled data networked control system this study deals with the problem of h infty tracking control for a sampled data networked control system based on a takagi sugeno fuzzy model an error model is established by combining the input delay and parallel distributed compensation techniques so as to transform the sampling period of a sampler a signal transmission delay and data packet dropouts to the refreshing interval of a zero order hold the method introduces a new augmented lyapunov krasovskii functional to derive a sufficient condition to ensure a prescribed h infty tracking performance with less conservativeness than others a fuzzy controller can easily be designed using the condition a numerical example demonstrates the validity of the method

fuzzy controller design for nonlinear impulsive fuzzy systems with time delay the stabilization problem is investigated for continuous time takagi sugeno t s fuzzy systems with time delay and impulsive effects in this paper some delay independent and delay dependent stabilization approaches are developed for both state feedback and observer based feedback cases which are based on the lyapunov krasovskii functional approach and a parallel distributed compensation scheme the time delay is dealt by lyapunov theory allied with the halanay lemma the restriction on the interval between each impulsive instant and output sampled instant needs not be equal to or less than a constant scalar but it only requires an inequality satisfaction when the impulsive effects vanish the results can be extended to the corresponding sufficient conditions for the cases of a nonlinear continuous time delay system with a state feedback and observer based sampled output feedback finally some examples are given to demonstrate the effectiveness of the proposed method

fuzzy affine model based memory filter design of nonlinear systems with time varying delay this paper studies the piecewise affine memory mathscr h infty filtering problem for nonlinear systems with time varying delay in a delay dependent framework the nonlinear plant is characterized by a continuous time takagi sugeno fuzzy affine model with parametric uncertainties the purpose is to develop a new approach for filter synthesis procedure with less conservatism specifically by constructing a novel lyapunov krasovskii functional together with a wirtinger based integral inequality reciprocally convex inequality and s procedure an improved criterion is first attained for analyzing the mathscr h infty performance of the filtering error system and then via some linearization techniques the piecewise affine memory filter synthesis is carried out it is shown that the existence of desired filter gains can be explicitly determined by the solution of a convex optimization problem finally simulation studies are presented to reveal the effectiveness and less conservatism of the developed approaches it is anticipated that the proposed scheme can be further extended to the analysis and synthesis of continuous time fuzzy affine dynamic systems with integrated communication delays in the networked circumstance

knowledge based fuzzy control of systems a method of fuzzy control of systems based on a concept of human thinking is investigated the fuzzy controller consists of a knowledge base containing a number of time responses of a process the elements of this base are cells in which an input and a corresponding output of a system are stored the cells are organized according to different types of relations the result is a knowledge structure which contains a model of the process to be controlled the following phases are distinguished the learning phase during which the relation between the imput and the output of a system is learned and the knowledge structure is constructed and a phase in which the knowledge structure is applied to control the process the method also provides an indication of the reliability of the control action

scaling limits of markov branching trees with applications to galton watson and random unordered trees we consider a family of random trees satisfying a markov branching property roughly this property says that the subtrees above some given height are independent with a law that depends only on their total size the latter being either the number of leaves or vertices such families are parameterized by sequences of distributions on partitions of the integers that determine how the size of a tree is distributed in its different subtrees under some natural assumption on these distributions stipulating that macroscopic splitting events are rare we show that markov branching trees admit the so called self similar fragmentation trees as scaling limits in the gromov hausdorff prokhorov topology applications include scaling limits of consistent markov branching model and convergence of galton watson trees towards the brownian and stable continuum random trees we also obtain that random uniform unordered trees have the brownian tree as a scaling limit hence extending a result by marckert miermont and fully proving a conjecture made by aldous

identification of fuzzy relational model and its application to control abstract in the case of control systems where physical mechanisms are not well known due to high complexity and nonlinearity a fuzzy relational model may be useful in this paper we propose a recursive parameter tuning algorithm for the identification of fuzzy relational model for an unknown dynamic system furthermore using the fact that a dynamic system is represented by the relational strength between a few reference input and output fuzzy sets in the fuzzy relational model we construct a control input fuzzy set inducing a desired output fuzzy set by calculating the possibility between the model output and the desired output fuzzy set for the control purpose simulation results show the usefulness of the proposed identification and control algorithms

