comment on discrete time optimal fuzzy controller design global concept approach in this correspondence we show that the relationship between the finite optimal trajectory and the infinite optimal trajectory in lemma 3 of the aforementioned paper cannot act as a theory basis for the further implementation of other theorems and the dynamic decomposition algorithm

deviation inequalities for random walks we study random walks on groups with the feature that roughly speaking successive positions of the walk tend to be aligned we formalize and quantify this property by means of the notion of deviation inequalities we show that deviation inequalities have several consequences including central limit theorems the local lipschitz continuity of the rate of escape and entropy as well as linear upper and lower bounds on the variance of the distance of the position of the walk from its initial point in the second part of this article we show that the exponential deviation inequality holds for measures with exponential tail on acylindrically hyperbolic groups these include nonelementary relatively hyperbolic groups mapping class groups many groups acting on cat 0 spaces and small cancellation groups

affine ts model based fuzzy regulating servo control design an affine t s fuzzy system is derived naturally from linearizing a nonlinear system or from some data driven identification techniques for example cluster based algorithms or soft computation learning structures little research is proposed for the intrinsic analysis of an affine type fuzzy system further the controllers to regulate or to achieve servo control of affine ts based nonlinear systems are also few both affine type fuzzy regulation and servo control design scheme are theoretically derived a simple lyapunov based stability criterion and some extra conditions are proposed to guarantee the global stability of the generated closed loop fuzzy systems the exponential stability of the feedback fuzzy system is ensured under some conditions the performance of the proposed fuzzy controllers and fuzzy servo controllers is examined by three case studies simulation results show that the proposed controllers can stabilize these affine fuzzy systems and the proposed servomechanism can adapt itself to various incoming signals in very short time spans

design and analysis of optimal controller for fuzzy systems with input constraint in this paper we present a design method of the optimal and robust controller subject to the constraint on control inputs for continuous time takagi sugeno ts fuzzy systems in order to establish this design method we consider an optimal and robust control problem for nonlinear dynamic systems for this problem we present an analytic way which can provide the optimal controller for nonlinear dynamic systems by the dynamic programming approach and the inverse optimal approach moreover we analyze the robustness property of the proposed optimal controller with respect to a class of input uncertainties by the passivity approach then based on the theoretical results presented in this paper we formulate the design problem of the optimal and robust controller with input constraint for continuous time ts fuzzy systems as the semidefinite programming problem and find the controller by solving it the usefulness of the proposed approach is illustrated by considering the three axis attitude stabilization problem of rigid spacecraft

the geometry of purely loxodromic subgroups of right angled artin groups we prove that finitely generated purely loxodromic subgroups of a right angled artin group a fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups mod s in particular such subgroups are quasiconvex in a in addition we identify a milder condition for a finitely generated subgroup of a that guarantees it is free undistorted and retains finite generation when intersected with a for subgraphs of these results have applications to both the study of convex cocompactness in mod s and the way in which certain groups can embed in right angled artin groups

design of stable fuzzy control systems using lyapunov s method in fuzzy hypercubes in this paper a systematic procedure is presented to analyze and design a stable fuzzy controller for a class of nonlinear systems based on the lyapunov s directive method we account for the relationship between the stability of the control system and the i o sets of the fuzzy controller first the state space is partitioned into fuzzy hypercubes according to the product space of the input fuzzy sets of the states then all fuzzy hypercubes are considered and made to satisfy the lyapunov s stability condition by choosing proper output centers of the associated fuzzy rules through the proposed design guideline it is also possible to determine the performance and accuracy of fuzzy control systems an example with a fuzzy controller for a chaotic system is presented to illustrate the design procedure

global optimal fuzzy tracker design based on local concept approach in this paper we propose a global optimal fuzzy tracking controller implemented by fuzzily blending the individual local fuzzy tracking laws for continuous and discrete time fuzzy systems with the aim of solving respectively the continuous and discrete time quadratic tracking problems with moving or model following targets under finite or infinite horizon time the differential or recursive riccati equations and more the differential or difference equations in tracing the variation of the target are derived moreover in the case of time invariant fuzzy tracking systems we show that the optimal tracking controller can be obtained by just solving algebraic riccati equations and algebraic matrix equations grounding on this several fascinating characteristics of the resultant closed loop continuous or discrete time invariant fuzzy tracking systems can be elicited easily the stability of both closed loop fuzzy tracking systems can be ensured by the designed optimal fuzzy tracking controllers the optimal closed loop fuzzy tracking systems cannot only be guaranteed to be exponentially stable but also be stabilized to any desired degree moreover the resulting closed loop fuzzy tracking systems possess infinite gain margin that is their stability is guaranteed no matter how large the feedback gain becomes two examples are given to illustrate the performance of the proposed optimal fuzzy tracker design schemes and to demonstrate the proved stability properties

the second homology group of the mapping class group of an orientable surface in i 7 mumford shows that the picard group p ic is isomorphic to h2 f 2 and conjectures the latter is rank one g 3 we prove this below for g 5 another interpretation of this theorem may be obtained by identifying h2 f as bordism classes of fiber bundles f w4 t where t is a closed oriented surface sect 0 when f is closed every such bundle is bordant to f w t a bundle admitting a section s t w the theorem then says that

generalized receding horizon control of fuzzy systems based on numerical optimization algorithm the optimal control of fuzzy systems with constraints is still an open problem our focus concerns the optimal control problem of fuzzy systems derived from receding horizon control rhc schemes we consider methods to numerically compute the value function for general fuzzy systems the numerical method that is developed using the finite difference with sigmoidal transformation is a stable and convergent algorithm for the hamilton jacobi bellman hjb equation an optimization procedure is developed to increase the calculation accuracy with less computation time a parallel processing method is employed in the optimization procedure the optimization results are applied to the controller design of general fuzzy dynamic systems employing the principle of conventional rhc schemes rhc form controllers are designed for some classes of fuzzy dynamic systems the basic ideas are as follows first the value function is calculated by numerical methods then the value function is used as controller design parameters to redesign rhc controllers for fuzzy systems which is motivated by the inverse lyapunov function design method it is proven that the closed loop system is asymptotically stable an engineering implementation of the controller redesign scheme is discussed meanwhile the parallel processing framework that can improve the closed loop performance is also introduced

trajectory stabilization of a model car via fuzzy control abstract this paper deals with trajectory stabilization of a computer simulated model car via fuzzy control stability conditions of fuzzy systems are given in accordance with the definition of stability in the sense of lyapunov first we approximate a computer simulated model car whose dynamics is nonlinear by t s takagi and sugeno fuzzy model fuzzy control rules which guarantee stability of the control system under a condition are derived from the approximated fuzzy model the simulation results show that the fuzzy control rules effectively realize trajectory stabilization of the model car along a given reference trajectory from all initial positions under a condition and the dynamics of the approximated fuzzy model agrees well with that of the model car

are large distance heegaard splittings generic in a previous paper we introduced a notion of genericity for countable sets of curves in the curve complex of a surface s based on the lebesgue measure on the space of projective measured laminations in s with this definition we prove that for each fixed g 1 the set of irreducible genus g heegaard splittings of high distance is generic in the set of all irreducible heegaard splittings our definition of genericity is different and more intrinsic then the one given via random walks

neural network based optimal fuzzy controller design for nonlinear systems a neural learning fuzzy technique is proposed for t s fuzzy model identification of model free physical systems further an algorithm with a defined modelling index is proposed to integrate and to guarantee that the proposed neural based optimal fuzzy controller can stabilize physical systems the modelling index is defined to denote the modelling error evolution and to ensure that the training data for neural learning can describe the physical system behavior very well the algorithm which integrates the neural based fuzzy modelling and optimal fuzzy controlling process can implement off line modelling and on line optimal control for model free physical systems the neural fuzzy inference network is a self organizing inference system to learn fuzzy membership functions and fuzzy subsystems parameters as data feeding in based on the generated t s fuzzy models for the continuous mass spring damper system and chua s chaotic circuit discrete time model car system and articulated vehicle their corresponding fuzzy controllers are formulated from both local concept and global concept fuzzy approach respectively the simulation results demonstrate the performance of the proposed neural based fuzzy modelling technique and of the integrated algorithm of neural based optimal fuzzy control structure

