stabilization of a class of stochastic differential equations with markovian switching stability of stochastic differential equations with markovian switching has been studied quite extensively for a number of years for example by basak et al j math anal appl 202 1996 604 622 ji and chizeck ieee trans automat control 35 1990 777 788 mariton jump linear systems in automatic control marcel dekker new york 1990 mao et al stochastic process appl 79 1999 45 67 bernoulli 6 2000 73 90 and yuan and lygeros in r alur g pappas eds hybrid systems computation and control seventh international workshop hscc 2004 lecture notes in computer science vol 2993 springer berlin 2004 pp 646 659 by contrast the problem of designing controllers to stabilize systems of this type has received relatively little attention in this paper we study the problem of mean square exponential stabilization for a class of stochastic differential equations with markovian switching

global stabilization of composite stochastic systems abstract the aim of this paper is to investigate the stabilizability problem for composite stochastic systems and to apply the results to partially linear composite stochastic systems in particular we state sufficient conditions under which there exists a feedback law which renders the equilibrium solution of the closed loop system deduced from a composite stochastic system exponentially stable in mean square in the case of partially linear composite stochastic systems the stabilizing feedback law is linear and is related to the solution of a stochastic riccati type equation

feature extraction on local jet space for texture classification abstract the proposal of this study is to analyze the texture pattern recognition over the local jet space looking forward to improve the texture characterization local jets decompose the image based on partial derivatives allowing the texture feature extraction be exploited in different levels of geometrical structures each local jet component evidences a different local pattern such as flat regions directional variations and concavity or convexity subsequently a texture descriptor is used to extract features from 0th 1st and 2nd derivative components four well known databases brodatz vistex usptex and outex and four texture descriptors fourier descriptors gabor filters local binary pattern and local binary pattern variance were used to validate the idea showing in most cases an increase of the success rates

discrete finite element characterizations of source fields for volume and boundary constraints in electromagnetic problems the consideration of electromagnetic field sources in potential formulations necessitates the definition of source fields such source fields are first defined for both volume and boundary constraints in static electromagnetic models then automatic procedures are proposed to conveniently and efficiently characterize discrete source fields with regard to their use in finite element formulations their supports their direct expression requiring no pre computation and their associated constraints two application examples are proposed to illustrate the approach

the hierarchical structure of images using a gaussian scale space one can use the extra dimension viz scale for investigation of built in properties of the image in scale space we show that one of such induced properties is the nesting of special iso intensity manifolds which yield an implicitly present hierarchy of the critical points and regions of their influence in the original image its very nature allows one not only to segment the original image automatically but also to apply logical filters to it obtaining simplified images we give an algorithm deriving this hierarchy and show its effectiveness on two different kinds of images both with respect to segmentation and simplification

invertible apertured orientation filters in image analysis a unitary approach for locally apertured orientation analysis of 2d and 3d scalar images is proposed the size of the local aperture the scale needed for the orientation representation induces in general a lost of spatial acuity or blur our construction permits a compensation of the blur by a reconstruction procedure for this purpose a special scale dependent orientation bundle map of the visual space into function of both position and orientation is build from the local gaussian derivatives jet of a scalar image in this construction there is an invertible relation between the orientation bundle and the original image this invertible transformation is used to regain the original acuity in the spatial domain after analyzing orientation features at any given scale the approach turns out to be highly effective for the detection of elongated structures and for removal of elongated artifacts in 2d images

multi element generalized polynomial chaos for arbitrary probability measures we develop a multi element generalized polynomial chaos me gpc method for arbitrary probability measures and apply it to solve ordinary and partial differential equations with stochastic inputs given a stochastic input with an arbitrary probability measure its random space is decomposed into smaller elements subsequently in each element a new random variable with respect to a conditional probability density function pdf is defined and a set of orthogonal polynomials in terms of this random variable is constructed numerically then the generalized polynomial chaos gpc method is implemented element by element numerical experiments show that the cost for the construction of orthogonal polynomials is negligible compared to the total time cost efficiency and convergence of me gpc are studied numerically by considering some commonly used random variables me gpc provides an efficient and flexible approach to solving differential equations with random inputs especially for problems related to long term integration large perturbation and stochastic discontinuities

solving elliptic boundary value problems with uncertain coefficients by the finite element method the stochastic formulation this work studies a linear elliptic problem with uncertainty the introduction gives a survey of different formulations of the uncertainty and resulting numerical approximations the major emphasis

uncertainty propagation using wiener haar expansions an uncertainty quantification scheme is constructed based on generalized polynomial chaos pc representations two such representations are considered based on the orthogonal projection of uncertain data and solution variables using either a haar or a legendre basis governing equations for the unknown coefficients in the resulting representations are derived using a galerkin procedure and then integrated in order to determine the behavior of the stochastic process the schemes are applied to a model problem involving a simplified dynamical system and to the classical problem of rayleigh benard instability for situations involving random parameters close to a critical point the computational implementations show that the wiener haar wha representation provides more robust predictions that those based on a wiener legendre wle decomposition however when the solution depends smoothly on the random data the wle scheme exhibits superior convergence suggestions regarding future extensions are finally drawn based on these experiences