branching processes in levy processes the exploration process the main idea of the present work is to associate with a general continuous branching process an exploration process that contains the desirable information about the genealogical structure the exploration process appears as a simple local time functional of a levy process with no negative jumps whose laplace exponent coincides with the branching mechanism function this new relation between spectrally positive levy processes and continuous branching processes provides a unified perspective on both theories in particular we derive the adequate formulation of the classical ray knight theorem for such levy processes as a consequence of this theorem we show that the path continuity of the exploration process is equivalent to the almost sure extinction of the branching process

scaling limits of random graphs from subcritical classes we study the uniform random graph c n with n vertices drawn from a subcritical class of connected graphs our main result is that the resealed graph c n root n converges to the brownian continuum random tree t e multiplied by a constant scaling factor that depends on the class under consideration in addition we provide sub gaussian tail bounds for the diameter d c n and height h c n center dot of the rooted random graph c n center dot we give analytic expressions for the scaling factor in several cases including for example the class of outerplanar graphs our methods also enable us to study first passage percolation on c n where we also show the convergence to t e under an appropriate rescaling

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

on identification in fuzzy systems and its applications in control problems abstract the problem of identification in fuzzy systems described by the use of fuzzy equation is considered the identification method and its performance index is also presented the formal procedure of the identification algorithm is illustrated by means of a numerical example the possibility of using the proposed algorithm for the solution of a control problem is given as well

fuzzy seasonality forecasting abstract in this paper a fuzzy forecasting technique for seasonality in the time series data is presented using the following procedure first with the fuzzy regression analysis the fuzzy trend of a time series is analyzed then the fuzzy seasonality is defined by realizing the membership grades of the seasons to the fuzzy regression model both making fuzzy forecast and crisp forecast are investigated seasonal fuzziness and trends are analyzed the method is applied to the sales forecasting problem of a food distribution company

sampled data fuzzy control of chaotic systems based on a t s fuzzy model in this paper a sampled data fuzzy controller is designed to stabilize a class of chaotic systems a takagi sugeno t s fuzzy model is employed to represent the chaotic systems based on this general model the exponential stability issue of the closed loop systems with an input constraint is first investigated by a novel time dependent lyapunov functional which is positive definite at sampling times but not necessary between the sampling times then two sufficient conditions are developed for sampled data fuzzy controller synthesis of the underlying t s fuzzy model with or without input constraint all the proposed results in this paper depend on both the upper and lower bounds on a sampling interval and the available information about the actual sampling pattern is fully utilized the proposed sampled data fuzzy control scheme is successfully applied to the chaotic lorenz system which is shown to be effective and less conservative compared with existing results

h_ bm infty fuzzy filtering of nonlinear systems with intermittent measurements this paper is concerned with the problem of h infin fuzzy filtering of nonlinear systems with intermittent measurements the nonlinear plant is represented by a takagi sugeno t s fuzzy model the measurements transmission from the plant to the filter is assumed to be imperfect and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the phenomenon of the missing measurements attention is focused on the design of an h infin filter such that the filter error system is stochastically stable and preserves a guaranteed h infin performance a basis dependent lyapunov function approach is developed to design the h infin filter by introducing some slack matrix variables the coupling between the lyapunov matrix and the system matrices is eliminated which greatly facilitates the filter design procedure the developed theoretical results are in the form of linear matrix inequalities lmis finally an illustrative example is provided to show the effectiveness of the proposed approach

neuro fuzzy relational systems for nonlinear approximation and prediction abstract there are many machine learning systems developed so far fuzzy systems along with neural network are the most commonly used learning systems researchers mainly use mamdani linguistic and takagi sugeno fuzzy systems and in the paper relational neuro fuzzy systems are proposed for better flexibility linguistic systems store an input output mapping in the form of fuzzy if then rules with linguistic terms both in antecedents and consequents relational fuzzy systems bond input and output fuzzy linguistic values by a binary relation thus fuzzy rules have additional weights thanks to this the system is better adjustable to learning data described systems are tested on several known benchmarks and compared with other machine learning solutions from the literature