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

the mapping class groups of reducible heegaard splittings of genus two the first named author was supported by the basic science research program through the national research foundation of korea nrf funded by the ministry of science ict and future planning nrf 2015r1a1a1a05001071 and by the ministry of education nrf 201800000001768 the second author was supported by jsps kakenhi grant numbers 15h03620 17k05254 17h06463 and jst crest grant number jpmjcr17j4

curve complexes are rigid any quasi isometry of the curve complex is bounded distance from a simplicial automorphism as a consequence the quasi isometry type of the curve complex determines the homeomorphism type of the surface

switched fuzzy output feedback control and its application to a mass spring damping system this paper investigates the dynamic output feedback control problem for interval type 2 it2 fuzzy systems a switched output feedback controller which depends on the values of membership functions is constructed the membership functions of it2 fuzzy systems contain parameter uncertainties and are different from the type 1 takagi sugeno fuzzy systems based on the it2 fuzzy set theory the parameter uncertainties can be effectively obtained by upper and lower membership functions a novel it2 switched output feedback controller is designed to ensure that the closed loop system is asymptotically stable with an h infty performance finally a mass spring damping system is proposed to show the feasibility and the merit of the proposed scheme over the other existing ones

quadratic forms over c t1 t2 abstract we show that dimension 4 quadratic forms over c t1 t2 ti transcendental do not satisfy what might be naturally taken as a strong hasse principle though a weak hasse principle exists we reduced solvability to a question of determining the quadratic reciprocity group for the discriminant d the classes modulo d of elements x such that d is a quadratic residue modulo x we determine this group in terms of the class group of a function field we prove that the weak hasse principle does not hold for forms over c t1 d therefore witt and brauer groups of 2 dimensional function fields over c do not restrict monomorphically to their localizations

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

measure equivalence rigidity of the mapping class group we show that the mapping class group of a compact orientable surface with higher complexity satisfies the following rigidity in the sense of measure equivalence if the mapping class group is measure equivalent to a discrete group then they are commensurable up to finite kernels moreover we describe all locally compact second countable groups containing a lattice isomorphic to the mapping class group we obtain similar results for finite direct products of mapping class groups

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

connectivity of the space of ending laminations we prove that for any closed surface of genus at least four and any punctured surface of genus at least two the space of ending laminations is connected a theorem of e klarreich 28 theorem 1 3 implies that this space is homeomorphic to the gromov boundary of the complex of curves it follows that the boundary of the complex of curves is connected in these cases answering the conjecture of p storm other applications include the rigidity of the complex of curves and connectivity of spaces of degenerate kleinian groups

the geometry of the disk complex we give a distance estimate for the disk complex we use the distance estimate to prove that the disk complex is gromov hyperbolic as another application of our techniques we find an algorithm which computes the hempel distance of a heegaard splitting up to an error depending only on the genus

fuzzy linear pulse transfer function based sliding mode control for nonlinear discrete time systems in this paper a nonlinear discrete time system in the presence of input disturbance and measurement noise is approximated by n subsystems described by the linear pulse transfer functions although the input disturbance and the measurement noise are unknown they are modeled as known pulse transfer functions the approximation error between the nonlinear discrete time system and the fuzzy linear pulse transfer function system is represented by the linear time invariant dynamic system in every subsystem whose degree can be larger than that of the corresponding subsystem besides the input disturbance and the measurement noise uncertainties are caused by the approximation error of the fuzzy model and the interconnected dynamics resulting from the other subsystems owing to the presence of input disturbance measurement noise or uncertainties a disadvantageous response occurs based on lyapunov redesign the switching control in every subsystem is designed to reinforce the system performance due to the time invariant feature for a constant reference input the operating point can approach the sliding surface in the manner of finite time steps the stability of the overall system is verified by lyapunov stability theory

finite covers of random 3 manifolds a 3 manifold is haken if it contains a topologically essential surface the virtual haken conjecture posits that every irreducible 3 manifold with infinite fundamental group has a finite cover which is haken in this paper we study random 3 manifolds and their finite covers in an attempt to shed light on this difficult question in particular we consider random heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface for this model of random 3 manifold we are able to compute the probabilities that the resulting manifolds have finite covers of particular kinds our results contrast with the analogous probabilities for groups coming from random balanced presentations giving quantitative theorems to the effect that 3 manifold groups have many more finite quotients than random groups the next natural question is whether these covers have positive betti number for abelian covers of a fixed type over 3 manifolds of heegaard genus 2 we show that the probability of positive betti number is 0

optimal fuzzy controller design local concept approach in this paper we present a global optimal and stable fuzzy controller design method for both continuous and discrete time fuzzy systems under both finite and infinite horizons first a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers based on this sufficient condition we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory the stability of the entire closed loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller the optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable but also be stabilized to any desired degree also the total energy of system output is absolutely finite moreover the resultant feedback continuous fuzzy system possesses an infinite gain margin that is its stability is guaranteed no matter how large the feedback gain becomes two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

optimal fuzzy controller design in continuous fuzzy system global concept approach we propose a design method for a global optimal fuzzy controller to control and stabilize a continuous fuzzy system with free or fixed end point under finite or infinite horizon time a linear like global system representation of continuous fuzzy system is first proposed by viewing a continuous fuzzy system in global concept and unifying the individual matrices into synthetical matrices based on this the optimal control law which can achieve global minimum effect is developed theoretically the nonlinear segmental two point boundary value problem is derived for the finite horizon problem and a forward riccati like differential equation for the infinite horizon problem the stability of the closed loop fuzzy system can be ensured by the designed optimal fuzzy controller the optimal closed loop fuzzy system cannot only be guaranteed to be exponentially stable but also be stabilized to any desired degree also the total energy of system output is absolutely finite moreover the resultant closed loop fuzzy system possesses an infinite gain margin

exceptional and cosmetic surgeries on knots we show that the bridge distance of a knot determines a lower bound on the genera of essential surfaces and heegaard surfaces in the manifolds that result from non trivial dehn surgeries on the knot in particular knots with high bridge distance do not admit non trivial non hyperbolic surgeries or non trivial cosmetic surgeries we further show that if a knot has bridge distance at least 3 then its bridge number is bounded above by a function of seifert genus or indeed by the genus of almost any essential surface or heegaard surface in the surgered manifold

stabilization for mapping class groups of 3 manifolds we prove that the homology of the mapping class group of any 3manifold stabilizes under connected sum and boundary connected sum with an arbitrary 3 manifold when both manifolds are compact and orientable the stabilization also holds for the quotient group by twists along spheres and disks and includes as particular cases homological stability for symmetric automorphisms of free groups automorphisms of certain free products and handlebody mapping class groups our methods also apply to manifolds of other dimensions in the case of stabilization by punctures the main result of this paper is a homological stability theorem for mapping class groups of 3 manifolds where the stabilization is by connected sum with an arbitrary 3 manifold more precisely we show that given any two compact connected oriented 3 manifolds n and p with n 6 the homology group hi 0diff n p p rel n z is independent of the number n of copies of p in the connected sum as long as n 2i 2 i e each homology group stabilizes with p we also prove an analogous result for boundary connected sum and a version for the quotient group of the mapping class group by twists along spheres and disks a group closely related to the automorphism group of the fundamental group of the manifold homological stability theorems were first found in the sixties for symmetric groups by nakaoka 36 and linear groups by quillen and now form the foundation of modern algebraic k theory see for example 28 part iv and 42 stability theorems for mapping class groups of surfaces were obtained in the eighties by harer and ivanov 14 25 and recently turned out to be a key ingredient to a solution of the mumford conjecture about the homology of the riemann moduli space 30 the other main examples of families of groups for which stability has been known are braid groups 1 and automorphism groups of free groups 17 18 the present paper extends significantly the class of groups for which homological stability is known to hold it suggests that it is a widespread phenomenon among families of groups containing enough symmetries in addition to the already mentioned stability theorems for mapping class groups of 3 manifolds corollaries of our main result include stability for handlebody subgroups of surface mapping class groups symmetric automorphism groups of free groups and automorphism groups of free products ng for many groups g using similar techniques we obtain stability results also for mapping class groups 0diff m n points rel m for m any m dimensional manifold with boundary m 2 even the case m 2 is new here as well as for the fundamental group 1conf m n of the configuration space of n unordered points in m our paper thus also unifies previous known results as we recover stability for braid groups as 1conf d n symmetric groups as 1conf d n and automorphism groups of free groups as aut nz

the virtual cohomological dimension of the mapping class group of an orientable surface let f f r be the mapping class group of a surface f of genus g with s punctures and r boundary components the purpose of this paper is to establish cohomology properties of f parallel to those of the arithmetic groups if g is a linear algebraic group defined over q x is the symmetric space associated to g and a is an arithmetic subgroup of g then a is virtually torsion free and acts properly discontinuously on x the rational homology of a is the same as that of x a furthermore there is a bordification of x bs to a manifold with corners 3 and an extension of the action of a to a properly discontinuous action on jf so that the quotient x a is compact the boundary of jf is homotopy equivalent to a wedge of spheres say of dimension d and the virtual cohomological dimension of a is n d 1 where n is the dimension of x in the case of the mapping class group there is no analog for g ivanov unpublished has proven that f is not arithmetic nevertheless f acts properly discontinuously on teichmiiller space r which is homeomorphic to euclidean space of dimension 6 g 6 2 s 3 will play the role of the symmetric space the quotient of 9by f is the moduli space of curves whose rational homology is then identified with that of e harvey har has constructed a borel serre bordification j of 3 by analytic methods in the case where f has punctures we will build g by a different combinatorial method in addition we will explicitly describe inside y a cell complex y of dimension 4 g 4 s onto which j may be f equivariantly retracted thus establishing an analog of the constructions for sl n by serre soul6 sol and ash a this complex will be of the lowest possible dimension because we will use j to prove our main result

discrete time optimal fuzzy controller design global concept approach proposes a systematic and theoretically sound way to design a global optimal discrete time fuzzy controller to control and stabilize a nonlinear discrete time fuzzy system with finite or infinite horizon time a linear like global system representation of a discrete time fuzzy system is first proposed by viewing such a system in a global concept and unifying the individual matrices into synthetic matrices then based on this kind of system representation a discrete time optimal fuzzy control law which can achieve a global minimum effect is developed theoretically a nonlinear two point boundary value problem tpbvp is derived as a necessary and sufficient condition for the nonlinear quadratic optimal control problem to simplify the computation a multi stage decomposition of the optimization scheme is proposed and then a segmental recursive riccati like equation is derived moreover in the case of time invariant fuzzy systems we show that the optimal controller can be obtained by just solving discrete time algebraic riccati like equations based on this several fascinating characteristics of the resultant closed loop fuzzy system can easily be elicited the stability of the closed loop fuzzy system can be ensured by the designed optimal fuzzy controller the optimal closed loop fuzzy system can not only be guaranteed to be exponentially stable but also stabilized to any desired degree also the total energy of system output is absolutely finite moreover the resultant closed loop fuzzy system possesses an infinite gain margin i e its stability is guaranteed no matter how large the feedback gain becomes an example is given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proven stability properties

guaranteed cost control of t s fuzzy systems with state and input delays this paper focuses on the problem of guaranteed cost control for t s fuzzy systems with state and input delays stability and stabilization conditions are first proposed which are delay dependent for state delay and delay independent for input delay further the guaranteed cost problem is addressed all the results are presented in terms of linear matrix inequalities lmis some examples are used to illustrate the effectiveness and feasibility of the approaches proposed in this paper

a global exponential fuzzy observer design for time delay takagi sugeno uncertain discrete fuzzy bilinear systems with disturbance a robust h fuzzy observer is proposed for a class of time delay takagi sugeno t s uncertain discrete fuzzy bilinear systems with disturbance utilizing the lipschitz conditions and some variable transformations a linear matrix inequality lmi approach is developed and a sufficient condition is obtained to design the robust h fuzzy observer the robust h fuzzy observer for time delay t s uncertain discrete fuzzy bilinear systems with disturbance can be obtained directly through the lmis with no preassigned matrices the convergent rate of the error state can be estimated from the initial conditions and the delay time of t s uncertain discrete fuzzy bilinear systems the designed robust h fuzzy observer can guarantee the dynamics of the observer error to be globally exponentially stable and has a prescribed h performance a numerical example is given to demonstrate the feasibility and effectiveness of the proposed observer design method

a novel takagi sugeno based robust adaptive fuzzy sliding mode controller in this paper a nonlinear dynamic system is first approximated by n fuzzy based linear state space subsystems to track a trajectory dominant by a specific frequency the reference models with desired amplitude and phase features are established by the same fuzzy sets of the system rule similarly the same fuzzy sets of the system rule are employed to design robust fuzzy sliding mode control rfsmc and adaptive fuzzy sliding mode control afsmc the difference between rfsmc and afsmc is that afsmc contains an updating law to learn system uncertainties and then an extra compensation is designed it is different from the most previous papers to learn the whole nonlinear functions as the norm of the sliding surface is inside of a defined set the updating law starts simultaneously as it is outside of the other set the updating law stops for the purpose of smoothing the possibility of discontinuous control input a transition between rfsmc and afsmc is also assigned under the circumstances the proposed control robust adaptive fuzzy sliding mode control rafsmc can automatically tune as a rfsmc or an afsmc then the advantages coming from the rfsmc and afsmc are obtained finally the stabilities of the overall system of rfsmc afsmc and rafsmc are verified by lyapunov stability theory the compared simulations among rfsmc afsmc and rafsmc are also carried out to confirm the usefulness of the proposed control scheme

the classification of punctured torus groups thurston s ending lamination conjecture proposes that a flnitely generated kleinian group is uniquely determined up to isometry by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends we present a proof of this conjecture for punctured torus groups these are free two generator kleinian groups with parabolic commutator which should be thought of as representations of the fundamental group of a punctured torus as a consequence we verify the conjectural topological description of the deformation space of punctured torus groups including bers conjecture that the quasi fuchsian groups are dense in this space and prove a rigidity theorem two punctured torus groups are quasi conformally conjugate if and only if they are topologically conjugate

oe and w superrigidity results for actions by surface braid groups we show that several important normal subgroups of the mapping class group of a surface satisfy the following property any free ergodic probability measure preserving action y x is stablyoe superrigid these include the central quotients of most surface braid groups and most torelli groups and johnson kernels in addition we show that all these groups satisfy the measure equivalence rigidity and we describe all their lattice embeddings using these results in combination with previous results from cik13 we deduce that any free ergodic probabilitymeasure preserving action of almost any surface braid group is stablyw superrigid i e it can be completely reconstructed from its vonneumann algebra

robust fuzzy observer based fuzzy control design for nonlinear discrete time systems with persistent bounded disturbances to date nonlinear l infin gain control problems have not been solved by the conventional control methods for nonlinear discrete time systems with persistent bounded disturbances this study introduces fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer to deal with the nonlinear l infin gain control problem the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables first the takagi sugeno t s fuzzy model is employed to represent the nonlinear discrete time system next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to minimize the upper bound of l infin gain of the closed loop system under some nonlinear matrix inequality non lmi constraints a novel decoupled method is proposed in this study to transform the non lmi conditions into some linear matrix inequality lmi forms by the proposed decoupled method and the genetic algorithm the l infin gain fuzzy observer based fuzzy control problem for the nonlinear discrete time systems can be easily solved by an lmi based optimization method the proposed methods which efficiently attenuate the peak of perturbation due to persistent bounded disturbances extend the l infin gain control problems from linear discrete time systems to nonlinear discrete time systems a simulation example is given to illustrate the design procedures and to confirm the l infin gain performance of the proposed method

