fora a fuzzy set based framework for online reputation management the social web offers increasingly simple ways to publish and disseminate personal or opinionated information which can rapidly exhibit a disastrous influence on the online reputation of organizations based on social web data this study describes the building of an ontology based on fuzzy sets at the end of a recurring harvesting of folksonomies by web agents the aggregated tags are purified linked and transformed to a so called fuzzy grassroots ontology by means of a fuzzy clustering algorithm this self updating ontology is used for online reputation analysis a crucial task of reputation management with the goal to follow the online conversation going on around an organization to discover and monitor its reputation in addition an application of the fuzzy online reputation analysis fora framework lessons learned and potential extensions are discussed in this article

distortion theorems of plane quasiconformal mappings abstract the authors prove a conjecture on elliptic integrals and obtain sharp bounds for k r and k by using teichmuller s module theorem the authors obtain a distortion theorem of k quasiconformal mappings on the plane

adaptive systems and time varying plants abstract the behaviour of four adaptive algorithms lms equation error output error identification and the goodwin ramadge caines adaptive control algorithm are examined in the face of plant parameter variations the key point to note is that persistency of excitation conditions in the time invariant parameter case guarantees exponential convergence then standard and newly developed lyapunov stability results allow us to guarantee tracking error and parameter error boundedness when the plant parameters are actually time varying

stochastic mean square performance analysis of an adaptive hammerstein filter this paper presents an almost sure mean square performance analysis of an adaptive hammerstein filter for the case when the measurement noise in the desired response signal is a martingale difference sequence the system model consists of a series connection of a memoryless nonlinearity followed by a recursive linear filter a bound for the long term time average of the squared a posteriori estimation error of the adaptive filter is derived using a basic set of assumptions on the operating environment this bound consists of two terms one of which is proportional to a parameter that depends on the step size sequences of the algorithm and the other that is inversely proportional to the maximum value of the increment process associated with the coefficients of the underlying system one consequence of this result is that the long term time average of the squared a posteriori estimation error can be made arbitrarily close to its minimum possible value when the underlying system is time invariant

what about fuzzy logic s linguistic soundness a fuzzy set does represent a concrete use of an imprecise predicate in a given context that is its meaning a la wittgenstein the diverse theories of fuzzy sets come from accepting that also the connectives are to be used in different ways that they do have meaning this paper aims to suggest the importance of finding counterparts of the theories of fuzzy sets in either natural or artificial languages as a first step towards a new experimental view of theoretical fuzzy logic

local convexity properties of quasihyperbolic balls in punctured space this paper deals with local convexity properties of the quasihyperbolic metric in the punctured space we consider convexity and starlikeness of the quasihyperbolic balls

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

dimension free quasiconformal distortion in n space most distortion theorems for k quasiconformal mappings in rn n 2 depend on both n and k in an essential way with bounds that become infinite as n tends to oo the present authors obtain dimension free versions of four well known distortion theorems for quasiconformal mappings namely bounds for the linear dilatation the schwarz lemma the e distortion theorem and the r1 quasisymmetry property of these mappings they show that the upper estimates they have obtained in each of these four main results remain bounded as n tends to oo with k fixed the proofs are based on a dimensioncancellation property of the function t h r 1 r t k t 0 k 0 where r t is the capacity of a teichmiiller extremal ring in rn the authors also prove a dimension free distortion theorem for the absolute cross ratio under k quasiconformal mappings of n from which several other distortion theorems follow as special cases

decomposition properties of john domains in normed vector spaces abstract let e be a real normed vector space with dim e 2 in this paper we characterize john domains in e in terms of john domain decomposition property

the quasiconformal subinvariance property of john domains in mathbb r n and its applications the main aim of this paper is to give a complete solution to one of the open problems raised by heinonen from 1989 concerning the subinvariance of john domains under quasiconformal mappings in mathbb r n as application the quasisymmetry of quasiconformal mappings is discussed

capacity densities and angular limits of quasiregular mappings it is shown that if a bounded quasiregular mapping of the unit ball bn c rn n 2 has a limit at b e abn through a set e c bn with b ee e then it has an angular limit at b provided that e is contained in an open cone c c bn with vertex b and that e is thick enough at b the thickness condition is expressed in terms of the n capacity density

on reduced order adaptive output error identification and adaptive iir filtering the reduced order application of landau s adaptive output error identifier results in a perturbed error system where the perturbation signal is a moving average of the unmodeled portion of the unknown plant output or desired signal in adaptive filter parlance it is proven in this paper that if this perturbation signal is sufficiently small and a reduced order dimension model is sufficiently excited then the output and parameter estimates of this adaptive identifier filter remain bounded the influence of various operating conditions on this quantitatively defined bound are noted this robustness property is crucial in all real applications which due to nonlinearities and distributed effects are subject to reduced order modeling

robustness of discrete time direct adaptive controllers the problem of preserving stability of discrete time adaptive controllers in spite of reduced order modeling and output disturbances is addressed in this paper conditions for global stability convergence of the tracking error with bounded signals are derived for a discrete time pole zero placement adaptive controller where the parameter estimator is modified in terms of normalized signals following an input output perpective the overall system is decomposed into two subsystems reflecting the parameter estimation and modeling errors respectively and its stability is studied using the sector stability and passivity theorems first the analysis is carried for the class of disturbances and reference inputs that are either decaying or can be exactly hulled by a linear controller of the chosen structure in this l 2 framework it is shown that the only substantive assumption to assure stability is the existence of a linear controller such that the closed loop transfer function verifies certain conicity conditions the convergence speed and alertness properties of various parameter adaptation algorithms regarding this condition are discussed the results are further extended to a broader class of l infty disturbances and reference inputs

adaptive system stability robustness via burst recovery abstract adaptive systems which are based on a posteriori parameter update algorithms are shown to possess a specific type of self stabilization property termed burst recovery this results in bounded disturbance bounded error stability provided that unbounded parameter drift does not occur persistent excitation prevents unbounded parameter drift but only when both upper and lower bounds on excitation exist for many adaptive systems an upper bound on excitation cannot be assured using standard perturbation analyses which require the disturbance to be suitably small compared to the lower bound on excitation this paper proves that burst recovery in conjunction with only a lower bound on excitation provides bounded disturbance bounded error stability the disturbance need not be small and additional algorithm modifications such as parameter projection are not necessary

on computing pi coefficients abstract introduced by lawrence and johnson in 1986 the concept of pi sharing can be used to analyze the stability of discrete time systems however to determine the suitable pi coefficients required in the application of pi sharing theory is in general a difficult task it involves checking the negative semi definiteness n s d of a complicated matrix this paper formulates an alternative problem the max p problem for determining the best pi coefficients and proposes a solution method for the problem the n s d condition is turned into conditions on the coefficients of a series of polynomials which are easier to solve than the original one an example is used to illustrate the procedure in detail

non linear dynamics in adaptive control chaotic and periodic stabilization abstract in this paper the non linear features of adaptive control algorithms are highlighted using a simple linear discrete time example based on classical design it is demonstrated that in the presence of undermodelling errors non linear phenomena in the feedback gain such as limit cycles and even chaos arise despite these complicated dynamics robust stabilization of the plant can still occur for the class of undermodelling errors considered the set of plants stabilizable by this adaptive controller is completely characterized

sharp distortion theorems for quasiconformal mappings continuing their earlier work on distortion theory the authors prove some dimension free distortion theorems for k quasiconformal mappings in r for example one of the present results is the following sharp variant of the schwarz lemma if f is a k quasiconformal self mapping of the unit ball bn n 2 with f 0 0 then 41 k2ixik i if x i 411 k2ixil k for all x in b

on the subinvariance of uniform domains in banach spaces abstract suppose that e and e denote real banach spaces with dimension at least 2 that d e and d e are domains and that f d d is a homeomorphism in this paper we prove the following subinvariance property for the class of uniform domains suppose that f is a freely quasiconformal mapping and that d is uniform then the image f d 1 of every uniform subdomain d 1 in d under f is still uniform this result answers an open problem of vaisala in the affirmative