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

a novel control design on discrete time takagi sugeno fuzzy systems with time varying delays this paper focuses on analyzing a new model transformation of discrete time takagi sugeno t s fuzzy systems with time varying delays and applying it to dynamic output feedback dof controller design a new comparison model is proposed by employing a new approximation for time varying delay state and then a delay partitioning method is used to analyze the scaled small gain of this comparison model a sufficient condition on discrete time t s fuzzy systems with time varying delays which guarantees the corresponding closed loop system to be asymptotically stable and has an induced l2 disturbance attenuation performance is derived by employing the scaled small gain theorem then the solvability condition for the induced l2 dof control is also established by which the dof controller can be solved as linear matrix inequality optimization problems finally examples are provided to illustrate the effectiveness of the proposed approaches

scaling limits of random planar maps with large faces we discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index alpha in 1 2 when the number n of vertices of the map tends to infinity the asymptotic behavior of distances from a distinguished vertex is described by a random process called the continuous distance process which can be constructed from a centered stable process with no negative jumps and index alpha in particular the profile of distances in the map rescaled by the factor n 1 2 alpha converges to a random measure defined in terms of the distance process with the same rescaling of distances the vertex set viewed as a metric space converges in distribution as n to infty at least along suitable subsequences towards a limiting random compact metric space whose hausdorff dimension is equal to 2 alpha

on the concept of fuzzy probabilistic controllers the paper deals with a new approach to the construction of a so called fuzzy probabilistic controller where input output data are treated as probabilistic sets it is shown that the notion of a fuzzy controller is embedded in the concept discussed here first of all the distribution characterization of probabilistic sets is discussed some operations on probabilistic sets are presented and next the construction of the controller is performed numerical examples form an illustration of theoretical investigations

sub gaussian tail bounds for the width and height of conditioned galton watson trees we study the height and width of a galton watson tree with offspring distribution satisfying e 1 0 var conditioned on having exactly n nodes under this conditioning we derive sub gaussian tail bounds for both the width largest number of nodes in any level and height greatest level containing a node the bounds are optimal up to constant factors in the exponent under the same conditioning we also derive essentially optimal upper tail bounds for the number of nodes at level k for 1 k n

fuzzy weighting dependent approach to h_ infty filter design for time delay fuzzy systems this correspondence is concerned with the hinfin filter design for takagi sugeno t s fuzzy systems with state delay a delay dependent design method is proposed in terms of linear matrix inequalities lmi the main contribution is the use of fuzzy weighting dependent lyapunov functionals which can reduce the conservatism arisen from the quadratic lyapunov functional approach an illustrative example is given to show the effectiveness of the present method

parameter dependent stability and stabilization of uncertain time delay systems a new robust delay dependent stability test is introduced that determines the asymptotic stability of linear systems with state delays the parameters of the system are not exactly given they are known to reside in a given polytope the test provides an efficient sufficient condition for the stability of the system over the uncertainty polytope this condition is parameter dependent and it therefore improves previous results that were derived using a single lyapunov krasovskii functional the stability test is readily extended to provide a criterion for robust stabilization via state feedback

h_ infty filter design for nonlinear systems with time delay through t s fuzzy model approach this paper is concerned with the hinfin filter design for nonlinear systems with time varying delay via takagi sugeno fuzzy model approach delay dependent design method is proposed in terms of linear matrix inequalities lmis which forms the main contribution of this paper the main technique used is the free weighting matrix method combined with a matrix decoupling approach the results for rate independent case delay independent case and delay free case are also given as easy corollaries an illustrative example is given to show the effectiveness of the present method

an improved result on exponential stabilization of sampled data fuzzy systems this brief paper studies the exponential stabilization problem for the takagi sugeno fuzzy systems with a variable sampling different from previous results the gains of fuzzy state feedback controller adopted in this paper are time varying during two consecutive sampling instants which can contribute to the enlargement of the allowable sampling interval by choosing a suitable design parameter to reduce the design conservativeness a novel fuzzy time dependent lyapunov functional ftdlf is put forward to fully exploit the accessible information about the sampling pattern and the fuzzy basis functions moreover a more relaxed constraint condition is presented to ensure the positive definiteness of the ftdlf on sampling intervals by resorting to the novel ftdlf and the relaxed constraint condition new exponential stabilization criteria dependent on and independent of upper bounds on time derivatives of fuzzy basis functions are established by which a larger sampling interval can be achieved one example is offered to demonstrate the validity and superiorities of the obtained new results

an identification algorithm in fuzzy relational systems abstract the paper presents an effective identification method in fuzzy relational systems we propose an algorithm for constructing models on the basis of fuzzy and nonfuzzy data with the aid of fuzzy discretization and clustering techniques the usefulness of the method provided is demonstrated by means of two numerical examples also a possible way of generating a linguistic decision making algorithm is discussed

adaptive output feedback fuzzy tracking control for a class of nonlinear systems this paper is concerned with the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems the dynamic feedback strategy begins with an input driven filter by utilizing fuzzy logic systems to approximate unknown and desired control input signals directly instead of the unknown nonlinear functions an output feedback fuzzy tracking controller is designed via a backstepping approach it is shown that the proposed fuzzy adaptive output controller can guarantee that all the signals remain bounded and that the tracking error converges to a small neighborhood of the origin simulations results are presented to demonstrate the effectiveness of the proposed methods

percolation on random triangulations and stable looptrees we study site percolation on angel and schramm s uniform infinite planar triangulation we compute several critical and near critical exponents and describe the scaling limit of the boundary of large percolation clusters in all regimes subcritical critical and supercritical we prove in particular that the scaling limit of the boundary of large critical percolation clusters is the random stable looptree of index 3 2 which was introduced in curien and kortchemski random stable looptrees arxiv 1304 1044 2014 we also give a conjecture linking looptrees of any index alpha in 1 2 with scaling limits of cluster boundaries in random triangulations decorated with o n models

a limit theorem for the contour process of condidtioned galton watson trees in this work we study asymptotics of the genealogy of galton watson processes conditioned on the total progeny we consider a fixed aperiodic and critical offspring distribution such that the rescaled galton watson processes converges to a continuous state branching process csbp with a stable branching mechanism of index 1 2 we code the genealogy by two different processes the contour process and the height process that le gall and le jan recently introduced we show that the rescaled height process of the corresponding galton watson family tree with one ancestor and conditioned on the total progeny converges in a functional sense to a new process the normalized excursion of the continuous height process associated with the stable csbp we deduce from this convergence an analogous limit theorem for the contour process in the brownian case 2 the limiting process is the normalized brownian excursion that codes the continuum random tree the result is due to aldous who used a different method

fuzzy model identification for classification of gait events in paraplegics fuzzy system identification was applied to a biomedical system for classification purposes gait achieved through functional electrical stimulation fes of paraplegics was divided using sensor measurements of kinematic variables as inputs to five discrete events two identification algorithms were used to estimate the system model both max min and max product composition were used membership functions were either trapezoidal or triangular and all membership functions in a particular universe of discourse had the same shape and size the universe of discourse was varied by altering the overlap between membership functions the classification performance was assessed quantitatively by measuring the percentage of time steps in which the correct event was found and qualitatively by observing types of errors the identification algorithm affected system performance no difference in classification was found between max min and max product composition the performance was dependent on membership function overlap a comparison of the classification found using the fuzzy rule base versus that found using a traditional look up table demonstrated that the fuzzy approach was superior it is speculated that the use of fuzzy logic decreased errors stemming from sensor noise and or small variations in the input signals the performance of this approach was compared to that of a feedforward neural network and the fuzzy system is found superior

