co volume methods for degenerate parabolic problems a complementary volume co volume technique is used to develop a physically appealing algorithm for the solution of degenerate parabolic problems such as the stefan problem it is shown that these algorithms give rise to a discrete semigroup theory that parallels the continuous problem in particular the discrete stefan problem gives rise to nonlinear semigroups in both the discretel 1 andh 1 spaces

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

anisotropic singular perturbations the vectorial case we obtain the l 1 limit of the sequence where e e is the family of anisotropic perturbations of the nonconvex functional of vector valued functions the proof relies on the blow up argument introduced by fonseca and muller

an alternating crank nicolson method for decoupling the ginzburg landau equations the time dependent ginzburg landau model of superconductors consists of coupled nonlinear partial differential equations which presents difficulties in the numerical solution we present an alternating crank nicolson method for this model that leads to two decoupled algebraic subsystems one is linear and the other is semilinear both have nice numerical properties and can be solved by efficient matrix solvers we show the stability and convergence and derive error estimates for this scheme numerical results are also reported

the postulations a la d alembert and a la cauchy for higher gradient continuum theories are equivalent a review of existing results in order to found continuum mechanics two different postulations have been used the first introduced by lagrange and piola starts by postulating how the work expended by internal interactions in a body depends on the virtual velocity field and its gradients then by using the divergence theorem a representation theorem is found for the volume and contact interactions which can be exerted at the boundary of the considered body this method assumes an a priori notion of internal work regards stress tensors as dual of virtual displacements and their gradients deduces the concept of contact interactions and produces their representation in terms of stresses using integration by parts the second method conceived by cauchy and based on the celebrated tetrahedron argument starts by postulating the type of contact interactions which can be exerted on the boundary of every suitably regular part of a body then it proceeds by proving the existence of stress tensors from a balance type postulate in this paper we review some relevant literature on the subject discussing how the two postulations can be reconciled in the case of higher gradient theories finally we underline the importance of the concept of contact surface edge and wedge s order forces

phase field computations of single needle crystals crystal growth and motion by mean curvature the phase field model for free boundaries consists of a system of parabolic differential equations in which the variables represent a phase or order parameter and temperature respectively the parameters in the equations are related directly to the physical observables including the interfacial width epsilon which we can regard as a free parameter in computation the phase field equations can be used to compute a wide range of sharp interface problems including the classical stefan model its modification to incorporate surface tension and or surface kinetic terms the cahn allen motion by mean curvature the hele shaw model etc also included is anisotropy in the equilibrium and dynamical forms generally considered by materials scientists by adjusting the parameters the computations can be varied continuously from single needle dendritic to faceted crystals the computational method consists of smoothing a sharp interface problem within the scaling of distinguished limits of the phase field e

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

computational simulation of flux trapping and vortex pinning in type ii superconductors effects of pointwise thickness variations and material inhomogeneities in the dynamics of vorticies are investigated by means of appropriately formulated time dependent ginzburg landau tdgl based models for inhomogeneous thin films having constant thickness and homogeneous thin films having variable thickness the resulting models are solved numerically using a nonstandard finite difference method for spatial discretization and a modified forward euler method for temporal discretization in particular vortex pinning and flux trapping phenomena in both types of films are investigated our numerical simulations indicate that the dynamics of vortices are mostly affected by inhomogeneities introduced in the chemical composition of a material as compared to variations introduced in thickness of the material

spherical harmonics and basic coupling coefficients for the group so 5 in an so 3 basis an easily programmable algorithm is given for the computation of so 5 spherical harmonics needed to complement the radial beta wave functions to form an orthonormal basis of wave functions for the five dimensional harmonic oscillator it is shown how these functions can be used to compute the clebsch gordan a k a wigner coupling coefficients for combining pairs of irreps in this space to other irreps this is of particular value for the construction of the matrices of hamiltonians and transition operators that arise in applications of nuclear collective models tables of the most useful coupling coefficients are given in the appendix

resolution of missing label problems a new perspective on k matrix theory k matrix theory is an effective algebraic way of determining inner products and constructing orthonormal bases vectors for the carrier spaces of induced representations of lie groups and lie algebras the theory is applied in this paper to give canonical resolutions of missing label problems

numerical study of quantized vortex interaction in complex ginzburg landau equation on bounded domains in this paper we study numerically quantized vortex dynamics and their interaction in the two dimensional complex ginzburg landau equation cgle with a dimensionless parameter e 0 on bounded domains under either dirichlet or homogeneous neumann boundary condition we begin with a review of the reduced dynamical laws rdls for time evolution of quantized vortex centers in cgle and show how to solve these nonlinear ordinary differential equations numerically then we present efficient and accurate numerical methods for solving the cgle on either a rectangular or a disk domain under either dirichlet or homogeneous neumann boundary condition based on these efficient and accurate numerical methods for cgle and the rdls we explore rich and complicated quantized vortex dynamics and interaction of cgle with different e and under different initial physical setups including single vortex vortex pair vortex dipole and vortex lattice compare them with those obtained from the corresponding rdls and identify the cases where the rdls agree qualitatively and or quantitatively as well as fail to agree with those from cgle on vortex interaction finally we also obtain numerically different patterns of the steady states for quantized vortex lattices in the cgle dynamics on bounded domains

representation of the five and six dimensional harmonic oscillators in a u 5 so 5 so 3 basis the duality that exists between the two subgroups su 1 1 and o 5 of sp 5 r to construct basis states for the five dimensional harmonic oscillator which simultaneously reduce the sp 5 r u 5 o 5 so 3 and sp 5 r su 1 1 u 1 subgroup chains is used it is shown that the vector coherent state wave functions of the fundamental five dimensional so 5 irrep 1 0 realize the traceless bosons introduced by lohe and hurst to classify the irreps of the orthogonal groups and employed in chacon moshinsky and sharp s construction of a basis for the five dimensional harmonic oscillator moreover it is shown that vcs theory provides a simple mechanism for constructing matrix elements of the traceless boson operators these matrix elements are used to extend the vcs representations of so 5 in an so 3 basis given in a previous paper to irreps of u 5 in an so 5 so 3 basis the extension to u 6 u 5 so 5 so 3 is also given

quadrupole collective variables in the natural cartan weyl basis the matrix elements of the quadrupole collective variables emerging from collective nuclear models are calculated in the natural cartan weyl basis of o 5 which is a subgroup of a covering su 1 1 o 5 structure making use of an intermediate set method explicit expressions of the matrix elements are obtained in a pure algebraic way fixing the rotational structure of collective quadrupole models

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

analysis and approximation of the ginzburg landau model of superconductivity the authors consider the ginzburg landau model for superconductivity first some well known features of superconducting materials are reviewed and then various results concerning the model the resultant differential equations and their solution on bounded domains are derived then finite element approximations of the solutions of the ginzburg landau equations are considered and error estimates of optimal order are derived

a lyapunov type theorem for dissipative numerical integrators with adaptive time stepping the asymptotic behavior of continuous dissipative systems and dissipative numerical integrators with fixed time stepping can be fully investigated by a lyapunov type theorem on continuous and discrete dynamical systems respectively however once adaptive time stepping is involved such theories cease to work and usually the dynamics should be investigated from the past instead of the standard forward way such as in terms of pullback attractors in this paper we present a different approach we stick to a forward definition of limit sets and show that still we can establish a lyapunov type theorem which reveals the precise asymptotic behavior of adaptive time stepping integrators in the presence of a discrete lyapunov functional

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

second variation of liquid crystal energy at x x dagger a new and simplified proof of the sign of the second variation of the oseen frank energy in terms of the elastic constants is given the proof relies on the frame indifference of the energy and a new expression for the second invariant null lagrangian as a surface integral

a dynamic programming approach to nonlinear boundary control problems of parabolic type abstract in this paper we study a hamilton jacobi equation related to the boundary control of a parabolic equation with neumann boundary conditions the state space of this problem is a hilbert space and the equation is defined classically only on a dense subset of the state space moreover the hamiltonian appearing in the equation contains fractional powers of an unbounded operator these facts render the problem difficult in this paper we give a revised definition of a viscosity solution to accommodate the unboundness of the hamiltonian we then obtain existence and uniqueness results for viscosity solutions in particular we show that under suitable assumptions the value function of the boundary control problem is the unique viscosity solution of the related hamilton jacobi equation

vector coherent state theory of the generic representations of so 5 in an so 3 basis for applications of group theory in quantum mechanics one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some hamiltonian of interest here we use vector coherent state techniques to develop an algorithm for constructing the matrices for arbitrary finite dimensional irreps of the so 5 lie algebra in an so 3 basis the so 3 subgroup of so 5 is defined by regarding so 5 as linear transformations of the five dimensional space of an so 3 irrep of angular momentum two a need for such irreps arises in the nuclear collective model of quadrupole vibrations and rotations the algorithm has been implemented in maple and some tables of results are presented

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

finite element methods for the time dependent ginzburg landau model of superconductivity abstract the initial boundary value problem for the time dependent ginzburg landau equations that model the macroscopic behavior of superconductors is considered the convergence of finite dimensional semidiscrete galerkin approximations is studied as is a fully discrete scheme the results of some computational experiments are presented

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

construction of su 3 irreps in canonical so 3 coupled bases alternative methods for defining canonical so 3 coupled bases for su 3 irreps are considered and compared it is shown that a basis that diagonalizes a particular linear combination of so 3 invariants in the su 3 universal enveloping algebra gives basis states that have good k quantum numbers in the asymptotic rotor model limit

unconditional superconvergence analysis of a linearized crank nicolson galerkin fem for generalized ginzburg landau equation abstract in this paper we study an effective numerical method for the generalized ginzburg landau equation gle based on the linearized crank nicolson difference method in time and the standard galerkin finite element method with bilinear element in space the time discrete and space time discrete systems are both constructed we focus on a rigorous analysis and consideration of unconditional superconvergence error estimates of the discrete schemes firstly by virtue of the temporal error results the regularity for the time discrete system is presented secondly the classical ritz projection is used to obtain the spatial error with order o h 2 in the sense of l 2 norm thanks to the relationship between the ritz projection and the interpolated projection the superclose estimate with order o 2 h 2 in the sense of h 1 norm is derived thirdly it follows from the interpolated postprocessing technique that the global superconvergence result is deduced finally some numerical results are provided to confirm the theoretical analysis

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

numerical approximations of the ginzburg landau models for superconductivity in this paper we review various methods for the numerical approximations of the ginzburg landau models of superconductivity particular attention is given to the different treatment of gauge invariance in both the finite element finite difference and finite volume settings representative theoretical results typical numerical simulations and computational challenges are presented generalizations to other relevant models are also discussed

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

a regularized equation for anisotropic motion by curvature for realistic interfacial energies the equations of anisotropic motion by curvature exhibit backward parabolic behavior over portions of their domain thereby inducing phenomena such as the formation of facets and wrinkles in this paper a physically consistent regularized equation that may be used to analyze such phenomena is derived

a rotor expansion of the su 3 lie algebra vector coherent state vcs theory is used to give a rotor expansion of the su 3 lie algebra in a way that parallels the boson expansions that have been made for other lie algebras the construction provides a systematic procedure for calculating hermitian matrix elements of su 3 in an so 3 coupled basis and represents a new development in vcs theory and in the theory of induced representations

singular perturbations in manufacturing an asymptotic analysis for a large class of stochastic optimization problems arising in manufacturing is presented a typical example of the problems considered in this paper is a production planning problem with random capacity and demand in this example it is assumed that the capacity of the system fluctuates faster than the other quantities the general model considered here also has a fast controlled markov process in its state description by using the difference in the time scales of different quantities the problem is simplified by averaging out the fast process then asymptotically optimal strategies are constructed from the optimal solutions of the limiting problems the proofs of these results use the theory of viscosity solutions to dynamic programming equations however the formal construction of the asymptotically optimal strategies does not require knowledge of this theory

a double rotor coherent state construction of the wigner supermultiplet su 4 contains implies su 2 su 2 a double rotor vector coherent state construction of the su 4 3 su 2 x sup wigner supermultiplet leads to a simple matrix representation of this scheme matrix elements of the vector coherent state realizations of the group generators are given by very simple expressions in tem of ordinary spin s and isospin t wigner coefficients with intrinsic projection labels ks and kg the k mawix technique is used to effectively elevate these labels lo the status of good quantum numbers the kkt matrices bre given in analytic form for a number of impomt irreducible representations

a new mathematical foundation for contact interactions in continuum physics the investigation of contact interactions such as traction and heat flux that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics however the traditional theory of stress established by cauchy and extended by noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks corner singularities and fracture this paper provides a new mathematical foundation for the treatment of contact interactions based on mild physically motivated postulates which differ essentially from those used before the existence of a corresponding interaction tensor is established while in earlier treatments contact interactions are basically defined on surfaces here contact interactions are rigorously considered as maps on pairs of subbodies this allows the action exerted on a subbody to be defined not only as usual for sets with a sufficiently regular boundary but also for borel sets which include all open and all closed sets in addition to the classical representation of such interactions by means of integrals on smooth surfaces a general representation using the distributional divergence of the tensor is derived in the case where concentrations occur this new approach allows a description of contact phenomena more precise than before

discrete gauge invariant approximations of a time dependent ginzburg landau model of superconductivity we present here a mathematical analysis of a nonstandard difference method for the numerical solution of the time dependent ginzburg landau models of superconductivity this type of method has been widely used in numerical simulations of the behavior of superconducting materials we also illustrate some of their nice properties such as the gauge invariance being retained in discrete approximations and the discrete order parameter having physically consistent pointwise bound

memory effects in homogenisation linear second order equations the theory of homogenisation treats the question if the solutions u of the problems a u f converge weakly to the function u 0 can an operator a 0 be found such that u 0 is a solution of the problem a 0 u 0 f and is a 0 of the same type as a we study an example where the answer is negative we take a a varepsilon t text partial x 2 b varepsilon t text partial x c varepsilon t and show that a 0 a text eff t text partial x 2 b text eff t text partial x c text eff t k is an integrodifferential operator the expression for k is deduced under two different sets of assumptions bounds in l 1 or l 2 the l 2 setting uses the fourier transform and natural assumptions on the coefficients a b and c boundedness in l and uniform ellipticity the answer in the l 1 setting is obtained only under additional assumptions which seem to be unnecessary finally the description of the memory term is given for a problem on a bounded interval by using the eigenfunction expansion and a representation theorem for nevanlinna functions in one space dimension the equation a varepsilon t text partial x 2 u varepsilon x t b varepsilon t text partial x u varepsilon x t c varepsilon t text u varepsilon x t f x t is studied while in several space dimensions x 2 is replaced by the laplace operator computations are done in several examples

approximation of analytic functions a method of enhanced convergence we deal with a method of enhanced convergence for the approximation of analytic functions this method introduces conformal transformations in the approximation problems in order to help extract the values of a given analytic function from its taylor expansion around a point an instance of this method based on the euler transform has long been known recently we introduced more general versions of it in connection with certain problems in wave scattering in 2 we present a general discussion of this approach as is known in the case of the euler transform conformal transformations can enlarge the region of convergence of power series and can enhance substantially the convergence rates inside the circles of convergence we show that conformal maps can also produce a rather dramatic improvement in the conditioning of pade approximation this improvement which we discuss theoretically for stieltjes type functions is most notorious in cases of very poorly conditioned pade problems in many instances an application of enhanced convergence in conjunction with pade approximation leads to results which are many orders of magnitude more accurate than those obtained by either classical pade approximants or the summation of a truncated enhanced series

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

representation of the five dimensional harmonic oscillator with scalar valued u 5 so 5 so 3 coupled vcs wave functions vector coherent state methods which reduce the u 5 so 5 so 3 subgroup chain are used to construct basis states for the five dimensional harmonic oscillator algorithms are given to calculate matrix elements in this basis the essential step is the construction of so 5 so 3 irreps of type v 0 the methodology is similar to that used in two recent papers except that one dimensional as opposed to multidimensional vector valued wave functions are used to give conceptually simpler results another significant advance is a canonical resolution of the so 5 so 3 multiplicity problem

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

vector coherent state theory and its application to the orthogonal groups vector coherent state theory is developed and presented in a form that explicitly exhibits its general applicability to the ladder representations of all semisimple lie groups and their lie algebras it is shown that in a suitable basis the vector coherent state inner product can be inferred algebraically by k matrix theory and changed to a simpler bargmann inner product thereby facilitating the explicit calculation of the matrix representaions of lie algebras applications are made to the even and odd orthogonal lie algebras

on the slow dynamics for the cahn hilliard equation in one space dimension we study the limiting behaviour of the solution of the cahn hilliard equation using energy type methods we assume that the initial data has a transition layer structure i e u epsilon approx pm 1 except near finitely many transition points we show that in the limit as epsilon rightarrow 0 the solution maintains its transition layer structure and the transition layers move slower than any power of epsilon

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

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 phase field approach in the numerical study of the elastic bending energy for vesicle membranes in this paper we compute the equilibrium configurations of a vesicle membrane under elastic bending energy with prescribed volume and surface area a variational phase field method is developed for such a problem discrete finite difference approximations and numerical simulations are carried out in the axial symmetrical cases different energetic bifurcation phenomena are discussed

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

analysis and convergence of a covolume approximation of the ginzburg landau model of superconductivity in this paper we present the mathematical analysis of a covolume method for the approximations of the ginzburg landau gl model for superconductivity a nice feature of this approach is that the gauge invariance properties are retained in discrete approximations based on triangular grids we also use properties of discrete vector fields to study issues such as the gauge choices and their enforcement