radial basis function approximation from gridded centres to scattered centres abstract the paper studies l infinity ir d norm approximations from a space spanned by a discrete set of translates of a basis function theta attention here is restricted to functions theta whose fourier transform is smooth on ird 0 and has a singularity at the origin examples of such basis functions are the thin plate splines and the multiquadrics as well as other types of radial basis functions that are employed in approximation theory the above approximation problem is well understood in case the set of points used for translating theta forms a lattice in ir d and many optimal and quasi optimal approximation schemes can already be found in the literature in contrast only few mostly specific results are known for a set of scattered points the main objective of this paper is to provide a general tool for extending approximation schemes that use integer translates of a basis function to the non uniform case we introduce a single relatively simple conversion method that preserves the approximation orders provided by a large number of schemes presently in the literature more precisely to almost all stationary schemes in anticipation of future introduction of new schemes for uniform grids an effort is made to impose only a few mild conditions on the function theta which still allow for a unified error analysis to hold in the course of the discussion here the recent results of budl on scattered center approximation are reproduced and improved upon

a non stationary approximation scheme on scattered centers in r d by radial basis functions a nonstationary approximation scheme on rd using scattered translates of a smooth radial basis function e g gaussian is developed the scheme is nonstationary and shown to provide spectral approximation orders i e approximation orders that depend only on the smoothness of the approximands

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

estimate of solutions for differential and difference functional equations with applications to difference methods abstract the theorems on the estimate of solutions for nonlinear second order partial differential functional equations mainly of parabolic type with dirichlet s condition and for the suitable explicit finite difference functional schemes are proved the proofs are based on the comparison technique the convergent difference method given is considered without an assumption of the global generalized perron condition on the functional variable but with local one in some sense only it is a consequence of our estimate theorems the functional dependence is of the volterra type

the approximation power of moving least squares a general method for near best approximations to functionals on r d using scattered data information is discussed the method is actually the moving least squares method presented by the backus gilbert approach it is shown that the method works very well for interpolation smoothing and derivatives approximations for the interpolation problem this approach gives mclain s method the method is near best in the sense that the local error is bounded in terms of the error of a local best polynomial approximation the interpolation approximation in r d is shown to be a c function and an approximation order result is proven for quasi uniform sets of data points

numerical differentiation of 2d functions from noisy data abstract in this paper we present a method for the numerical differentiation of bivariate functions when a set of noisy data is given we suppose we have a sample coming from an independent process with unknown covariance matrix we construct the gradient estimator using a multiresolution analysis and the usual difference operators the asymptotic properties of the estimator are studied and convergence results are provided the method is suitable for any data configuration

hermite type moving least squares approximations the moving least squares approach first presented by mclain 1 is a method for approximating multivariate functions using scattered data information the method is using local polynomial approximations incorporating weight functions of different types some weights with certain singularities induce c interpolation approximation in n in this work we present a way of generalizing the method to enable hermite type interpolation namely interpolation to derivatives data as well the essence of the method is the use of an appropriate metric in the construction of the local polynomial approximations

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

the uniform convergence of thin plate spline interpolation in two dimensions let f be a function from cal r 2 to cal r that has square integrable second derivatives and let s be the thin plate spline interpolant to f at the points underline v i i 1 2 ldots n in cal r 2 we seek bounds on the error f underline x s underline x when underline x is in the convex hull of the interpolation points or when underline x is close to at least one of the interpolation points but need not be in the convex hull we find for example that if underline x is inside a triangle whose vertices are any three of the interpolation points then f underline x s underline x is bounded above by a multiple of h where h is the length of the longest side of the triangle and where the multiplier is independent of the interpolation points further if cal d is any bounded set in cal r 2 that is not a subset of a single straight line then we prove that a sequence of thin plate spline interpolants converges to f uniformly on cal d specifically we require h rightarrow 0 where h is now the least upper bound on the numbers d underline x cal v underline x in cal d and where d underline x cal v underline x in cal r 2 is the least euclidean distance from underline x to an interpolation point our method of analysis applies integration by parts and the cauchy schwarz inequality to the scalar product between second derivatives that occurs in the variational calculation of thin plate spline interpolation

image interpolation via regularized local linear regression the linear regression model is a very attractive tool to design effective image interpolation schemes some regression based image interpolation algorithms have been proposed in the literature in which the objective functions are optimized by ordinary least squares ols however it is shown that interpolation with ols may have some undesirable properties from a robustness point of view even small amounts of outliers can dramatically affect the estimates to address these issues in this paper we propose a novel image interpolation algorithm based on regularized local linear regression rllr starting with the linear regression model where we replace the ols error norm with the moving least squares mls error norm leads to a robust estimator of local image structure to keep the solution stable and avoid overfitting we incorporate the l2 norm as the estimator complexity penalty moreover motivated by recent progress on manifold based semi supervised learning we explicitly consider the intrinsic manifold structure by making use of both measured and unmeasured data points specifically our framework incorporates the geometric structure of the marginal probability distribution induced by unmeasured samples as an additional local smoothness preserving constraint the optimal model parameters can be obtained with a closed form solution by solving a convex optimization problem experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance with the state of the art interpolation algorithms especially in image edge structure preservation

pole placement via static output feedback is np hard this note proves that the problem of pole placement via static output feedback for linear time invariant systems is np hard

higher order averaging of fokker planck equations for nonlinear fiber lay down processes we investigate stochastic models for the lay down of flexible fibers on a moving conveyor belt for the case of small stochasticity and small belt velocity using a suitable scaling we obtain a singularly perturbed problem for a stochastic hamiltonian system and the corresponding fokker planck equation these equations are investigated using averaging methods in the present case the impact of the deterministic forcing i e the belt velocity is not captured by the stochastic averaging theorem to overcome this problem a formal energy projection method previously introduced by the authors is used which allows the computation of higher order stochastic averages for the present highly nonlinear system the resulting second order coefficients are computed numerically and a suitably precise scheme is developed finally we illustrate the results of our method with several examples

image interpolation via graph based bayesian label propagation in this paper we propose a novel image interpolation algorithm via graph based bayesian label propagation the basic idea is to first create a graph with known and unknown pixels as vertices and with edge weights encoding the similarity between vertices then the problem of interpolation converts to how to effectively propagate the label information from known points to unknown ones this process can be posed as a bayesian inference in which we try to combine the principles of local adaptation and global consistency to obtain accurate and robust estimation specially our algorithm first constructs a set of local interpolation models which predict the intensity labels of all image samples and a loss term will be minimized to keep the predicted labels of the available low resolution lr samples sufficiently close to the original ones then all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on all samples moreover a graph laplacian based manifold regularization term is incorporated to penalize the global smoothness of intensity labels such smoothing can alleviate the insufficient training of the local models and make them more robust finally we construct a unified objective function to combine together the global loss of the locally linear regression square error of prediction bias on the available lr samples and the manifold regularization term it can be solved with a closed form solution as a convex optimization problem experimental results demonstrate that the proposed method achieves competitive performance with the state of the art image interpolation algorithms

an error analysis for radial basis function interpolation radial basis function interpolation refers to a method of interpolation which writes the interpolant to some given data as a linear combination of the translates of a single function and a low degree polynomial we develop an error analysis which works well when the fourier transform of has a pole of order 2m at the origin and a zero at of order 2 in case 0 m we derive error estimates which fill in some gaps in the known theory while in case m we obtain previously unknown error estimates in this latter case we employ dilates of the function where the dilation factor corresponds to the fill distance between the data points and the domain

comparison between some explicit and implicit difference schemes for hamilton jacobi functional differential equations abstract initial boundary value problems of dirichlet type for first order partial functional differential equations are considered explicit difference schemes and implicit difference methods are investigated sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented it is proved that assumptions on the regularity of given functions are the same for both the methods it is shown that conditions on the mesh for explicit difference schemes are more restrictive than suitable assumptions for implicit methods there are implicit difference schemes which are convergent and corresponding explicit difference methods are not convergent error estimates for both the methods are constructed numerical examples are presented

adaptive boundary control for unstable parabolic pdes part i lyapunov design we develop adaptive controllers for parabolic partial differential equations pdes controlled from a boundary and containing unknown destabilizing parameters affecting the interior of the domain these are the first adaptive controllers for unstable pdes without relative degree limitations open loop stability assumptions or domain wide actuation it is the first necessary step towards developing adaptive controllers for physical systems such as fluid thermal and chemical dynamics where actuation can be only applied non intrusively the dynamics are unstable and the parameters such as the reynolds rayleigh prandtl or peclet numbers are unknown because they vary with operating conditions our method builds upon our explicitly parametrized control formulae to avoid solving riccati or bezout equations at each time step most of the designs we present are state feedback but we present two benchmark designs with output feedback which have infinite relative degree

improved accuracy of lp approximation to derivatives by radial basis function interpolation the present paper considers the approximation to a function and its derivatives by radial basis function interpolation and its derivatives respectively on the sobolev space it is known that due to edge effects we lose some accuracy near the boundary thus the goal of this paper is to show that the convergence rate of the approximation error can be at least doubled when a certain boundary condition is met

stability analysis of dissipative systems subject to nonlinear damping via lyapunov techniques in this paper we provide a general strategy based on lyapunov functionals to analyze global asymptotic stability of linear infinite dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is globally asymptotically stable with a linear damping to do so we use the fact that for any linear infinite dimensional system that is globally exponentially stable there exists a lyapunov functional then we derive a lyapunov functional for the nonlinear system which is the sum of a lyapunov functional coming from the linear system and another term that compensates the nonlinearity our results are then applied to the linearized korteweg de vries equation and some wave equations

robust l_ 2 e estimation of transformation for non rigid registration we introduce a new transformation estimation algorithm using the l 2 e estimator and apply it to non rigid registration for building robust sparse and dense correspondences in the sparse point case our method iteratively recovers the point correspondence and estimates the transformation between two point sets feature descriptors such as shape context are used to establish rough correspondence we then estimate the transformation using our robust algorithm this enables us to deal with the noise and outliers which arise in the correspondence step the transformation is specified in a functional space more specifically a reproducing kernel hilbert space in the dense point case for nonrigid image registration our approach consists of matching both sparsely and densely sampled sift features and it has particular advantages in handling significant scale changes and rotations the experimental results show that our approach greatly outperforms state of the art methods particularly when the data contains severe outliers

finite difference reaction diffusion systems with coupled boundary conditions and time delays abstract this paper is concerned with finite difference solutions of a coupled system of reaction diffusion equations with nonlinear boundary conditions and time delays the system is coupled through the reaction functions as well as the boundary conditions and the time delays may appear in both the reaction functions and the boundary functions the reaction diffusion system is discretized by the finite difference method and the investigation is devoted to the finite difference equations for both the time dependent problem and its corresponding steady state problem this investigation includes the existence and uniqueness of a finite difference solution for nonquasimonotone functions monotone convergence of the time dependent solution to a maximal or a minimal steady state solution for quasimonotone functions and local and global attractors of the time dependent system including the convergence of the time dependent solution to a unique steady state solution also discussed are some computational algorithms for numerical solutions of the steady state problem when the reaction function and the boundary function are quasimonotone all the results for the coupled reaction diffusion equations are directly applicable to systems of parabolic ordinary equations and to reaction diffusion systems without time delays

learning performance of regularized moving least square regression abstract moving least square regression is an important local learning algorithm in this paper we consider a regularized moving least square regression algorithm in reproducing kernel hilbert space the localized representer theorem is different from the classical representer theorems for regularized kernel machines it shows that regularization not only ensures the computational stability it is also necessary for the algorithm to preserve localization property we also studied the learning performance of the regularized moving least square algorithm and conducted a rigorous error analysis compared with the unregularized method convergence analysis of regularized moving least square regression requires more natural and much simpler conditions and achieves fast rates

construction and characterization of non uniform local interpolating polynomial splines this paper presents a general framework for the construction of piecewise polynomial local interpolants with given smoothness and approximation order defined on non uniform knot partitions we design such splines through a suitable combination of polynomial interpolants with either polynomial or rational compactly supported blending functions in particular when the blending functions are rational our approach provides spline interpolants having low and sometimes minimum degree thanks to its generality the proposed framework also allows us to recover uniform local interpolating splines previously proposed in the literature to generalize them to the non uniform case and to complete families of arbitrary support width furthermore it provides new local interpolating polynomial splines with prescribed smoothness and polynomial reproduction properties