analysis and design for a class of complex control systems part i fuzzy modelling and identification this paper is the first of two dealing with the analysis and design of a class of complex control systems this part deals with fuzzy modelling and identification the second paper is concerned with fuzzy controller design we believe that these two papers show a way to analyze and design complex control systems using a combination of fuzzy logic and modern control theory the complex systems studied in these two papers can be represented by a fuzzy aggregation of a set of local linear models the identification can be divided into two procedures the first procedure is the identification of the membership functions including the determination of the number of fuzzy rules and the estimation of the parameters in the membership functions the second is the identification of the local linear models including the determination of the structure and the parameters of the local rule maps and the global rule interpolation two examples are used to demonstrate the application of the modelling method

further comment on optimal fuzzy controller design local concept approach stability analysis and optimality are important in any systems in the paper optimal fuzzy controller design local concept approach optimal fuzzy controller is design for takagi sugeno fuzzy model unfortunately it seems that some errors are happen and no simple correction can be done in this paper we show that some errors exit in the aforementioned paper with simple and clear examples

surjectivity of the total clifford invariant and brauer dimension abstract a celebrated theorem of merkurjev that the 2 torsion of the brauer group is represented by clifford algebras of quadratic forms is in general false when the base is no longer a field the first counterexamples when the base is among certain arithmetically subtle hyperelliptic curves over local fields were constructed by parimala scharlau and sridharan we prove that considering clifford algebras of all line bundle valued quadratic forms such counterexamples disappear and we recover merkurjev s theorem in these cases for any smooth curve over a local field or any smooth surface over a finite field the 2 torsion of the brauer group is always represented by clifford algebras of line bundle valued quadratic forms

robust h control of takagi sugeno fuzzy systems with state and input time delays this paper addresses the robust h fuzzy control problem for nonlinear uncertain systems with state and input time delays through takagi sugeno t s fuzzy model approach the delays are assumed to be interval time varying delays and no restriction is imposed on the derivative of time delay based on lyapunov krasoviskii functional method delay dependent sufficient conditions for the existence of an h controller are proposed in linear matrix inequality lmi format illustrative examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology

anomalous partially hyperbolic diffeomorphisms ii stably ergodic examples we construct examples of robustly transitive and stably ergodic partially hyperbolic diffeomorphisms f on compact 3 manifolds with fundamental groups of exponential growth such that f n is not homotopic to identity for all n 0 these provide counterexamples to a classification conjecture of pujals

comment on optimal fuzzy controller design local concept approach with reply this paper points out some errors existing in the aforementioned paper unfortunately it seems that no immediate correction can be done the authors reply is provided

stable and optimal fuzzy control of linear systems a number of stable and optimal fuzzy controllers are developed for linear systems based on some classical results in control theory we design the structure and parameters of fuzzy controllers such that the closed loop fuzzy control systems are stable provided that the process under control is linear and satisfies certain conditions it turns out that if stability is the only requirement there is much freedom in choosing the fuzzy controller parameters therefore a performance criterion is set to optimalize the parameters using the pontryagin minimum principle we design an optimal fuzzy controller for linear systems with quadratic cost function finally the optimal fuzzy controller is applied to a ball and beam system

a recipe for short word pseudo anosovs given any generating set of any subgroup g of the mapping class group of a surface we find an element f with word length bounded by a constant k depending only on the surface and with the property that the minimal subsurface supporting a power of f is as large as possible for elements of g in particular if g contains a pseudo anosov map we find one of word length at most k we also find new examples of convex cocompact free subgroups of the mapping class group

frequency shaping for fuzzy control systems with unknown non linear plants by a learning method of neural network abstract this paper deals with a frequency shaping which means an improvement of frequency response for fuzzy control systems with unknown non linear plants by a learning method of neural network we derive an important theorem which is related to phase lead compensation by introducing concept of frequency characteristics such as gain crossover frequency and phase margin using the theorem a fuzzy phase lead compensator which have parameters for effectively compensating phase characteristics of control systems is constructed after proposing a design procedure of the fuzzy phase lead compensator for linear plants we extend it to a design procedure for unknown non linear plants a frequency shaping for unknown non linear plants is realized by widrow hoff learning rule which is a basic learning algorithm of neural networks simulation results show the effect of frequency shaping by widrow hoff learning rule