quantitative phase field modeling of dendritic growth in two and three dimensions we report the results of quantitative phase field simulations of the dendritic crystallization of a pure melt in two and three dimensions these simulations exploit a recently developed thin interface limit of the phase field model a karma and w j rappel phys rev e 53 r3017 1996 which is given here a detailed exposition this limit makes it possible to perform efficient computations with a smaller ratio of capillary length to interface thickness and with an arbitrary interface kinetic coefficient simulations in one and two dimensions are first carried out to test the accuracy of phase field computations performed within this limit dendrite tip velocities and tip shapes are found to be in excellent quantitative agreement with exact numerical benchmarks of solvability theory obtained by a boundary integral method both with and without interface kinetics simulations in three dimensions exploit in addition to the asymptotics a methodology to calculate grid corrections due to the surface tension and kinetic anisotropies they are used to test basic aspects of dendritic growth theory that pertain to the selection of the operating state of the tip and to the three dimensional morphology of needle crystals without sidebranches for small crystalline anisotropy simulated values of ensuremath sigma are slightly larger than solvability theory predictions computed by the boundary integral method assuming an axisymmetric shape and agree relatively well with experiments for succinonitrile given the uncertainty in the measured anisotropy in contrast for large anisotropy simulated ensuremath sigma values are significantly larger than the predicted values this disagreement however does not signal a breakdown of solvability theory it is consistent with the finding that the amplitude of the mathrm cos 4 ensuremath varphi mode which measures the departure of the tip morphology from a shape of revolution increases with anisotropy this departure can therefore influence the tip selection in a way that is not accurately captured by the axisymmetric approximation for large anisotropy finally the tail shape at a distance behind the tip that is large compared to the diffusion length is described by a linear law r ensuremath sim z with a slope dr dz that is nearly equal to the ratio of the two dimensional and three dimensional steady state tip velocities furthermore the evolution of the cross section of a three dimensional needle crystal with increasing distance behind the tip is nearly identical to the evolution of a two dimensional growth shape in time in accord with the current theory of the three dimensional needle crystal shape

universal spectral statistics in wigner dyson chiral and andreev star graphs ii semiclassical approach a semiclassical approach to the universal ergodic spectral statistics in quantum star graphs is presented for all known ten symmetry classes of quantum systems the approach is based on periodic orbit theory the exact semiclassical trace formula for star graphs and on diagrammatic techniques the appropriate spectral form factors are calculated up to one order beyond the diagonal and self dual approximations the results are in accordance with the corresponding random matrix theories which supports a properly generalized bohigas giannoni schmit conjecture

multigrid solution of the two dimensional euler equations on unstructured triangular meshes a multigrid algorithm has been developed to accelerate the convergence of the euler equations to a steady state on unstructured triangular meshes the method operates on a sequence of coarse and fine unstructured meshes and assumes no relation exists between the various meshes a tree search algorithm is used to efficiently identify regions of overlap between coarse and fine grid cells the multigrid method is applied to two different discretizations of the euler equations and results about multi element airfoils are presented for both discretization schemes convergence is accelerated by an order of magnitude resulting in convergence rates comparable to those obtained with structured multigrid algorithms

fuzzy gain scheduling controller and observer design based on lyapunov method and convex optimization addresses model based fuzzy control a constructive and automated method for the design of a gain scheduling controller is presented based on a given takagi sugeno fuzzy model of the plant the controller is designed such that stability and prescribed performance of the closed loop are guaranteed these properties are valid in a wide working range around an equilibrium without restrictions to slowly varying trajectories the synthesis is based on linear matrix inequalities and convex optimization techniques if required a fuzzy state estimator and an extended controller can be included providing a zero steady state error in the presence of disturbances and modeling errors the proposed method has been applied to a control of a laboratory liquid level process hence the performance has been evaluated in simulations as well as in real time control