globally convergent algorithms for robust pole assignment by state feedback it is observed that an algorithm proposed in 1985 by kautsky nichols and van dooren knv amounts to maximizing at each iteration the determinant of the candidate closed loop eigenvector matrix x with respect to one of its columns with unit length constraint subject to the constraint that it remains an achievable closed loop eigenvector matrix this interpretation is used to prove convergence of the knv algorithm it is then shown that a more efficient algorithm is obtained if det x is concurrently maximized with respect to two columns of x and such a scheme is easily extended to the case where the eigenvalues to be assigned include complex conjugate pairs variations exploiting the availability of multiple processors are suggested convergence properties of the proposed algorithms are established their superiority is demonstrated numerically

galerkin proper orthogonal decomposition methods for parabolic problems in this work error estimates for galerkin proper orthogonal decomposition pod methods for linear and certain non linear parabolic systems are proved the resulting error bounds depend on the number of pod basis functions and on the time discretization numerical examples are included

an lmi approach to stability analysis of coupled parabolic systems we analyze the exponential stability of a class of distributed parameter systems the system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients we approximate the coefficients by splitting space domains but take into account approximation errors during stability analysis using a quadratic lyapunov function we obtain sufficient conditions for exponential stability in terms of linear matrix inequalities

error estimate in fractional differential equations using multiquadratic radial basis functions the purpose of this paper is to investigate the collocation method based on multiquadric mq radial basis functions rbfs for fractional differential equations fdes in the process of doing this a scattered data rbf interpolation is considered a posterior error bound for the smooth solutions of fdes in the proposed method is established in the l 2 norm using an alternate characterization of the native space numerical results are presented which confirm the theoretical prediction of the convergence behavior of the proposed method

stability analysis of linear partial differential equations with generalized energy functions we present a method for the stability analysis of a large class of linear partial differential equations pdes in one spatial dimension we rely on lyapunov analysis to establish the exponential stability of the systems under consideration the proposed test for the verification of the underlying lyapunov inequalities relies on the existence of solutions of a system of coupled differential equations we illustrate the application of this method using a pde actuated by a backstepping computed feedback law furthermore for the case of pdes defined by polynomial data we formulate a numerical methodology in the form of a convex optimization problem which can be solved algorithmically we show the effectiveness of the proposed numerical methodology using examples of different types of pdes

enhancement of the material point method using b spline basis functions the mpm material point method enhanced with b spline basis functions referred to as bsmpm b spline mpm is developed and demonstrated using representative quasi static and dynamic example problems smooth b spline basis functions could significantly reduce the cell crossing error as known for the original mpm a gauss quadrature scheme is designed and shown to be able to diminish the quadrature error in the bsmpm analysis of large deformation problems for the improved accuracy and convergence especially with the quadratic b splines moreover the increase in the order of the b spline basis function is also found to be an effective way to reduce the quadrature error and to improve accuracy and convergence for plate impact examples it is demonstrated that the bsmpm outperforms the generalized interpolation material point gimp and convected particle domain interpolation cpdi methods in term of the accuracy of representing stress waves thus the bsmpm could become a promising alternative to the mpm gimp and cpdi in solving certain types of transient problems

brief paper an lmi approach to h boundary control of semilinear parabolic and hyperbolic systems exponential stability analysis and l 2 gain analysis are developed for scalar uncertain distributed parameter systems governed by semilinear partial differential equations of parabolic and hyperbolic types sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities lmis for both systems these conditions are then utilized to synthesize h static output feedback boundary controllers of the systems in question

rate of convergence of shepard s global interpolation formula given any data points xl x in rw and values f x f x of a function f shepard s global interpolation formula reads as follows sof x ef xi wi x wi x i x xi i p elx xjl p where i denotes the euclidean norm in wr this interpolation scheme is stable but if p 1 the gradient of the interpolating function vanishes in all data points the interpolation operator spq is defined by replacing the values f xi in spf by taylor polynomials of f of degree q e n in this paper we investigate the approximating power of spq for all values of p q and s

