modular forms on non linear double covers of algebraic groups we construct automorphic representations of non linear two fold covers of simply connected chevalley groups via residues of eisenstein series in the process we establish some basic results in representation theory of local groups

unitary shimura correspondences for split real groups we find a relationship between certain complementary series representations for nonlinear coverings of split simple groups and spherical complementary series for different linear groups the main technique is barbasch s method of calculating some intertwining operators purely in terms of the weyl group

new design and stability analysis of fuzzy proportional derivative control systems this paper describes the design principle tracking performance and stability analysis of a fuzzy proportional derivative pd controller first the fuzzy pd controller is derived from the conventional continuous time linear pd controller then the fuzzification control rule base and defuzzification in the design of the fuzzy pd controller are discussed in detail the resulting controller is a discrete time fuzzy version of the conventional pd controller which has the same linear structure in the proportional and the derivative parts but has nonconstant gains both the proportional and derivative gains are nonlinear functions of the input signals the new fuzzy pd controller thus preserves the simple linear structure of the conventional pd controller yet enhances its self tuning control capability computer simulation results have demonstrated this advantage of the fuzzy pd controller particularly when the process to be controlled is nonlinear after a detailed stability analysis where a simple and realistic sufficient condition for the bounded input bounded output stability of the overall feedback control system was derived several computer simulation results are compared with the conventional pd controller although the conventional and fuzzy pd controllers are not exactly comparable the authors compare them in order to have a sense of how well the fuzzy pd controller performs for this reason in the simulations several first order and second order linear systems with or without time delays are first used to test the performance of the fuzzy pd controller for step reference inputs the fuzzy pd control systems show remarkable performance as well as if not better than the conventional pd control systems moreover the fuzzy pd controller is compared to the conventional pd controller for a particular second order linear system showing the advantage of the fuzzy pd controller over the conventional one in the sense that in order to obtain the same control performance the conventional pd controller has to employ an extremely large gain while the fuzzy controller uses a reasonably small gain finally in the case of nonlinear systems the authors provide some examples to show that the fuzzy pd controller can track the set points satisfactorily but the conventional pd controller cannot

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

robust design of rule based fuzzy controllers this paper deals with the design of stable and robust rule based fuzzy control systems new expressions to compute indices which provide a measure of the stability and robustness of fuzzy control systems are presented the relation between the modification of the rules and the stability is studied through the so called sensitivity indices the paper presents procedures that make use of these indices to improve the design of fuzzy control systems including the modification of the rules to obtain the global stability of an unstable system with multiple attractors and to improve the dynamic behavior or the robustness of a non linear plant an example with a fuzzy controller for a system with non linear damping and saturation in the actuation is presented to illustrate the design procedure

stable adaptive control of fuzzy dynamic systems this paper discusses fuzzy model reference adaptive control for a class of nonlinear systems the system concerned is represented by a family of local transfer function models smoothly connected together by fuzzy membership functions the model reference adaptive control law is first designed in each local region and then constructed in global domain it is shown that the resulting fuzzy adaptive control system is globally stable based on a suitable piecewise differentiable lyapunov function a simulation example is given for demonstration of the application of the method

quadratic functions in geometry topology and m theory we describe an interpretation of the kervaire invariant of a riemannian manifold of dimension 4k 2 in terms of a holomorphic line bundle on the abelian variety h 2k 1 m otimes r z our results are inspired by work of witten on the fivebrane partition function in m theory hep th 9610234 hep th 9609122 our construction requires a refinement of the algebraic topology of smooth manifolds better suited to the needs of mathematical physics and is based on our theory of differential functions these differential functions generalize the differential characters of cheeger simons and the bulk of this paper is devoted to their study

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

semiglobal stabilization of nonlinear systems using fuzzy control and singular perturbation methods singular perturbation methods based on a lyapunov approach are implemented for the derivation of sufficient conditions for the semiglobal stabilization with output tracking of nonlinear systems having internal dynamics the key idea of this approach lies in the decomposition of the full system into a subsystem exhibiting fast dynamics and to a subsystem with slow dynamics resulting in a substantial simplification of the stability analysis this two time scale behavior is achieved by implementing a properly designed fuzzy logic controller the key element of the proposed model based composite controller for the construction of the model based controller a new identification technique based on both classical and fuzzy tools is proposed results are presented for the semiglobal stabilization of a continuous stirred tank reactor which is a process with high nonlinear behavior

a methodology to design stable nonlinear fuzzy control systems the stability of nonlinear systems has to be investigated without making linear approaches in order to do this there are several techniques based on lyapunov s second method for example krasovskii s method allows to prove the sufficient condition for the asymptotic stability of nonlinear systems this method requires the calculation of the jacobian matrix in this paper an equivalent mathematical closed loop model of a multivariable nonlinear control system based on fuzzy logic theory is developed later this model is used to compute the jacobian matrix of a closed loop fuzzy system next an algorithm to solve the jacobian matrix is proposed the algorithm uses a methodology based on the extension of the state vector the developed algorithm is completely general it is independent of the type of membership function that is chosen for building the fuzzy plant and controller models and it allows the compound of different membership functions in a same model we have developed a matlab s function that implements the improved algorithm together with a series of additional applications for its use the designed software provides complementary functions to facilitate the reading and writing of fuzzy systems as well as an interface that makes possible the use of all the developed functions from the matlab s environment which allows to complement and to extend the possibilities of the matlab s fuzzy logic toolbox an example with a fuzzy controller for a nonlinear system to illustrate the design procedure is presented the work developed in this paper can be useful for the analysis and synthesis of fuzzy control systems

the pfaffian line bundle we analyze the holomorphic pfaffian line bundle defined over an infinite dimensional isotropic grassmannian manifold using the infinite dimensional relative pfaffian we produce a fock space structure on the space of holomorphic sections of the dual of this bundle on this fock space an explicit and rigorous construction of the spin representations of the loop groupslo n is given we also discuss and prove some facts about the connection between the pfaffian line bundle over the grassmannian and the pfaffian line bundle of a dirac operator

stable and optimal adaptive fuzzy control of complex systems using fuzzy dynamic model a design method is presented for the stabilization of multivariable complex nonlinear systems which can be represented by fuzzy dynamic model firstly an adaptive fuzzy control law is addressed then the closed loop fuzzy system is robustly stabilized under some bounded perturbations and disturbances by adding a supervising controller based on the variable structure control theory of uncertain systems a sufficient condition for the stability of the closed loop fuzzy system is also derived using the concept of connective stability in decentralized control of large scale systems under this condition an optimal fuzzy controller is designed with genetic algorithms two examples are given to illustrate the application of the method

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

l 2 stabilization design for fuzzy control systems system s stability is the most important requirement in control system designs fuzzy control system fcs should satisfy this requirement also this paper shows that a linear plant with the formulated fuzzy logic controller flc is a nonlinear system and its stability can be analyzed by applying the small gain theorem or the circle criterion by these two criteria three flc design procedures are introduced to guarantee the stabilization of the fcs finally two examples are given to confirm the availability of the proposed design approaches

bundle gerbes for chern simons and wess zumino witten theories we develop the theory of chern simons bundle 2 gerbes and multiplicative bundle gerbes associated to any principal g bundle with connection and a class in h4 bg for a compact semi simple lie group g the chern simons bundle 2 gerbe realises differential geometrically the cheeger simons invariant we apply these notions to refine the dijkgraaf witten correspondence between three dimensional chern simons functionals and wess zumino witten models associated to the group g we do this by introducing a lifting to the level of bundle gerbes of the natural map from h4 bg to h3 g the notion of a multiplicative bundle gerbe accounts geometrically for the subtleties in this correspondence for non simply connected lie groups the implications for wess zumino witten models are also discussed

observer based robust fuzzy control of nonlinear systems with parametric uncertainties this paper addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties and the state variables unavailable for measurement the takagi sugeno t s fuzzy model system with parametric uncertainties is adopted for modeling the nonlinear system and establishing fuzzy state observer sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability and are formulated in the format of linear matrix inequalities lmis the effectiveness of the proposed fuzzy controller and fuzzy observer design methodology is finally demonstrated through numerical simulations on an inverted pendulum system

a general and formal methodology to design stable nonlinear fuzzy control systems the price to be paid for the great dynamic richness of nonlinear systems is the lack of a unitary theory that allows control system design to be tacked in a way that is parallel or analogous to that of linear systems we propose a general methodology that uses fuzzy logic to systematically and formally synthesize nonlinear control systems which are stable by design although this methodology is based on lyapunov theory it avoids searching for lyapunov functions this allows the synthesis procedure to be systematic as well as formal and especially independent of heuristics some examples of nonlinear control are solved in this paper thus allowing assessment of the proposed methodology

robust stability analysis of fuzzy control systems abstract robust stability of fuzzy control systems is studied through the popov lyapunov approach first we transform a fuzzy control system into a lur e system with uncertainties or nonlinearities second the lyapunov s direct method is used to guarantee the stability of the perturbed lur e system and then a robustness measurement which gives the bound on allowable uncertainties or nonlinearities is derived also if the bound of the uncertainties nonlinearities of the system is known we can find an estimated region of asymptotic stability in phase space a nonlinear numerical example and a magnetic bearing experiment demonstrating the feasibility of the method are illustrated

covers of tori over local and global fields langlands has described the irreducible admissible representations of t when t is the group of points of an algebraic torus over a local field also langlands described the automorphic representations of t bbb a when t bbb a is the group of adelic points of an algebraic torus over a global field f we describe irreducible in the local setting and automorphic in the global setting epsilon genuine representations for covers of tori also known as metaplectic tori which arise from a framework of brylinski and deligne in particular our results include a description of spherical hecke algebras in the local unramified setting and a global multiplicity estimate for automorphic representations of covers of split tori for automorphic representations of covers of split tori we prove a multiplicity one theorem

eta invariants and their adiabatic limits 0 introduction 1 algebraic preliminaries 2 the finite dimensional case superconnections a odd dimensional base spaces b even dimensional base spaces appendix 1 coupling to general superconnections 3 auxiliary grassman variables and auxiliary adiabatic limits 4 the infinite dimensional case fibrations a elementary geometry of fibrations b odd dimensional base spaces c even dimensional base spaces d the case in which the dirac operator on the fiber is not invertible appendix 2 multifibrations

stability analysis and synthesis of multivariable fuzzy systems using interval arithmetic abstract this paper deals with the design of stable rule based fuzzy control systems interval analysis is applied to design a stable fuzzy takagi sugeno kang controller using a robust condition to ensure the stability the presented methodology starts with a state model of the plant finds a candidate fuzzy controller and uses an interval arithmetic algorithm to verify the stability of closed loop fuzzy model it is important to emphasize the generality of the presented methodology for fuzzy controller synthesis since there are no constraints in the state vector nor in the control vector this methodology can also be used with nonlinear plant models in previous works we showed the applicability of the interval analysis to design a controller that ensures the stability of first order nonlinear system in this paper we extend the analysis and the synthesis of stable fuzzy control system to the multivariable case an example with a fuzzy controller for a nonlinear system is presented to illustrate the design procedure

gain tuning of fuzzy pid controllers for mimo systems a performance driven approach a new methodology for tuning the scaling factors or gains of fuzzy proportional integral derivative controllers by taking explicitly into account the closed loop system performance is proposed in this study the solution is obtained by solving a nonlinear constrained optimization problem considering a set of constraints on the scaling factors of the mamdani type fuzzy system and on the plant s inputs and outputs two distinct approaches are presented which are associated with the optimization being carried out offline or in real time the offline tuning scheme assumes the system dynamics described by a nonlinear model while for the real time implementation the plant s dynamics is locally approximated by a linear model with the underlying parameters recursively updated in order to cope with rather stringent sampling time requirements the constrained online optimization problem is implemented based on the grid computing paradigm given the adaptive nature of the real time scheme time varying dynamics and unknown disturbances can be accommodated in such a way that the closed loop performance is effectively maximized while avoiding wind up phenomena induced by the integrator term the proposed tuning methodologies are assessed on a benchmark three tank system and compared against a conventional based tuning approach results from experiments illustrate the feasibility of the proposed approaches and also all the relevance in optimal control systems based on mamdani type fuzzy controllers

setting the quantum integrand of m theory in anomaly free quantum field theories the integrand in the bosonic functional integral the exponential of the effective action after integrating out fermions is often defined only up to a phase without an additional choice we term this choice setting the quantum integrand in the low energy approximation to m theory the e8 model for the c field allows us to set the quantum integrand using geometric index theory we derive mathematical results of independent interest about pfaffians of dirac operators in 8k 3 dimensions both on closed manifolds and manifolds with boundary these theorems are used to set the quantum integrand of m theory for closed manifolds and for compact manifolds with either temporal global or spatial local boundary conditions in particular we show that m theory makes sense on arbitrary 11 manifolds with spatial boundary generalizing the construction of heterotic m theory on cylinders

stability and stabilizability of fuzzy neural linear control systems this paper discusses stability analysis of fuzzy neural linear fnl control systems which consist of combinations of fuzzy models neural network nn models and linear models the authors consider a relation among the dynamics of nn models those of fuzzy models and those of linear models it is pointed out that the dynamics of linear models and nn models can be perfectly represented by takagi sugeno t s fuzzy models whose consequent parts are described by linear equations in particular the authors present a procedure for representing the dynamics of nn models via t s fuzzy models next the authors recall stability conditions for ensuring stability of fuzzy control systems in the sense of lyapunov the stability criteria is reduced to the problem of finding a common lyapunov function for a set of lyapunov inequalities the stability conditions are employed to analyze stability of fnl control systems finally stability analysis for four types of fnl control systems is demonstrated

an integral riemann roch theorem for surface bundles abstract this paper is a response to a conjecture by t akita about an integral riemann roch theorem for surface bundles

bundle 2 gerbes we make the category textbf bgrb m of bundle gerbes on a manifold m into a 2 category by providing 2 cells in the form of transformations of bundle gerbe morphisms this description of textbf bgrb m as a 2 category is used to define the notion of a bundle 2 gerbe to every bundle 2 gerbe on m is associated a class in h 4 m mathbb z we define the notion of a bundle 2 gerbe connection and show how this leads to a closed integral differential 4 form on m which represents the image in real cohomology of the class in h 4 m mathbb z some examples of bundle 2 gerbes are discussed including the bundle 2 gerbe associated to a principal g bundle p to m it is shown that the class in h 4 m mathbb z associated to this bundle 2 gerbe coincides with the first pontryagin class of p this example was previously considered from the point of view of 2 gerbes by brylinski and mclaughlin

string structures and trivialisations of a pfaffian line bundle the present paper is a contribution to categorial index theory its main result is the calculation of the pfaffian line bundle of a certain family of real dirac operators as an object in the category of line bundles furthermore it is shown how string structures give rise to trivialisations of that pfaffian