pi coefficient analysis of update algorithms for adaptive systems abstract this paper finds the appropriate pi coefficients for a parameter estimation adaptive system and uses them to analyze the stability of two estimation algorithms the estimation error dynamics of the system are modeled by a linear time invariant subsystem and a nonlinear time varying update law in a feedback loop then the so called max p problems are formulated and solved to obtain the pi coefficients for the linear subsystem and nonlinear update low for the investigated system the quantitative results show that the least squares update algorithm has larger stability range than that of the gradient algorithm and the modification scheme gives larger stability ranges for both algorithms

a recursive algorithm for armax model identification in closed loop the joint problem of the recursive estimation of an optimal predictor for the closed loop system and the unbiased parameter estimation of an armax plant model in closed loop operation is considered a special reparameterized optimal predictor for the closed loop is introduced this allows a parameter estimation algorithm for the plant model to be derived which is globally asymptotically stable in a deterministic environment and gives asymptotically unbiased parameters estimates under richness conditions

recursive parameter identification algorithm stability analysis via pi sharing pi sharing is introduced as an extension of the application of passivity and hyperstability concepts for discrete time systems providing connections between input output and state space stability notions using tools developed within the pi sharing framework new stability results for the output error class identification algorithm are derived this approach offers a clear interpretation of the role of the spr condition in the work of landau and silveira and its absence in the work of tomizuka and altay

multivariable pi sharing theory and its application on the lur e problem the pi sharing theory developed by lawrence and johnson 1986 is extended to handle square multivariable continuous time systems and for the most essential part of finding usable pi coefficients lmi formulations are utilized such that for any finite dimensional lti systems time invariant pi coefficients can be obtained easily furthermore pi coefficients are derived for sector bounded nonlinearities and the extended pi sharing theory is applied to the multivariable lur e problem with this approach not only can a lur e system with known sector bounds on nonlinearities be checked for stability but also the maximal bounds ensuring stability can be found under some conditions

on a relaxation of spr condition in parallel mras continuous time case it is shown that the strict positive realness spr condition for asymptotic stability of the continuous time parallel model reference adaptive system mras can be removed provided that the parameter adaption law includes a proportional term and the information matrix is made sufficiently large the present result a continuous time counterpart of an earlier result m tomizuka ibid vol 27 no 4 p 505 6 1982 on the discrete time parallel mras

an analytic approach for computing pi coefficients of continuous time systems the pi sharing theory for continuous time systems is discussed in this paper an analytic approach is proposed for computing pi coefficients of lti systems for the two scalar pi coefficients feasible regions are characterized graphically on a plane and for the other two matrix pi coefficients the corresponding values are obtained by solving a riccati equation the results are applied in an example to determine the stability of a feedback system containing both linear and nonlinear subsystems

technical communique gradient expressions for a closed loop identification scheme with a tailor made parametrization in this paper we present gradient expressions for a closed loop parametric identification scheme the method is based on the minimization of a standard identification criterion and a parametrization that is tailored to the closed loop configuration it is shown that for both linear and nonlinear plants and controllers the gradient signals can be computed exactly

fuzzy inferences and conditional possibility distributions abstract let x i i 1 2 be two variables taking values in finite universes of discourse u i and associated with possibility distributions f i u i 0 1 after an observation of x 1 we can deduce a characterization of x 2 by means of an inference process we define q x 2 x 1 for x i u i as some fuzzy implication and we introduce the possibility distribution p x 1 x 2 f 1 x 1 q x 2 x 1 for a t norm we exhibit some reasons to say that q and f may be respectively regarded as a conditional and a joint possibility distribution corresponding to marginal properties with regard to the use of a t conorm a property of non interactivity of the variables with respect to is bound with the definition of q and p in this way we suggest justifications of the choice of particular implications in inference processes