a meshless method for solving the time fractional advection diffusion equation with variable coefficients abstract in this paper an efficient and accurate meshless method is proposed for solving the time fractional advection diffusion equation with variable coefficients which is based on the moving least square mls approximation in the proposed method firstly the time fractional derivative is approximated by a finite difference scheme of order o t 2 0 1 and then the mls approach is employed to approximate the spatial derivative where time fractional derivative is expressed in the caputo sense also the validity of the proposed method is investigated in error analysis discussion the main aim is to show that the meshless method based on the mls shape functions is highly appropriate for solving fractional partial differential equations fpdes with variable coefficients the efficiency and accuracy of the proposed method are verified by solving several examples

multivariate interpolation of arbitrarily spaced data by moving least squares methods abstract given a function f in scattered data points x1 xn r s we solve the least squares problem i 1 n j o q a j x b j x i f x i 2 v i x min in order to generate interpolants aj x bj x here the bj denote basis functions e g polynomials and the vi x are inverse distance weight functions we express the unknowns aj x the interpolant and the interpolation error in terms of moving convex combinations of functions corresponding to those of classical interpolation at q 1 points with respect to these basis functions further we discuss properties of moving least squares methods and in the case of polynomial basis functions we test various methods and give perspective plots

a restrictive pade approximation for the solution of the generalized fisher and burger fisher equations solving generalized fisher and burger fisher equations by the finite difference technique yields difficult nonlinear system of equations in this paper linearization and restrictive pade approximation is considered it yields more accurate and faster results also the stability analysis is discussed numerical results are treated

stability of partial difference equations governing control gains in infinite dimensional backstepping abstract we examine the stability properties of a class of ltv difference equations on an infinite dimensional state space that arise in backstepping designs for parabolic pdes the nominal system matrix of the difference equation has a special structure all of its powers have entries that are 1 0 or 1 and all of the eigenvalues of the matrix are on the unit circle the difference equation is driven by initial conditions additive forcing and a system matrix perturbation all of which depend on problem data for example viscosity and reactivity in the case of a reaction diffusion equation and all of which go to zero as the discretization step in the backstepping design goes to zero all of these observations combined with the fact that the equation evolves only in a number of steps equal to the dimension of its state space combined with the discrete gronwall inequality establish that the difference equation has bounded solutions this in turn guarantees the existence of a state feedback gain kernel in the backstepping control law with this approach we greatly expand relative to our previous results the class of parabolic pdes to which backstepping is applicable

quadratic optimal control of stable well posed linear systems we consider the infinite horizon quadratic cost minimization problem for a stable time invariant well posed linear system in the sense of salamon and weiss and show that it can be reduced to a spectral factorization problem in the control space more precisely we show that the optimal solution of the quadratic cost minimization problem is of static state feedback type if and only if a certain spectral factorization problem has a solution if both the system and the spectral factor are regular then the feedback operator can be expressed in terms of the riccati operator and the riccati operator is a positive self adjoint solution of an algebraic riccati equation this riccati equation is similar to the usual algebraic riccati equation but one of its coefficients varies depending on the subspace in which the equation is posed similar results are true for unstable systems as we have proved elsewhere

the numerical solution of nonlinear high dimensional generalized benjamin bona mahony burgers equation via the meshless method of radial basis functions in this paper a numerical technique is proposed for solving the nonlinear generalized benjamin bona mahony burgers equation firstly we obtain a time discrete scheme by approximating the first order time derivative via forward finite difference formula then we use kansa s approach to approximate the spatial derivatives we prove that the time discrete scheme is unconditionally stable and convergent in time variable using the energy method also we show that convergence order of the time discrete scheme is o t we solve the two dimensional version of this equation using the method presented in this paper on different geometries such as the rectangular triangular and circular domains and also the three dimensional case is solved on the cubical and spherical domains the aim of this paper is to show that the meshless method based on the radial basis functions and collocation approach is also suitable for the treatment of the nonlinear partial differential equations also several test problems including the three dimensional case are given numerical examples confirm the efficiency of the proposed scheme

improved error bounds for scattered data interpolation by radial basis functions if additional smoothness requirements and boundary conditions are met the well known approximation orders of scattered data interpolants by radial functions can roughly be doubled

quadratic optimal control of well posed linear systems we study the infinite horizon quadratic cost minimization problem for a well posed linear system in the sense of salamon and weiss the quadratic cost function that we seek to minimize need not be positive but it is convex and bounded from below we assume the system to be jointly stabilizable and detectable and give a feedback solution to the cost minimization problem moreover we connect this solution to the computation of either a j s inner or an s normalized coprime factorization of the transfer function depending on how the problem is formulated we apply the general theory to get factorization versions of the bounded and positive real lemmas in the case where the system is regular it is possible to show that the feedback operator can be expressed in terms of the riccati operator and that the riccati operator is a stabilizing self adjoint solution of an algebraic riccati equation this riccati equation is nonstandard in the sense that the weighting operator in the quadratic term differs from the expected one and the computation of the correct weighting operator is a nontrivial task

l p error estimates for shifted surface spline interpolation on sobolev space the accuracy of interpolation by a radial basis function is usually very satisfactory provided that the approximant f is reasonably smooth however for functions which have smoothness below a certain order associated with the basis function no approximation power has yet been established hence the purpose of this study is to discuss the lp approximation order 1 p of interpolation to functions in the sobolev space wpk with k max 0 d 2 d p we are particularly interested in using the shifted surface spline which actually includes the cases of the multiquadric and the surface spline moreover we show that the accuracy of the interpolation method can be at least doubled when additional smoothness requirements and boundary conditions are met

stability analysis of a system coupled to a heat equation as a first approach to the study of systems coupling finite and infinite dimensional natures this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a lyapunov functional technique inspired from recent developments in the area of time delay systems a new methodology to study the stability of such a class of distributed parameter systems is presented here the idea is to use a polynomial approximation of the infinite dimensional state of the heat equation in order to build an enriched energy functional a well known efficient integral inequality bessel inequality will allow to obtain stability conditions expressed in terms of linear matrix inequalities we will eventually test our approach on academic examples in order to illustrate the efficiency of our theoretical results

difference methods for parabolic equations with robin condition abstract classical solutions of nonlinear second order partial differential functional equations of parabolic type with the robin condition are approximated in the paper by solutions of associated boundedness preserving implicit difference functional equations it is proved that the discrete solutions uniquely exist they are uniformly bounded with respect to meshes and the numerical method is convergent and stable we also find the error estimate and its asymptotic behavior the properties of some auxiliary nonlinear discrete recurrent equations are showed the proofs are based on the comparison technique and the banach fixed point theorem

on the stationary lp approximation power to derivatives by radial basis function interpolation in this paper we consider approximation to derivatives of a function by using radial basis function interpolation most of well known theories for this problem provide error analysis in terms of the so called native space say c f however if a basis function f is smooth the space c f is extremely small thus the purpose of this study is to extend this result to functions in the homogenous sobolev space

exponential stabilization of well posed systems by colocated feedback we consider well posed linear systems whose state trajectories satisfy dot x ax bu where u is the input and a is an essentially skew adjoint and dissipative operator on the hilbert space x this means that the domains of a and a are equal and a a q where q geq 0 is bounded on x the control operator b is possibly unbounded but admissible and the observation operator of the system is b such a description fits many wave and beam equations with colocated sensors and actuators and it has been shown for many particular cases that the feedback u ka y v with ka 0 stabilizes the system strongly or even exponentially here y is the output of the system and v is the new input we show by means of a counterexample that if b is sufficiently unbounded then such a feedback may be unsuitable the closed loop semigroup may even grow exponentially our counterexample is a simple regular system with feedthrough operator zero however we prove that if the original system is exactly controllable and observable and if ka is sufficiently small then the closed loop system is exponentially stable

an isogeometric meshfree coupling approach for analysis of cracks summary this paper presents a new concurrent simulation approach to couple isogeometric analysis iga with the meshfree method for studying of crack problems in the present method the overall physical domain is divided into two sub domains which are formulated with the iga and meshfree method respectively in the meshfree sub domain the moving least squares mls shape function is adopted for the discretization of the area around crack tips and the iga sub domain is adopted in the remaining area meanwhile the interface region between the two sub domains is represented by coupled shape functions the resulting shape function which comprises both iga and meshfree shape functions satisfies the consistency condition thus ensuring convergence of the method moreover the meshfree shape functions augmented with the enriched basis functions to predict the singular stress fields near a crack tip are presented the proposed approach is also applied to simulate the crack propagation under a mixed mode condition several numerical examples are studied to demonstrate the utility and robustness of the proposed method this article is protected by copyright all rights reserved

adaptive boundary control for unstable parabolic pdes part ii estimation based designs the certainty equivalence approach to adaptive control is commonly used with two types of identifiers passivity based identifiers and swapping identifiers the passive also known as observer based approach is the prevalent identification technique in existing results on adaptive control for pdes but has so far not been used in boundary control problems the swapping approach prevalent in finite dimensional adaptive control is employed here for the first time in adaptive control of pdes for a class of unstable parabolic pdes we prove a separation principle result for both the passive and swapping identifiers combined with the backstepping boundary controllers the result is applicable in any dimension for physical reasons we restrict our attention to dimensions no higher than three the results of the paper are illustrated by simulations

brief paper adaptive boundary control for unstable parabolic pdes part iii output feedback examples with swapping identifiers we develop output feedback adaptive controllers for two benchmark parabolic pdes motivated by a model of thermal instability in solid propellant rockets both benchmark plants are unstable have infinite relative degree and are controlled from the boundary one plant has an unknown parameter in the pde and the other in the boundary condition in both cases the unknown parameter multiplies the measured output of the system which is obtained with a boundary sensor located on the opposite side of the domain from the actuator in comparison with the lyapunov output feedback adaptive controllers in krstic and smyshlyaev 2005 adaptive boundary control for unstable parabolic pdes part i lyapunov design ieee transactions on automatic control submitted for publication the controllers presented here employ much simpler update laws and do not require a priori knowledge about the unknown parameters we show how our two benchmarks examples can be combined and illustrate the adaptive stabilization design by simulation

approximating surfaces by the moving least absolute deviations method in this paper we are going to consider the problem of global data approximation on the basis of data containing outliers for that purpose a new method entitled the moving least absolute deviations method is proposed in the region of data in the network of knots weighted least absolute deviations local planes are constructed by means of which a global approximant is defined the method is tested on the well known franke s function an application in gridding of sonar data is also shown

a sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems this paper presents a sum of squares sos approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems the proposed sos based framework provides a number of innovations and improvements over the existing linear matrix inequality lmi based approaches to takagi sugeno t s fuzzy modeling and control first we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well known t s fuzzy modeling and control secondly we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial lyapunov functions that contain quadratic lyapunov functions as a special case hence the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing lmi based approaches to t s fuzzy modeling and control moreover the derived stability and stabilizability conditions are represented in terms of sos and can be numerically partially symbolically solved via the recently developed sostools to illustrate the validity and applicability of the proposed approach a number of analysis and design examples are provided the first example shows that the sos approach renders more relaxed stability results than those of both the lmi based approaches and a polynomial system approach the second example presents an extensive application of the sos approach in comparison with a piecewise lyapunov function approach the last example is a design exercise that demonstrates the viability of the sos based approach to synthesizing a stabilizing controller

a convex sum of squares approach to analysis state feedback and output feedback control of parabolic pdes we present an optimization based framework for analysis and control of linear parabolic partial differential equations pdes with spatially varying coefficients without discretization or numerical approximation for controller synthesis we consider both full state feedback and point observation output feedback the input occurs at the boundary point actuation we use positive definite matrices to parameterize positive lyapunov functions and polynomials to parameterize controller and observer gains we use duality and an invertible state variable transformation to convexify the controller synthesis problem finally we combine our synthesis condition with the luenberger observer framework to express the output feedback controller synthesis problem as a set of lmi sdp constraints we perform an extensive set of numerical experiments to demonstrate the accuracy of the conditions and to prove the necessity of the lyapunov structures chosen we provide numerical and analytical comparisons with alternative approaches to control including sturm liouville theory and backstepping finally we use numerical tests to show that the method retains its accuracy for alternative boundary conditions