thin interface asymptotics for an energy entropy approach to phase field models with unequal conductivities karma and rappel phys rev e 57 1998 4342 recently developed a new sharp interface asymptotic analysis of the phase field equations that is especially appropriate for modeling dendritic growth at low undercoolings their approach relieves a stringent restriction on the interface thickness that applies in the conventional asymptotic analysis and has the added advantage that interfacial kinetic effects can also be eliminated however their analysis focussed on the case of equal thermal conductivities in the solid and liquid phases when applied to a standard phase field model with unequal conductivities anomalous terms arise in the limiting forms of the boundary conditions for the interfacial temperature that are not present in conventional sharp interface solidification models as discussed further by almgren siam j appl math 59 1999 2086 in this paper we apply their asymptotic methodology to a generalized phase field model which is derived using a thermodynamically consistent approach that is based on independent entropy and internal energy gradient functionals that include double wells in both the entropy and internal energy densities the additional degrees of freedom associated with the generalized phase field equations can be used to eliminate the anomalous terms that arise for unequal conductivities

morphological instability and dynamics of fronts in bacterial growth models with nonlinear diffusion depending on the growth condition bacterial colonies can exhibit different morphologies as argued by ben jacob et al there is biological and modeling evidence that a nonlinear diffusion coefficient of the type d b d 0 b k is a basic mechanism that underlies almost all of the patterns and generates a long wavelength instability we study a reaction diffusion system with a nonlinear diffusion coefficient and find that a unique planar traveling front solution exists whose velocity is uniquely determined by k and d d 0 d n where d n is the diffusion coefficient of the nutrient due to the fact that the bacterial diffusion coefficient vanishes when stackrel ensuremath rightarrow b 0 in the front solution b vanishes in a singular way as a result the standard linear stability analysis for fronts cannot be used we introduce an extension of the stability analysis that can be applied to singular fronts and use the method to perform a linear stability analysis of the planar bacteriological growth front we show that a nonlinear diffusion coefficient generates a long wavelength instability for kg0 and dl d c k we map out the region of stability in the d ensuremath k plane and determine the onset of stability that is given by d c k both for stackrel ensuremath rightarrow d 0 and stackrel ensuremath rightarrow k ensuremath infty the dynamics of the growth zone essentially reduces to that of a sharp interface problem that is reminiscent of a so called one sided growth problem where the growth velocity is proportional to the gradient of a diffusion field ahead of the interface the moving boundary approximation that we derive in these limits is quite accurate but surprisingly does not become a proper asymptotic theory in the strict mathematical sense in the limit stackrel ensuremath rightarrow d 0 due to lack of full separation of scales on all dynamically relevant length scales our linear stability analysis and sharp interface formulation will also be applicable to other examples of interface formation due to nonlinear diffusion like in porous media or in the problem of vortex motion in superconductors

pole assignment for uncertain systems in a specified disk by state feedback this paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system the uncertainty being norm bounded for this the quadratic d stabilizability concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived this condition expressed as a parameter dependent discrete riccati equation enables one to design the control gain matrix by solving iteratively a discrete riccati equation

cusp development in hele shaw flow with a free surface free surface flow in a hele shaw cell is considered it has been known for some time that when the fluid region is contracting a finite time blow up can occur in which a cusp forms in the free surface the solution does not exist beyond the time of blow up examples are presented of this blow up and also of a new process in which a cusp of a different type forms in the free surface but after which the solution continues to exist after a transformation of the dependent variable the pressure the new cusps are related to permissible singularities in the free boundary of the obstacle problem

pole assignment of linear uncertain systems in a sector via a lyapunov type approach the problem of designing robust control laws in performance and in stability for uncertain linear systems is considered performances are taken into account using root clustering of the closed loop dynamic matrix in a sector of the complex plane a synthesis procedure based on a sufficient condition for quadratic stabilization and root clustering such as stabilizability is given using an auxiliary convex problem the results are illustrated by a significant example from the literature