a sufficient condition of output feedback stabilization of uncertain systems a sufficient condition is derived for the existence of an output constant gain feedback controller which stabilizes a single input single output dynamical system with a linear nominal part and matched uncertainties the sufficient condition is significantly less restrictive than a recently derived one 1 if such a controller exists it may readily be computed

adaptive algorithms with nonlinear data and error functions the tools of nonlinear system theory are used to examine several common nonlinear variants of the lms algorithm and derive a persistence of excitation criterion for local exponential stability the condition is tight when the inputs are periodic and a generic counterexample is demonstrated which gives local instability for a large class of such nonlinear versions of lms specifically those which utilize a nonlinear data function the presence of a nonlinear error function is found to be relatively benign in that it does not affect the stability of the error system rather it defines the cost function the algorithm tends to minimize specific examples include the dead zone modification the cubed data nonlinearity the cubed error nonlinearity the signed regressor algorithm and a single layer version of the backpropagation algorithm

a new adaptive law for robust adaptation without persistent excitation a new adaptive law motivated by the work of loannou and kokotovic 1983 is proposed for the robust adaptive control of plants with unknown parameters in this adaptive law the output error plays a dual role in the adjustment of the control parameter vector the advantages of using the adaptive law over others proposed in the literature are discussed in the ideal case the adaptive system has bounded solutions in addition the origin of the error equations is exponentially stable when the reference input is persistently exciting and has a sufficiently large amplitude the adaptive system is also shown to be robust under bounded external disturbances finally it is shown that by suitably modifying the adaptive law the overall system can be made robust in the presence of a class of unmodeled dynamics of the plant simulation results are presented throughout the paper to complement the theoretical developments

an output error recursive algorithm for unbiased identification in closed loop the problem of unbiased recursive identification of a plant model in closed loop operation is considered a particular form of an output error predictor for the closed loop is introduced this allows one to derive a parameter estimation algorithm for the plant model that is globally asymptotically stable and asymptotically unbiased in the presence of noise the paper presents a stability analysis in a deterministic environment and a convergence analysis in the stochastic environment both require a mild sufficient passivity condition to be satisfied simulations and real time experiments on a flexible transmission illustrate the performances of the proposed algorithm

modified output error identification elimination of the spr condition in this note we present a modified adaptive output error algorithm for identification we refer to both the continuous time and the discrete time cases in the standard algorithm stability requires that a certain transfer function should be strictly positive real spr however in the present algorithm the spr condition which is difficult to satisfy is eliminated this is achieved by adding a fixed feedback gain when there exists an a priori partial knowledge about the parameters of the plant we provide a simple procedure to design that gain an illustrative example comparing the modified algorithm to the standard one is provided

paper unification of discrete time explicit model reference adaptive control designs various discrete time explicit mrac designs based on stability considerations are presented from a unified point of view a general structure and a design procedure are given which contain as particular cases various possible designs some of these designs have been already given in the literature but some are new the general structure considered removes some of the restrictions encountered in previous designs and solves the important problem of independent specification of tracking and regulation objectives the proof of boundedness of the control variables is also given simulations are included in order to evaluate the various designs in a deterministic environment

on robust stability of interval control systems the authors develop results on the robust stability of a nonlinear control system containing both parametric as well as unstructured uncertainty the basic system considered is that of the classical lur e problem of nonlinear control theory a robust version of the lur e problem consisting of a family of linear time invariant systems subjected simultaneously to bounded parameter variations and feedback perturbations from a family of sector bounded nonlinear gains is presently treated by using the kharitonov theorem to develop some extremal results on positive realness of interval transfer functions i e a family of rational transfer functions with bounded independent coefficient perturbations the authors determine the size of a sector of nonlinear feedback gains for which absolute stability can be guaranteed these calculations amount to the determination of the stability margin of the system under joint parametric and nonlinear feedback perturbations

logical foundations of rule based systems the evolution of a theory of fuzzy if then rules and its contribution to the establishment of fuzzy logic is a focus of this paper i am advocating in favour of hajek s fuzzy logic regarding it as a right methodology for special logical theories a theory of fuzzy if then rules as a special theory in the above considered sense is proposed this theory is for all practitioners who want to create a system of fuzzy if then rules free of conflicts logically consistent and rich enough to be able to make non trivial conclusions or answer inquires

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

what are fuzzy rules and how to use them abstract fuzzy rules have been advocated as a key tool for expressing pieces of knowledge in fuzzy logic however there does not exist a unique kind of fuzzy rules nor is there only one type of fuzzy logic this diversity has caused many a misunderstanding in the literature of fuzzy control the paper is a survey of different possible semantics for a fuzzy rule and shows how they can be captured in the framework of fuzzy set and possibility theory it is pointed out that the interpretation of fuzzy rules dictates the way the fuzzy rules should be combined the various kinds of fuzzy rules considered in the paper gradual rules certainty rules possibility rules and others have different inference behaviors and correspond to various intended uses and applications the representation of fuzzy unless rules is briefly investigated on the basis of their intended meaning the problem of defining and checking the coherence of a block of parallel fuzzy rules is also briefly addressed this issue has been neglected in the fuzzy control literature although it looks important for validation purposes

on the representation of fuzzy rules in terms of crisp rules there are two classical ways of viewing a fuzzy set in terms of a combination of crisp sets either as a weighted max aggregation of its level cuts or as a convex combination of the latter these views are applied to the particular case of fuzzy relations which are induced by fuzzy rules where the rules are modeled by implication connectives defined on a finite subset of the unit interval the paper studies more closely the representation of such fuzzy rules in terms of a convex combination of gradual rules a special type of implication based fuzzy rule inducing a crisp relation this representation which might be interpreted in a probabilistic way is shown to be unique on the assumption that the implication operator used for modeling the fuzzy rule does not satisfy a special kind of strict monotonicity condition in this case the crisp relations induced by the involved gradual rules correspond to level cuts of the fuzzy relation associated with the fuzzy rule however other representations might exist if the aforementioned property is not satisfied under a slightly stronger strict monotonicity condition the existence of further non consonant representations is even guaranteed then the crisp relations induced by gradual rules do not necessarily correspond to level cuts of the underlying fuzzy relation in this sense the decomposition of a fuzzy rule into a class of crisp implication based rules is more general than the classical decomposition of fuzzy sets

gradual inference rules in approximate reasoning abstract gradual inference rules of the form the more x is f the more y is g or of similar forms with the less instead of the more which express a progressive change of the degree to which the entity y satisfies the gradual property g when the degree to which the entity x satisfies the gradual property f is modified are often encountered in commonsense reasoning a representation of such rules by means of fuzzy sets is proposed and discussed this representation turns out to be based on a special implication function already considered in multiple valued logic patterns of reasoning involving gradual inference rules are formalized their links with interpolation mechanisms are pointed out

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

comparison of the closed loop identfication methods in terms of the bias distribution several schemes for plant model identification in closed loop operation including classical direct method two step identification and closed loop output error algorithms are considered these methods are analyzed and compared in terms of the bias distribution of the estimates for the case that the noise model is estimated as well as the case that a fixed model of noise is considered output error structure the problems concerning the filtered direct method which is often used in the iterative identification and control scheme are mentioned it is shown that these problems may be solved by the closed loop output error identification method

parallel mras without compensation block the parallel model reference adaptive system mras is shown to be asymptotically stable without the compensation block provided that a quadratic form of the adjustable model input output is lower bounded

adaptive algorithm structure impacts on stability and performance the structures of adaptive algorithms are examined for their impact on input output stability and performance measures three general algorithm structures are considered the a priori form the a posteriori form and the proportional integral pi form a parallel development is used to directly compare continuous and discrete time versions of the algorithms considered the standard a priori and a posteriori algorithm forms are shown to be special cases of a more flexible proportional plus integral algorithm which is implemented via normalization in the adaptive law it is shown that this normalization can enhance algorithm stability and input output performance of normalized errors but the performance unnormalized errors may not be significantly affected this direct comparison of simple algorithm structures serves to isolate the stability and performance properties due to these structures alone it provides information for algorithm design allowing the essential effects of design options to be traded off against the many other options

fuzzy prolog a new approach using soft constraints propagation we present a definition of a fuzzy prolog language that models b 0 1 valued fuzzy logic and subsumes former approaches because it uses a truth value representation based on a union of sub intervals on 0 1 and is defined using general operators that can model different logics this extension to prolog is implemented by interpreting fuzzy reasoning as a set of constraints that are propagated through the rules by means of aggregation operators declarative and procedural semantics for fuzzy logic programs are given and their equivalence is proven in addition we present the implementation of an interpreter for this conceived language using constraint logic programming over real numbers

robust adaptive control conditions for global stability an input output approach is presented for analyzing the global stability and robustness properties of adaptive controllers to unmodeled dynamics the concept of a tuned system is introduced i e the control system that could be obtained if the plant were known comparing the adaptive system to the tuned system results in the development of a generic adaptive error system passivity theory is used to derive conditions which guarantee global stability of the error system associated with the adaptive controller and ensure boundedness of the adaptive gains specific bounds are presented for certain significant signals in the control systems limitations of these global results are discussed particularly the requirement that a certain operator be strictly positive real spr a condition that is unlikely to hold due to unmodeled dynamics

recursive algorithms for identification in closed loop a unified approach and evaluation a unified presentation of recursive algorithms for plant model identification in closed loop is given from the basic formulation of the problem of finding the plant model that gives the best predictor for the closed loop system two families of algorithms using either a reparameterized predictor for the closed loop or a plant predictor operating on filtered data are presented and their asymptotic properties are examined validation tests for the models identified in closed loop are proposed a comparative evaluation of the various algorithms in simulation and on real time experiments concludes the paper

paper instability analysis and improvement of robustness of adaptive control the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed five possible types of instability mechanisms parameter drift linear instability fast adaptation instability high frequency instability and throughput instability are analyzed using simple examples a procedure is used to construct lyapunov like functions for a modified adaptive controller applied to a dominant plant of relative degree one in the presence of parasitics and disturbances and obtain sufficient conditions under which none of the five types of instability can occur the modified scheme is robust in the sense that it guarantees the existence of a large region of attraction from which all the trajectories remain bounded and the state errors converge exponentially to a much smaller residual set the size of the region of attraction depends on the speed of parasitics in such a way that as the parasitics become infinitely fast the region of attraction becomes the whole space

parameter drift in lms adaptive filters we examine general conditions under which the lms adaptive filter generates unbounded parameter estimates when driven by bounded sequences this unexpected parameter divergence or drift is related to the inadequacy of excitation in the input sequence and is characterized by slow i e nonexponential escape of the parameter estimate vector to infinity in spite of all other signals inputs outputs prediction errors remaining bounded or even decaying to zero the analysis proceeds by showing that in a general adaptive filtering setting the sequence of regressors information vectors provides a natural decomposition of the parameter estimate space into subspaces each corresponding to a characteristic class of filter excitation this subspace decomposition is applied to the lms adaptive filter yielding direct links between filter behavior and modes of excitation in particular stability and instability of the parameter estimates in the presence of bounded disturbances and prediction errors is obtained for various classes of excitation this behavior is examined in detail for the first and second order cases and is sufficient to characterize the behavior of higher order adaptive filters the instability drift results are due to modes of decaying excitation and bounds on the rates of drift are derived this drift mechanism is inherent in the algorithm and is not due to numerical implementation problems or violation of small step size conditions examples are presented where drift may occur in restricted complexity filtering and in the related stochastic gradient algorithm an analysis of leakage in terms of input excitation reveals a tradeoff in performance between parameter and prediction errors a modified form of leakage using the subspace decomposition is suggested to remove this difficulty