a fuzzy relational identification algorithm and its application to predict the behaviour of a motor drive system fuzzy relational identification builds a relational model describing a system s behaviour by a nonlinear mapping between its variables in this paper we propose a new fuzzy relational algorithm based on the simplified max min relational equation the algorithm presents an adaptation method applied to the gravity centre of each fuzzy set based on the error integral value between the measured and predicted system s output and uses the concept of time variant universe of discourse the identification algorithm also includes a method to attenuate the noise influence in the extracted system s relational model using a fuzzy filtering mechanism the algorithm is applied to a one step forward prediction of a simulated and experimental motor drive system the identified model has its input output variables stator reference current and motor speed signal treated as fuzzy sets whereas the relations existing between them are described by means of a matrix r defining the relational model extracted by the algorithm the results show the good potentialities of the algorithm in predicting the behaviour of the system and in attenuating through the fuzzy filtering method possible noise distortions in the relational model

robust adaptive controller design for nonlinear time delay systems via t s fuzzy approach the robust control problem is investigated for a class of uncertain nonlinear time delay systems via the takagi sugeno t s fuzzification we obtain the t s fuzzy systems with each local model in the form of time delay systems with uncertain nonlinear functions the mismatched nonlinear functions satisfy the lipschitz condition while the matched parts are bounded by nonlinear functions with unknown coefficients based on the input matrix the system is decomposed into two cascade subsystems the virtual controller is designed for the first subsystem and then a memoryless adaptive controller is presented by employing a new lyapunov krasovskii functional we show that the resulting closed loop system is exponentially stable and the solutions are uniformly ultimately bounded finally simulation examples are given to show the effectiveness of our main results

reliable h_ infty control for discrete time fuzzy systems with infinite distributed delay in this paper the problem of reliable h control is investigated for discrete time takagi sugeno t s fuzzy systems with infinite distributed delay and actuator faults a discrete time homogeneous markov chain is used to represent the stochastic behavior of actuator faults in terms of a stochastic fuzzy lyapunov functional a sufficient condition is proposed to ensure that the resultant closed loop system is exponentially stable in the mean square sense with an h performance index based on the derived condition the reliable h control problem is solved and an explicit expression of the desired controller is also given the case of no failure in the actuator is also considered a numerical example is given to demonstrate that our results are effective and less conservative

sub exponential tail bounds for conditioned stable bienayme galton watson trees we establish uniform sub exponential tail bounds for the width height and maximal outdegree of critical bienayme galton watson trees conditioned on having a large fixed size whose offspring distribution belongs to the domain of attraction of a stable law this extends results obtained for the height and width by addario berry devroye and janson in the finite variance case

brief paper a novel stability analysis of linear systems under asynchronous samplings this article proposes a novel approach to assess the stability of continuous linear systems with sampled data inputs the method which is based on the discrete time lyapunov theorem provides easy tractable stability conditions for the continuous time model sufficient conditions for asymptotic and exponential stability are provided dealing with synchronous and asynchronous samplings and uncertain systems an additional stability analysis is provided for the cases of multiple sampling periods and packet losses several examples show the efficiency of the method

conceptual proofs of l log l criteria for mean behavior of branching processes the kesten stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process showing that an l log l condition is decisive in critical and subcritical cases results of kolmogorov and later authors give the rate of decay of the probability that the process survives at least n generations we give conceptual proofs of these theorems based on comparisons of galton watson measure to another measure on the space of trees this approach also explains yaglom s exponential limit law for conditioned critical branching processes via a simple characterization of the exponential distribution

network based robust passive control for fuzzy systems with randomly occurring uncertainties this paper investigates the problem of robust passive control for networked fuzzy systems where randomly occurring uncertainties variable sampling intervals and constant network induced delay are taken into account a discontinuous lyapunov functional is introduced for the closed loop systems which takes full advantage of the sawtooth structure of the time varying interval delay induced by sample and hold and signal transmission a sufficient condition is proposed to ensure the closed loop system to be robustly stochastically passive then the problem of robust passive control is solved two examples are utilized to illustrate the advantages and effectiveness of the results that are proposed in this paper