robust stabilization of uncertain fuzzy systems using variable structure system approach based on the variable structure system vss theory we develop a fuzzy control system design method for a class of uncertain nonlinear multivariable systems that can be represented by a takagi sugeno fuzzy model we make the first attempt to relax the restrictive assumption that each nominal local system model shares the same input channel which is required in the traditional vss based fuzzy control design methods as the local controller we use a sliding mode controller with a switching feedback control term in terms of linear matrix inequalities lmis we derive a sufficient condition for the existence of linear sliding surfaces guaranteeing asymptotic stability of the reduced order equivalent sliding mode dynamics we present an lmi characterization of such sliding surfaces we also give an lmi based algorithm to design the switching feedback control term so that a stable sliding motion is induced in finite time finally we give a numerical design example

front propagation into unstable states universal algebraic convergence towards uniformly translating pulled fronts fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes pulled fronts and pushed fronts the term pulled front expresses that these fronts are pulled along by the spreading of linear perturbations about the unstable state accordingly their asymptotic speedv equals the spreading speed of perturbations whose dynamics is governed by the equations linearized about the unstable state the central result of this paper is the analysis of the convergence of asymptotically uniformly traveling pulled fronts towardsv we show that when such fronts evolve from sufficiently steep initial conditions which initially decay faster than e x forx 1 t hey have auniversal relaxation behavioras timet 1 the velocity of a pulled front always relaxes algebraically like v t d v 3 2t c 3 p d d 2 t 3 2 c o 1 t 2 the parametersv and d are determined through a saddle point analysis from the equation of motion linearized about the unstable invaded state this front velocity is independent of the precise value of the front amplitude which one tracks to measure the front position the interior of the front is essentially slaved to the leading edge and develops universally as x t d8v t x rt dt 0 v t 0 c o 1 t 2 where8v x vt is a uniformly translating front solution with velocity v v our result which can be viewed as a general center manifold result for pulled front propagation is derived in detail for the well known nonlinear diffusion equation of type t d 2 x c 3 where the invaded unstable state is d 0 even for this simple case the subdominant t 3 2 term extends an earlier result of bramson our analysis is then generalized to more general sets of partial differential equations with higher spatial or temporal derivatives to pdes with memory kernels and also to difference equations such as those that occur in numerical finite difference codes our universal result for pulled fronts thus implies independence i of the level curve which is used to track the front position ii of the precise nonlinearities iii of the precise form of the linear operators in the dynamical equation and iv of the precise initial conditions as long as they are sufficiently steep the only remainders of the explicit form of the dynamical equation are the nonlinear solutions 8v and the three saddle point parameters v and d as our simulations confirm all our analytical predictions in every detail it can be concluded that we have a complete analytical understanding of the propagation mechanism and relaxation behavior of pulled fronts if they are uniformly translating for t 1 an immediate consequence of the slow algebraic relaxation is that the standard moving boundary approximation breaks down for weakly curved pulled fronts in two or three dimensions in addition to our main result for pulled fronts we also discuss the propagation and convergence of fronts emerging from

numerical studies of the steklov eigenvalue problem via conformal mappings abstract in this paper spectral methods based on conformal mappings are proposed to solve the steklov eigenvalue problem and its related shape optimization problems in two dimensions to apply spectral methods we first reformulate the steklov eigenvalue problem in the complex domain via conformal mappings the eigenfunctions are expanded in fourier series so the discretization leads to an eigenvalue problem for coefficients of fourier series for shape optimization problem we use a gradient ascent approach to find the optimal domain which maximizes kth steklov eigenvalue with a fixed area for a given k the coefficients of fourier series of mapping functions from a unit circle to optimal domains are obtained for several different k

second order phase field asymptotics for unequal conductivities we extend karma and rappel s improved asymptotic analysis of the phase field model to different diffusivities in solid and liquid we consider both second order classical asymptotics in which the interface thickness is taken much smaller than the capillary length and the new isothermal asymptotics in which the two lengths are considered comparable in the first case if the phase field model is required to be gradient flow for an entropy functional then for unequal diffusivities it is impossible to construct a phase equation with finite kinetics which converges with second order accuracy to a gibbs thomson equilibrium condition with infinitely fast kinetics in the second case some error terms are pushed to higher orders and it is easy to eliminate the remaining errors with finite phase kinetics

an algebraic theory for multigrid methods for variational problems a convergence theory is developed for multigrid methods for symmetric positive definite problems in a variational setting the theory is based on a single algebraic approximation assumption which is satisfied for finite element discretizations of elliptic boundary value problems although the theory can be applied to problems without any continuous background as well in contrast to previous results we prove fast convergence with any positive number of smoothing steps for v and w cycles under discrete analogues of the h 2 and h 1 alpha regularity assumptions respectively we analyze a wide class of smoothers including arbitrary symmetric and nonsymmetric preconditioned iterations arbitrarily ordered gauss seidel steepest descent chebyshev iteration and conjugate gradients our estimates exhibit the usual asymptotic behavior for a large number of smoothing steps

global existence singular solutions and ill posedness for the muskat problem the muskat or muskat leibenzon problem describes the evolution of the interface between two immiscible fluids in a porous medium or hele shaw cell under applied pressure gradients or fluid injection extraction in contras t to the hele shaw problem the one phase version of the muskat problem there are few nontrivial exact solutions or analytic results for the muskat problem for the stable forward muskat problem in which the higher viscosity fluid ex pands into the lower viscosity fluid we show global in time existence for initial data that is a small perturbation of a flat interface the initial data in this result ma y contain weak e g curvature singularities for the unstable backwa rd problem in which the higher viscosity fluid contracts we construct singular solution s that start off with smooth initial data but develop a point of infinite curvature at fi nite time c 2004 wiley periodicals inc

convective stabilization of a laplacian moving boundary problem with kinetic undercooling we study the shape stability of disks moving in an external laplacian field in two dimensions the problem is motivated by the motion of ionization fronts in streamer type electric breakdown it is mathematically equivalent to the motion of a small bubble in a hele shaw cell with a regularization of kinetic undercooling type namely a mixed dirichlet neumann boundary condition for the laplacian field on the moving boundary using conformal mapping techniques linear stability analysis of the uniformly translating disk is recast into a single pde which is exactly solvable for certain values of the regularization parameter we concentrate on the physically most interesting exactly solvable and nontrivial case we show that the circular solutions are linearly stable against smooth initial perturbations in the transformation of the pde to its normal hyperbolic form a semigroup of automorphisms of the unit disk plays a central role it mediates the convection of perturbations to the back of the circle where

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

a moving boundary problem motivated by electric breakdown i spectrum of linear perturbations abstract an interfacial approximation of the streamer stage in the evolution of sparks and lightning can be written as a laplacian growth model regularized by a kinetic undercooling boundary condition we study the linear stability of uniformly translating circles that solve the problem in two dimensions in a space of smooth perturbations of the circular shape the stability operator is found to have a pure point spectrum except for the eigenvalue 0 0 for infinitesimal translations all eigenvalues are shown to have negative real part therefore perturbations decay exponentially in time we calculate the spectrum through a combination of asymptotic and series evaluation in the limit of vanishing regularization parameter all eigenvalues are found to approach zero in a singular fashion and this asymptotic behavior is worked out in detail a consideration of the eigenfunctions indicates that a strong intermediate growth may occur for generic initial perturbations both the linear and the nonlinear initial value problem are considered in a second paper

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

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

sharp interface limits of phase field models the use of continuum phase field models to describe the motion of well defined interfaces is discussed for a class of phenomena that includes order disorder transitions spinodal decomposition and ostwald ripening dendritic growth and the solidification of eutectic alloys the projection operator method is used to extract the sharp interface limit from phase field models which have interfaces that are diffuse on a length scale xi in particular phase field equations are mapped onto sharp interface equations in the limits xi kappa 1 and xi v d 1 where kappa and v are respectively the interface curvature and velocity and d is the diffusion constant in the bulk the calculations provide one general set of sharp interface equations that incorporate the gibbs thomson condition the allen cahn equation and the kardar parisi zhang equation

multiple steady bubbles in a hele shaw cell this paper presents new solutions in analytical form for the shapes of an assembly of steady co travelling bubbles in a hele shaw cell the associated velocity field is also derived the assembly can consist of any finite number of bubbles the solutions are expressed in terms of schottky klein prime functions and are derived by exploiting results on multiply connected conformal slit mappings

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

void electromigration as a moving free boundary value problem abstract the void electromigration process in the strip geometry is investigated analytically the void is assumed to travel steadily along the axis of symmetry of the metal strip when its length is large compared to the width of the metal ribbon a strong similarity with the classical saffman taylor viscous fingering is pointed out it allows us to adapt the hodograph method to predict both the width and the growth velocity at fixed applied current in the absence of surface tension the void shape is unique and has a relative width close to 2 3 a result in strong contradiction with the viscous fingering in the same geometry the propagation of symmetric bubbles is also investigated and shows that the set of solutions is less rich than the flow problem the addition of surface tension appears non standard in the area of pattern formation it does not allow large void propagation suppressing the unique infinite solution as for the bubbles the numerically computed shapes with surface tension appear rather circular this paper shows that the modification of a single boundary condition the dirichlet boundary condition is enough to strongly modify our intuition about pattern formation

phase field model for hele shaw flows with arbitrary viscosity contrast i theoretical approach we present a phase field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular hele shaw cell with asymptotic matching techniques we check the model to yield the right hele shaw equations in the sharp interface limit and compute the corrections to these equations to first order in the interface thickness we also compute the effect of such corrections on the linear dispersion relation of the planar interface we discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase field model to the limiting hele shaw dynamics in particular the convergence appears to be slower for high viscosity contrasts

shape selection of saffman taylor fingers among all problems of pattern selection the one posed by the saffman taylor finger is yet unsolved although numerics and experiments indicate the very simple property that the relative width of the finger tends to 1 2 in the low surface tension limit we explain this by performing an expansion beyond all orders leading to the formulation of a nonlinear eigenvalue problem with a discrete set of solutions in particular we predict that the relative width of the finger tends to 1 2 as the surface tension to the power 2 3 pacs numbers 47 10 g 03 40 gc 68 10 m

fuzzy constrained min max model predictive control based on piecewise lyapunov functions this paper proposes two novel stable fuzzy model predictive controllers based on piecewise lyapunov functions and the min max optimization of a quasi worst case infinite horizon objective function the main idea is to design state feedback control laws that minimize the worst case objective function based on fuzzy model prediction and thus to obtain the optimal transient control performance which is of great importance in industrial process control moreover in both of these predictive controllers piecewise lyapunov functions have been used in order to reduce the conservatism of those existent predictive controllers based on common lyapunov functions it is shown that the asymptotic stability of the resulting closed loop discrete time fuzzy predictive control systems can be established by solving a set of linear matrix inequalities moreover the controller designs of the closed loop control systems with desired decay rate and input constraints are also considered simulations on a numerical example and a highly nonlinear benchmark system are presented to demonstrate the performance of the proposed fuzzy predictive controllers

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

moving boundary approximation for curved streamer ionization fronts solvability analysis the minimal density model for negative streamer ionization fronts is investigated an earlier moving boundary approximation for this model consisted of a kinetic undercooling type boundary condition in a laplacian growth problem of hele shaw type here we derive a curvature correction to the moving boundary approximation that resembles surface tension the calculation is based on solvability analysis with unconventional features namely there are three relevant zero modes of the adjoint operator one of them diverging furthermore the inner outer matching ahead of the front must be performed on a line rather than on an extended region and the whole calculation can be performed analytically the analysis reveals a relation between the fields ahead and behind a slowly evolving curved front the curvature and the generated conductivity this relation forces us to give up the ideal conductivity approximation and we suggest to replace it by a charge neutrality approximation this implies that the electric potential in the streamer interior is no longer constant but solves a laplace equation this leads to a muskat type problem

a moving boundary model motivated by electric breakdown ii initial value problem abstract an interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a laplacian growth model regularized by a kinetic undercooling boundary condition using this model we study both the linearized and the full nonlinear evolution of small perturbations of a uniformly translating circle within the linear approximation analytical and numerical results show that perturbations are advected to the back of the circle where they decay an initially analytic interface stays analytic for all finite times but singularities from outside the physical region approach the interface for t which results in some anomalous relaxation at the back of the circle for the nonlinear evolution numerical results indicate that the circle is the asymptotic attractor for small perturbations but larger perturbations may lead to branching we also present results for more general initial shapes which demonstrate that regularization by kinetic undercooling cannot guarantee smooth interfaces globally in time

a general theory for matrix root clustering in subregions of the complex plane we consider the general problem of root clustering of a matrix in the complex plane let a in c n times n and s subset c find the largest class of s and an algebraic criterion which is necessary and sufficient for lambda i a in s i 1 2 n we introduce two types of regions which constitute the largest class of s known to date the criterion is presented both for open regions and closed ones the results are used to define a design methodology for control systems moreover all classical results are shown to be special cases of the present theory

weighted fuzzy observer based fault detection approach for discrete time nonlinear systems via piecewise fuzzy lyapunov functions the main focus of this paper is on the analysis and integrated design of mathcal l 2 observer based fault detection fd systems for discrete time nonlinear industrial processes to gain a deeper insight into this fd framework the existence condition is introduced first then an integrated design of mathcal l 2 observer based fd approach is realized by solving the proposed existence condition with the aid of takagi sugeno fuzzy dynamic modeling technique and piecewise fuzzy lyapunov functions most importantly a weighted piecewise fuzzy observer based residual generator is proposed aiming at achieving an optimal integration of residual evaluation and threshold computation into fd systems the core of this approach is to make use of the knowledge provided by fuzzy models of each local region and then to weight the local residual signal by means of different weighting factors in comparison with the standard norm based fuzzy observer based fd methods the proposed scheme may lead to a significant improvement of the fd performance in the end the effectiveness of the proposed method is verified by a numerical example and a case study on the laboratory setup of continuous stirred tank heater plant

lmi based nonlinear fuzzy observer controller design for uncertain mimo nonlinear systems based on the variable structure system theory we develop a nonlinear fuzzy observer controller design method for a class of uncertain nonlinear systems that can be represented by a takagi sugeno fuzzy model we use a sliding mode observer and a sliding mode controller as the local state observer and the local controller in terms of linear matrix inequalities lmis we derive sufficient conditions for the existence of the fuzzy observer and the fuzzy controller we also derive lmi conditions for the existence of the fuzzy observer and the fuzzy controller guaranteeing the alpha stability or generalized h2 hinfin performance constraints we show that the observer and the controller can be independently designed i e the separation property holds finally we give simple lmi based design algorithms together with an example

multigrid methods convergence theory in a variational framework to solve the symmetric variational problem u in h a u v l v forall v in h multigrid methods are constructed using a sequence of nested subspaces u k k 0 to m of h the convergence is studied relatively to the energy norm i e in the hilbert space h a cdot cdot and is based on the 2 level case m 1 for the m 1 level case rather sharp bounds for the convergence factor can be constructed recursively and their nondependence on the number of levels is established under certain hypothesis

streamer branching rationalized by conformal mapping techniques spontaneous branching of discharge channels is frequently observed but not well understood we recently proposed a new branching mechanism based on simulations of a simple continuous discharge model in high fields we here present analytical results for such streamers in the lozansky firsov limit where they can be modeled as moving equipotential ionization fronts this model can be analyzed by conformal mapping techniques which allow the reduction of the dynamical problem to finite sets of nonlinear ordinary differential equations our solutions illustrate that branching is generic for the intricate head dynamics of streamers in the lozansky firsov limit

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