norm inequalities for vector functions abstract we study vector functions of r n into itself which are of the form x g x x where g 0 0 is a continuous function and call these radial functions in the case when g t t c for some c r we find upper bounds for the distance of image points under such a radial function some of our results refine recent results of l maligranda and s s dragomir in particular we study quasiconformal mappings of this simple type and obtain norm inequalities for such mappings

comparison of fuzzy reasoning methods l a zadeh e h mamdani and m mizumoto et al have proposed methods for fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition if x is a then y is b with a and b being fuzzy concepts mizumoto et al have investigated the properties of their methods in the case of generalized modus ponens this paper deals with the properties of their methods in the case of generalized modus tollens and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems finally the properties of syllogism and contrapositive are investigated under each fuzzy reasoning method

parameter drift instability in disturbance free adaptive systems adaptive identification and control algorithms can exhibit local instability when certain ideal assumptions such as satisfaction of strictly positive real spr conditions are violated however conjectures suggest that due to a self stabilization mechanism global boundedness may still hold despite local instabilities counterexamples to these are presented showing that self stabilization is bypassed via hidden unbounded parameter drift although parameter drift instability is known to occur in adaptive systems with disturbances concrete examples are given to show that unbounded drift can also occur in the disturbance free case when spr conditions are violated

elimination of real positivity condition and error filtering in parallel mras for a particular degree of persistent excitation the commonly accepted strict positive realness spr condition and associated error filtering in the design of model reference adaptive system mras are removed it is shown that the parameter estimation vector remains bounded and the output error converges asymptotically to zero for a stable reference model the proof proceeds with simple algebra and does not rely on the commonly used hyperstability theorem and positivity concept

monotonicity theorems and inequalities for the complete elliptic integrals we prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind k and e these results lead to sharp symmetrical bounds for k and e which improve recently discovered inequalities

disturbance instabilities in an adaptive system two types of disturbance instability of simple adaptive schemes are analyzed a drift equation shows how stable equilibria are forced to infinity by infrequent but persistent switches of a constant disturbance the modification proposed by p ioannou counteracts these instabilities

brief on the relation between a bias eliminated least squares bels and an iv estimator in closed loop identification a bias correction method for closed loop identification introduced in the literature as the bias eliminated least squares bels method zheng feng automatica 31 1995 1019 is shown to be equivalent to a basic instrumental variable estimator applied to a predictor for the closed loop system this predictor is a function of the plant parameters and the known controller corresponding to the related method using a least squares criterion the method is referred to as the tailor made iv method for closed loop identification the indicated equivalence greatly facilitates the understanding and the analysis of the bels method

an adaptation algorithm for parallel model reference adaptive bilinear systems an adaptation algorithm is presented for parallel model reference adaptive bilinear systems the output error converges asymptotically to zero and the parameter estimates are bounded for stable reference models the convergence criterion depends only upon the input sequence and a priori estimates of the maximum parameter values a passivity condition which is generally difficult to verify is not required

on mori s theorem for quasiconformal maps in the n space r fehlmann and m vuorinen proved in 1988 that mori s constant m n k for k quasiconformal maps of the unit ball in r n onto itself keeping the origin fixed satisfies m n k 1 when k 1 we give here an alternative proof of this fact with a quantitative upper bound for the constant in terms of elementary functions our proof is based on a refinement of a method due to g d anderson and m k vamanamurthy we also give an explicit version of the schwarz lemma for quasiconformal self maps of the unit disk some experimental results are provided to compare the various bounds for the mori constant when n 2

dominant richness and improvement of performance of robust adaptive control abstract several recent robust adaptive control schemes guarantee stability and residual tracking errors which are small in the mean for any bounded initial conditions independent of any persistence of excitation condition since smallness in the mean does not always guarantee small bounds for the tracking error at steady state the tracking performance of these robust schemes may not be acceptable in this paper we show that the convergence and the tracking performance of these globally stable adaptive control schemes can be considerably improved if the reference input signal is chosen to be dominantly rich we show that dominantly rich signals maintain a high level of persistence of excitation relative to the level of the modeling error which guarantees exponential convergence and small bounds for the tracking and parameter error at steady state