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

feedback stabilization of affine in the control stochastic differential systems by the control lyapunov function method the purpose of this paper is to study the asymptotic stability in probability of affine in the control stochastic differential systems sufficient conditions for the existence of control lyapunov functions leading to the existence of stabilizing feedback laws which are smooth except possibly at the equilibrium point of the system are provided

the relevance of non generic events in scale space models in order to investigate the deep structure of gaussian scale space images one needs to understand the behaviour of spatial critical points under the influence of blurring we show how the mathematical framework of catastrophe theory can be used to describe and model the behaviour of critical point trajectories when various different types of generic events viz annihilations and creations of pairs of spatial critical points almost coincide although such events are non generic in mathematical sense they are not unlikely to be encountered in practice due to numerical limitations furthermore the behaviour of these trajectories leads to the observation that fine to coarse tracking of critical points doesn t suffice since they can form closed loops in scale space the modelling of the trajectories include these loops we apply the theory to an artificial image and a simulated mr image and show the occurrence of the described behaviour

verification of stochastic models in uncertain environments using the constitutive relation error method abstract this paper deals with local stress errors which occur in linear elastic fe analysis in an uncertain environment material loads the estimation technique described here uses the concept of error in constitutive relation but it can be adapted to other estimators first we review the principle of the method then extend it to the stochastic case this approach yields bounds on the stresses associated with a given confidence level we illustrate this presentation through a test example

the gaussian scale space paradigm and the multiscale local jet a representation of local image structure is proposed which takes into account both the image s spatial structure at a given location as well as its deep structure that is its local behaviour as a function of scale or resolution scale space this is of interest for several low level image tasks the proposed basis of scale space for example enables a precise local study of interactions of neighbouring image intensities in the course of the blurring process it also provides an extrapolation scheme for local image data obtained at a given spatial location and resolution to a finite scale space neighbourhood this is especially useful for the determination of sampling rates and for interpolation algorithms in a multilocal context another particularly straightforward application is image enhancement or deblurring which is an instance of data extrapolation in the high resolution direction a potentially interesting feature of the proposed local image parametrisation is that it captures a trade off between spatial and scale extrapolations from a given interior point that do not exceed a given tolerance this trade off suggests the possibility of a fairly coarse scale sampling at the expense of a dense spatial sampling large relative spatial overlap of scale space kernels the central concept developed in this paper is an equivalence class called the multiscale zocal jet which is a hierarchical local characterisation of the image in a full scale space neighbourhood for this local jet a basis of fundamental polynomials is constructed that captures the scale space paradigm at the local level up to any given order

error estimation in a stochastic finite element method in electrokinetics input data to a numerical model are not necessarily well known uncertainties may exist both in material properties and in the geometry of the device they can be due for instance to ageing or imperfections in the manufacturing process input data can be modelled as random variables leading to a stochastic model in electromagnetism this leads to solution of a stochastic partial differential equation system the solution can be approximated by a linear combination of basis functions rising from the tensorial product of the basis functions used to discretize the space nodal shape function for example and basis functions used to discretize the random dimension a polynomial chaos expansion for example some methods ssfem collocation have been proposed in the literature to calculate such approximation the issue is then how to compare the different approaches in an objective way one solution is to use an appropriate a posteriori numerical error estimator in this paper we present an error estimator based on the constitutive relation error in electrokinetics which allows the calculation of the distance between an average solution and the unknown exact solution the method of calculation of the error is detailed in this paper from two solutions that satisfy the two equilibrium equations in an example we compare two different approximations legendre and hermite polynomial chaos expansions for the random dimension using the proposed error estimator in addition we show how to choose the appropriate order for the polynomial chaos expansion for the proposed error estimator c

a passive system approach to feedback stabilization of nonlinear control stochastic systems the purpose of this paper is to provide sufficient conditions for asymptotic stabilization in probability of nonlinear control stochastic differential systems by means of smooth state feedback laws in particular we prove that as in the case of stochastic differential systems affine in the control one can compute stabilizing feedback laws provided the unforced stochastic differential system is lyapunov stable in probability and some rank conditions are fulfilled some well known stabilization results for stochastic differential systems affine in the control proved in the literature are extended to nonaffine nonlinear control stochastic differential systems

the second order local image structure solid characterization of second order local image structure by a 6d vector or jet of gaussian derivative measurements is considered we consider the affect on jets of a group of transformations affine intensity scaling image rotation and reflection and their compositions that preserve intrinsic image structure we show how this group stratifies the jet space into a system of orbits considering individual orbits as points a 3d orbifold is defined we propose a norm on jet space which we use to induce a metric on the orbifold the metric tensor shows that the orbifold is intrinsically curved to allow visualization of the orbifold and numerical computation with it we present a mildly distorting but volume preserving embedding of it into euclidean 3 space we call the resulting shape which is like a flattened lemon the second order local image structure solid as an example use of the solid we compute the distribution of local structures in noise and natural images for noise images analytical results are possible and they agree with the empirical results for natural images an excess of locally 1d structure is found

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

galerkin methods for linear and nonlinear elliptic stochastic partial differential equations abstract stationary systems modelled by elliptic partial differential equations linear as well as nonlinear with stochastic coefficients random fields are considered the mathematical setting as a variational problem existence theorems and possible discretisations in particular with respect to the stochastic part are given and investigated with regard to stability different and increasingly sophisticated computational approaches involving both wiener s polynomial chaos as well as the karhunen loeve expansion are addressed in conjunction with stochastic galerkin procedures and stability within the galerkin framework is established new and effective algorithms to compute the mean and covariance of the solution are proposed the similarities and differences with better known monte carlo methods are exhibited as well as alternatives to integration in high dimensional spaces hints are given regarding the numerical implementation and parallelisation numerical examples serve as illustration

feedback stabilizability of non linear stochastic systems with state dependent noise this paper deals with non linear stochastic systems with state dependent noise based on the solution of the stochastic algebraic riccati equation sufficient conditions are derived which assure the existence of state feedback control laws such that the closed loop system is locally and globally stable in probability

global stabilization of partially linear composite systems a linear stabilizable nonlinear asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if a the linear subsystem is right invertible and weakly minimum phase and b the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output both of these conditions are coordinate free and there is freedom of choice for the linear output variable this result generalizes several earlier sufficient conditions for stabilizability moreover the weak minimum phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem