direct model reference takagi sugeno fuzzy control of siso nonlinear systems this study presents a novel direct model reference fuzzy controller it relaxes the special conditions on the reference model that is required by some of the approaches described in the literature as well as covering a more general class of takagi sugeno t s systems the stability of the proposed method is proved using a proper lyapunov function in addition the effects of modeling errors on the proposed controller are considered and a robust modification algorithm to alleviate this problem is introduced and analyzed the proposed method is then simulated on a flexible joint robot in a feedback linearization form and on chua s chaotic electrical circuit finally it is implemented and tested on a nonlinear dc motor with nonlinear state dependent disturbance

output feedback direct adaptive fuzzy controller based on frequency domain methods this paper describes a design method that guarantees the stability of an adaptive fuzzy control system the system consists of an unstable plant with an irrational transfer function a takagi sugeno fuzzy adaptive controller a nonlinear reference model and an adaptation mechanism the gradient based adaptation mechanism changes the consequents of the controller rules in such a way that the closed loop system behaves like the reference model the proposed design procedure utilizes frequency domain methods in the forms of the nyquist and circle criteria it is assumed that the function of the fuzzy controller is a nonlinearity described by a sector condition this condition means that the controller function lies between two lines passing through the origin in this method the function of the fuzzy controller is verified during online adaptation therefore it stays in the allowed sector this method is illustrated by an example of a control system containing an unstable plant with a transport delay the main contribution of this paper is to use frequency methods combined with adaptive fuzzy control these methods have previously been used for nonadaptive fuzzy control but in this paper they are used for the first time for adaptive fuzzy control

high performance pcg solvers for fem structural analysis the preconditioned conjugate gradient algorithm is a well known and powerful method used to solve large sparse symmetric positive definite linear systems such system are generated by the finite element discretisation in structural analysis but users of finite elements in this contest generally still rely on direct methods it is our purpose in the present work to highlight the improvement brought forward by some new preconditioning techniques and show that the preconditioned conjugate gradient method performs better than efficient direct methods

preconditioned conjugate gradient methods for three dimensional linear elasticity finite element modelling of three dimensional elasticity problems give rise to large sparse matrices various preconditioning methods are developed for use in preconditioned conjugate gradient iterative solution techniques incomplete factorizations based on levels of fill drop tolerance and a two level hierarchical basis are developed various techniques for ensuring that the incomplete factors have positive pivots are presented computational tests are carried out for problems generated using unstructured tetrahedral meshes quadratic basis functions are used the performance of the iterative methods is compared to a standard direct sparse matrix solver problems with up to 70 000 degrees of freedom and small 1 element aspect ratio are considered

conditioning analysis of positive definite matrices by approximate factorizations abstract the conditioning analysis of positive definite matrices by approximate lu factorizations is usually reduced to that of stieltjes matrices or even to more specific classes of matrices by means of perturbation arguments like spectral equivalence we show in the present work that a wider class which we call almost stieltjes matrices can be used as reference class and that it has decisive advantages for the conditioning analysis of finite element approximations of large multidimensional steady state diffusion problems

design of an adaptive fuzzy model based controller for chaotic dynamics in lorenz systems with uncertainty this paper presents the control methodology for uncertain chaotic dynamics of lorenz systems an adaptive fuzzy control afc scheme based on well known takagi sugeno t s fuzzy models for the mimo plants is constructed the developed control law and adaptive law guarantee the boundedness of all signals in the closed loop system in addition the chaotic state tracks the state of the stable reference model srm asymptotically with time for any bounded reference input signal the proposed control is applied to control of an uncertain lorenz system such as stabilization synchronization and chaotic model following control cmfc

parallel mic 0 preconditioning of 3d elliptic problems discretized by rannacher turek finite elements novel parallel algorithms for the solution of large fem linear systems arising from second order elliptic partial differential equations in 3d are presented the problem is discretized by rotated trilinear nonconforming rannacher turek finite elements the resulting symmetric positive definite system of equations ax f is solved by the preconditioned conjugate gradient algorithm the preconditioners employed are obtained by the modified incomplete cholesky factorization mic 0 of two kinds of auxiliary matrices b that both are constructed as locally optimal approximations of a in the class of m matrices uniform estimates for the condition number k b 1a are derived two parallel algorithms based on the different block structures of the related matrices b are studied the numerical tests confirm theory in that the algorithm scales as o n 7 6 in the matrix order n

stability analysis of hereditary iterative processes by employing the theory of difference inequalities several comparison theorems in the context of vector lyapunov functions are developed these comparison theorems are applied to study various stability properties of the equilibrium state of the hereditary iterative processes examples are given to demonstrate the obtained results the method provides a tool to investigate the fundamental problem of stability versus hereditary effect

a survey of adaptive fuzzy controllers nonlinearities and classifications adaptive fuzzy controllers afcs i e fuzzy controllers using heuristic expert knowledge and equipped with adaption ability are widely used in the industry in the present days as they are capable of dealing with ill formulated nonlinear systems where exact mathematical formulas are not known or partially described nonlinear systems afcs have been widely deployed to control many nonlinear systems with different types of critical nonlinearities over the last two decades many different approaches toward adaptive fuzzy control have been reported in this paper we recapitulate the latest research works related to afcs and provide an up to date survey on the latest development made in adaptive fuzzy control theory and applications based on different types of fuzzy systems considered and nonlinearities associated with the nonlinear system to be controlled we categorize the different approaches based on different types of nonlinearities and consider basic nonlinear systems nonlinear systems with external disturbances nonlinear systems with some special type of nonlinearities nonaffine nonlinear systems and strict feedback nonlinear systems it turns out that many existing methods are subject to various limitations and none of them is capable of controlling a general nonlinear systems hence it is still an open problem to design and develop a universal afc for a general class of nonlinear systems

an algorithm for profile and wavefront reduction of sparse matrices summary an algorithm for reducing the profile and wavefront of a sparse matrix is described the scheme is applicable to any sparse matrix which has a symmetric pattern of zeros and may be used to generate efficient labellings for finite element grids in particular it is suitable for generating efficient labellings for profile and frontal solution schemes empirical evidence obtained from analysis of the 30 test problems collected by everstine suggests that the new algorithm is superior to existing methods for profile and wavefront reduction it is fast requires only a small amount of memory and is simple to program

numerical methods and applications iterative methods based on linearization for nonlinear elliptic grid systems e g dyakonov how to solve stiff systems of differential equations by explicit methods v i lebedev on numerical methods of solving navier stokes equations in velocity pressurevariables g m kobelkov stiff systems of ordinary differential equations r p fedorenko convergence rate estimates of finite element methods for second order hyperbolic equations a a zlotnik fictitious domain methods and computation of homogenized properties of composites n s bakhvalov and a v knyazev

delay effect in models of population growth first we systematize earlier results on the global stability of the model x x f x of population growth second we investigate the effect of delay on the asymptotic behavior when the nonlinearity f is a unimodal function our results can be applied to several population models elements of mathematical ecology 2001 7 appl anal 43 1992 109 124 math comput modelling in press funkt biol med 256 1982 156 164 math comput modelling 35 2002 719 731 mat stos 6 1976 25 40 because the function f does not need to be monotone or differentiable specifically our results generalize earlier result of delay differential equations with applications in population dynamics 1993 since our function f may not be differentiable

on the rate of convergence of the preconditioned conjugate gradient method we derive new estimates for the rate of convergence of the conjugate gradient method by utilizing isolated eigenvalues of parts of the spectrum we present a new generalized version of an incomplete factorization method and compare the derived estimates of the number of iterations with the number actually found for some elliptic difference equations and for a similar problem with a model empirical distribution function

numerical experiences of solving elasticity systems by pcg methods abstract in solving systems of linear equations derived from fem structural analysis by the conjugate gradient method an efficient way for preparing effective incomplete factorization preconditioner was published by saint georges 1 in 2 3 we prepared several variants of the cited method due to saint georges 1 and some of the relevant pcg solvers were found more efficient than the original ones 1 here we prepare some additional variants for producing good enough preconditioners by applying our spiral ordering 2 and execute some incomplete factorizations mic ric with the level of fill in dropping strategy which was found the best in 3 in the comparison of the considered solvers we analyze our computer results when systems from elastic frame structures with 3d beam elements were solved

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

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

deflated preconditioned conjugate gradient solvers for linear elasticity extensions of deflation techniques previously developed for the poisson equation to static elasticity are presented compared to the scalar poisson equation j comput phys 2008 227 24 10196 10208 int j numer meth engng 2010 doi 10 1002 nme 2932 int j numer meth biomed engng 2010 26 1 73 85 the elasticity equations represent a system of equations giving rise to more complex low frequency modes multigrid elsevier amsterdam 2000 in particular the straightforward extension from the scalar case does not provide generally satisfactory convergence however a simple modification allows to recover the remarkable acceleration in convergence and cpu time reached in the scalar case numerous examples and timings are provided in a serial and a parallel context and show the dramatic improvements of up to two orders of magnitude in cpu time for grids with moderate graph depths compared to the non deflated version furthermore a monotonic decrease of iterations with increasing subdomains as well as a remarkable acceleration for very few subdomains are also observed if all the rigid body modes are included copyright 2011 john wiley sons ltd

adaptive fuzzy sliding mode control for electrical servo drive in this study an adaptive fuzzy sliding mode control afsmc system with an integral operation switching surface is adopted to control the position of an electrical servo drive the afsmc system is comprised of a fuzzy control design and a hitting control design in the fuzzy control design a fuzzy controller is designed to mimic a feedback linearization fl control law in the hitting control design a hitting controller is designed to compensate the approximation error between the fl control law and the fuzzy controller the tuning algorithms are derived in the sense of the lyapunov stability theorem thus the stability of the system can be guaranteed moreover to relax the requirement for the bound of approximation error an error estimation mechanism is investigated to observe the bound of approximation error real time experimental results verify that the proposed control systems can achieve favorable tracking performance and robust with regard to parameter variations and external load disturbance

variable universe stable adaptive fuzzy control of a nonlinear system abstract a kind of stable adaptive fuzzy control of a nonlinear system is implemented based on the variable universe method proposed first in 1 first of all the basic structure of variable universe adaptive fuzzy controllers is briefly introduced then the contraction expansion factor which is a key tool of the variable universe method is defined by means of the integral regulation idea and then a kind of adaptive fuzzy controller is designed by using such a contraction expansion factor the simulation on the first order nonlinear system is done and as a result its simulation effect is quite good in comparison with the corresponding result in 2 3 second it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of liapunov theory the simulation on a second order nonlinear system shows that its simulation effect is also quite good in comparison with the corresponding result in 2 besides a useful tool called symbolic factor is proposed which may be of universal significance it can greatly reduce the setting time and enhance the robustness of the system

the adaptive control of nonlinear systems using the sugeno type of fuzzy logic an adaptive fuzzy controller is synthesized from a collection of fuzzy if then rules the parameters of the membership functions characterizing the linguistic terms in the fuzzy if then rules are changed according to some adaptive laws for the purpose of controlling a plant to track a reference trajectory in the paper a direct adaptive fuzzy control design method is developed for the general higher order nonlinear continuous systems we use the sugeno type of the fuzzy logic system to approximate the controller it is proved that the closed loop system using this adaptive fuzzy controller is globally stable in the sense that all signals involved are bounded finally we apply the method of direct adaptive fuzzy controllers to control an unstable system

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

lmi based robust stability analysis for fuzzy feedback linearization regulators with its applications in order to cope with parametric uncertainties of nonlinear systems a numerical analysis method of a robust feedback linearization control scheme based on fuzzy models is proposed the fuzzy feedback linearization control scheme ensures that the control operates stably under bounded parametric uncertainties for the system with known uncertainty bounds linear matrix inequality based robust stability condition is derived and a robust fuzzy feedback linearization regulators can be designed by choosing the control parameters satisfying the inequalities which give sufficient conditions for the closed loop system to be stable to verify the validity and effectiveness of the designed stability analysis methods the suggested analysis techniques are applied to a balancing control of inverted pendulum systems

delay model of glucose insulin systems global stability and oscillated solutions conditional on delays recently p palumbo s panunzi and a de gaetano analyzed a delay model of the glucose insulin system they proved its persistence the existence of a unique positive equilibrium point as well as the local stability of this point in this paper we consider further the uniform persistence of such equilibrium solutions and their global stability using the omega limit set of a persistent solution and constructing a full time solution we also investigate the effect of delays in connection with the behavior of oscillating solutions to the system the model is shown to admit global stability under certain conditions of the parameters it is also shown that the model admits slowly oscillating behavior which demonstrates that the model is physiologically consistent and actually applicable to diabetological research 2008 elsevier inc all rights reserved

rkc time stepping for advection diffusion reaction problems the original explicit runge kutta chebyshev rkc method is a stabilized second order integration method for pure diffusion problems recently it has been extended in an implicit explicit manner to also incorporate highly stiff reaction terms this implicit explicit rkc method thus treats diffusion terms explicitly and the highly stiff reaction terms implicitly the current paper deals with the incorporation of advection terms for the explicit method thus aiming at the implicit explicit rkc integration of advection diffusion reaction equations in a manner that advection and diffusion terms are treated simultaneously and explicitly and the highly stiff reaction terms implicitly

a low order galerkin finite element method for the navier stokes equations of steady incompressible flow a stabilization issue and iterative methods a galerkin finite element method is considered to approximate the incompressible navier stokes equations together with iterative methods to solve a resulting system of algebraic equations this system couples velocity and pressure unknowns thus requiring a special technique for handling we consider the navier stokes equations in velocity kinematic pressure variables as well as in velocity bernoulli pressure variables the latter leads to the rotation form of nonlinear terms this form of the equations plays an important role in our studies a consistent stabilization method is considered from a new view point theory and numerical results in the paper address both the accuracy of the discrete solutions and the effectiveness of solvers and a mutual interplay between these issues when particular stabilization techniques are applied 2002 published by elsevier science b v

numerical solution of a two dimensional hyperbolic transmission problem an initial boundary value problem for a two dimensional hyperbolic equation in two disjoint rectangles is investigated the existence and uniqueness and a priori estimates for weak solutions in appropriate sobolev like spaces are proved few finite difference schemes approximating this problem are proposed and analyzed

a general approach to the construction of nonconforming finite elements on convex polytopes this paper establishes a general approach for constructing a new class of nonconforming finite elements on arbitrary convex polytope our contributions generalize or complete several well known nonconforming finite elements such as the crouzeix raviart triangle element the han parallelogram element the nonconforming rotated parallelogram element of rannacher and turek and several others

incomplete factorization based preconditionings for solving the helmholtz equation preconditioning techniques based on incomplete factorization of matrices are investigated to solve highly indefinite complex symmetric linear systems a novel preconditioning is introduced the real part of the matrix is made positive definite or less indefinite by adding properly defined perturbations to the diagonal entries while the imaginary part is unaltered the resulting preconditioning matrix which is obtained by applying standard methods to the perturbed complex matrix turns out to perform significantly better than classical incomplete factorization schemes for realistic values of the gmres restart parameter spectacular reduction of iteration counts is observed a theoretical spectral analysis is provided in which the spectrum of the preconditioner applied to indefinite matrix is related to the spectrum of the same preconditioner applied to a stieltjes matrix extracted from the indefinite matrix results of numerical experiments are reported which display the efficiency of the new preconditioning copyright 2001 john wiley sons ltd

application of diagonally perturbed incomplete factorization preconditioned conjugate gradient algorithms for edge finite element analysis of helmholtz equations the diagonally perturbed incomplete factorization preconditioning scheme is applied to the conjugate gradient cg method for solving a large system of linear equations resulting from the use of edge based finite element method fem this scheme contains more global information about the coefficient matrix when compared with banded matrix schemes the efficient implementation of this preconditioned cg pcg algorithm is described in detail for complex coefficient matrix equation on several electromagnetic problems the pcg approach converges in cpu time which is 8 6 19 5 times shorter with respect to the cg approach by comparison with other preconditioned techniques the results demonstrate that incomplete factorization preconditioning strategy is especially effective for cg iterative method when edge fem is applied to solve large scale time harmonic electromagnetic field problems

fuzzy model reference adaptive control this paper investigates a fuzzy model reference adaptive controller fmrac for continuous time multiple input multiple output mimo nonlinear systems the proposed adaptive scheme uses a takagi seguno ts fuzzy adaptive system which allows for the inclusion of a priori information in terms of qualitative knowledge about the plant operating points or analytical regulators e g state feedback for those operating points a proportional integral update law is used to obtain a fast parameters adaptation stability and robustness of this adaptive scheme are established using lyapunov stability tools the simulation results for a two link robot confirm the performance of the proposed approach

on stabilized integration for time dependent pdes an integration method is discussed which has been designed to treat parabolic and hyperbolic terms explicitly and stiff reaction terms implicitly the method is a special two step form of the one step imex implicit explicit rkc runge kutta chebyshev method the special two step form is introduced with the aim of getting a non zero imaginary stability boundary which is zero for the one step method having a non zero imaginary stability boundary allows for example the integration of pure advection equations space discretized with centered schemes the integration of damped or viscous wave equations the integration of coupled sound and heat flow equations etc for our class of methods it also simplifies the choice of temporal step sizes satisfying the von neumann stability criterion by embedding a thin long rectangle inside the stability region embedding rectangles or other tractable domains with this purpose is an idea of wesseling

output tracking control of mimo fuzzy nonlinear systems using variable structure control approach the output tracking control problem for nonlinear systems in the presence of both parameter perturbations and external disturbances is studied our approach is based on the takagi sugeno t s fuzzy modeling method and a variable structure control vsc technique therefore the systems considered are not and need not be in the triangular and parametric strict feedback form which are prevalent among adaptive model following control for nonlinear systems or in the normal form which pervades almost all existing results in neuro fuzzy model following control approach we first study the problem of stabilization of t s fuzzy systems by using a vsc technique a method for the design of a switching surface based on linear matrix inequalities is developed and a stabilizing controller based on a reaching law concept in the presence of both parameter perturbations and external disturbances is proposed then the method is extended to design controllers for output tracking of t s fuzzy nonlinear systems in two cases i e systems which possess the so called strong passive subsystems and strong stable zero dynamics respectively finally illustrative examples are presented to demonstrate the whole design procedure from the original nonlinear systems to their fuzzification and finally to the realization of the desired controllers simulation results show that the goal of output tracking can be achieved by the proposed controllers

study of interlaminar stresses in composite laminates subjected to torsional loading a computational procedure for accurate determination of interlaminar stresses in thick and thin composite laminates subjected to torsional loading is presented a multilevel recursively defined preconditioner in conjunction with the preconditioned conjugate gradient pcg algorithm is constructed from a sequence of hierarchical vector spaces arising from the p version of the finite element method the computational procedure is used to model stress fields in thick and thin laminates in torsion using three dimensional and quasi three dimensional models results indicate that the preconditioner developed here can be used to produce an efficient iterative solver for the determination of two and three dimensional stress fields in composite structures

an approach to adaptive control of fuzzy dynamic systems this paper discusses adaptive control for a class of fuzzy dynamic models the adaptive control law is first designed in each local region and then constructed in the global domain it is shown that the resulting fuzzy adaptive control system is globally stable robustness issues of the adaptive control system are also addressed a simulation example is given for demonstration of the application of the approach

a new class of nonconforming finite elements for the enrichment of q1 element on convex polytope this paper establishes a new class of nonconforming finite elements by including additional enriched functions not necessary polynomials to the standard q 1 k element on convex polytope here we focus on their fundamental construction principles and some of their approximation properties in addition we show how this approach can be used to enrich locally the well known wilson element the present enrichment method for this class of wilson type nonconforming finite element is based on a single univariate function and some arbitrary number of free parameters we also obtain explicit expressions for the basis functions of the new enriched element

rkc an explicit solver for parabolic pdes the fortran program rkc is intended for the time integration of parabolic partial differential equations discretized by the method of lines it is based on a family of runge kutta chebyshev formulas with a stability bound that is quadratic in the number of stages remarkable properties of the family make it possible for the program to select at each step the most efficient stable formula as well as the most efficient step size moreover they make it possible to evaluate the explicit formulas in just a few vectors of storage these characteristics of the program make it especially attractive for problems in several spatial variables rkc is compared to the bdf solver vodpk on two test problems in three spatial variables

properties of positive definite solutions of the equation x a x 2a i abstract in this paper we discuss some properties of a positive definite solution of the matrix equation x a x 2 a i two effective iterative methods for computing a positive definite solution of this equation are proposed necessary and sufficient conditions for existence of a positive definite solution are derived numerical experiments are executed with these methods