on nonstability of the linear recurrence of order one abstract we show that under some assumptions the linear recurrence or difference equation of order one in a banach space is nonstable in the hyers ulam sense our results are also connected with the notion of shadowing in dynamical systems and computer sciences

fast algorithms for low level vision a recursive filtering structure is proposed that drastically reduces the computational effort required for smoothing performing the first and second directional derivatives and carrying out the laplacian of an image these operations are done with a fixed number of multiplications and additions per output point independently of the size of the neighborhood considered the key to the approach is first the use of an exponentially based filter family and second the use of the recursive filtering applications to edge detection problems and multiresolution techniques are considered and an edge detector allowing the extraction of zero crossings of an image with only 14 operations per output element at any resolution is proposed various experimental results are shown

brief terminal iterative learning control with an application to rtpcvd thickness control a special type of iterative learning control ilc problem is considered due to the insufficient measurement capability in many real control problems such as rapid thermal processing rtp it may happen that only the terminal output tracking error instead of the whole output trajectory tracking error is available in the rtp chemical vapor deposition cvd of wafer fab industry the ultimate control objective is to control the deposition thickness dt at the end of the rtp cycle the control profile for the next operation cycle has to be updated using the terminal dt tracking error alone a revised ilc method is proposed to address this terminal output tracking problem by parameterizing the control profile with a piecewise continuous functional basis the parameters are updated by a high order updating scheme a convergence condition is obtained for a class of uncertain discrete time time varying linear systems including the rtpcvd system as the subset simulation results for an rtpcvd thickness control problem are presented to demonstrate the effectiveness of the proposed iterative learning scheme

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

acceleration of the shiftable mbi o 1 algorithm for bilateral filtering and nonlocal means a direct implementation of the bilateral filter requires o s2 operations per pixel where s is the effective width of the spatial kernel a fast implementation of the bilateral filter that required o 1 operations per pixel with respect to s was recently proposed this was done by using trigonometric functions for the range kernel of the bilateral filter and by exploiting their so called shiftability property in particular a fast implementation of the gaussian bilateral filter was realized by approximating the gaussian range kernel using raised cosines later it was demonstrated that this idea could be extended to a larger class of filters including the popular non local means filter as already observed a flip side of this approach was that the run time depended on the width r of the range kernel for an image with dynamic range 0 t the run time scaled as o t2 r2 with r this made it difficult to implement narrow range kernels particularly for images with large dynamic range in this paper we discuss this problem and propose some simple steps to accelerate the implementation in general and for small r in particular we provide some experimental results to demonstrate the acceleration that is achieved using these modifications

on the gradient inverse weighted filter image processing d c c wang et al 1981 presented a gradient inverse weighted giw filter the proposed noise smoothing scheme is based on the observation that variations of gray levels inside a region are smaller than those between regions reducing noise without smearing edges is the advantage of this nonlinear filter as an improvement of the giw filter a new algorithm is introduced examples show that it can preserve edges and smooth noise more efficiently

on an equation characterizing multi additive quadratic mappings and its hyers ulam stability in this paper we unify the system of functional equations defining a multi additive quadratic mapping to obtain a single equation we also prove using the fixed point method the generalized hyers ulam stability of this equation thus generalizing some known results

improvements on fast space variant elliptical filtering using box splines it is well known that box filters can be efficiently computed using pre integration and local finite differences by generalizing this idea and by combining it with a nonstandard variant of the central limit theorem we had earlier proposed a constant time or o 1 algorithm that allowed one to perform space variant filtering using gaussian like kernels the algorithm was based on the observation that both isotropic and anisotropic gaussians could be approximated using certain bivariate splines called box splines the attractive feature of the algorithm was that it allowed one to continuously control the shape and size covariance of the filter and that it had a fixed computational cost per pixel irrespective of the size of the filter the algorithm however offered a limited control on the covariance and accuracy of the gaussian approximation in this paper we propose some improvements of our previous algorithm

spatially variant convolution with scaled b splines we present an efficient algorithm to compute multidimensional spatially variant convolutions or inner products between n dimensional signals and b splines or their derivatives of any order and arbitrary sizes the multidimensional b splines are computed as tensor products of 1 d b splines and the input signal is expressed in a b spline basis the convolution is then computed by using an adequate combination of integration and scaled finite differences as to have for moderate and large scale values a computational complexity that does not depend on the scaling factor to show in practice the benefit of using our spatially variant convolution approach we present an adaptive noise filter that adjusts the kernel size to the local image characteristics and a high sensitivity local ridge detector

recursive anisotropic 2 d gaussian filtering based on a triple axis decomposition we describe a recursive algorithm for anisotropic 2 d gaussian filtering based on separating the filter into the cascade of three rather two 1 d filters the filters operate along axes obtained by integer horizontal and or vertical pixel shifts this eliminates interpolation which removes spatial inhomogeneity in the filter and produces more elliptically shaped kernels it also results in a more regular filter structure which facilitates implementation in dsp chips finally it improves matching between filters with the same eccentricity and width but different orientations our analysis and experiments indicate that the computational complexity is similar to an algorithm that operates along two axes 11ms for a 512times512 image using a 3 2 ghz pentium 4 pc on the other hand given a limited set of basis filter axes there is an orientation dependent lower bound on the achievable aspect ratios

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

hyers ulam rassias stability of a linear recurrence abstract in this paper we give a hyers ulam rassias stability result for the first order linear recurrence in banach spaces

remarks on stability and non stability of the linear functional equation of the first order abstract we prove some results on stability and non stability of the linear functional equation of the first order in single variable moreover we suggest some possible definitions of stability and non stability

brief iterative learning control with initial rectifying action this paper addresses the initial shift problem in iterative learning control with system relative degree the tracking error caused by nonzero initial shift is detected when applying a conventional learning algorithm finite initial rectifying action is introduced in the learning algorithm and is shown effective in the improvement of tracking performance in particular robustness with respect to variable initial shifts the uniform convergence of the output trajectory to a desired one jointed smoothly with a specified transient trajectory from the starting position is ensured in the presence of fixed initial shift

robust optimal design and convergence properties analysis of iterative learning control approaches in this paper we address four major issues in the field of iterative learning control ilc theory and design the first issue is concerned with ilc design in the presence of system interval uncertainties targeting at time optimal fastest convergence and robustness properties concurrently we formulate the ilc design into a min max optimization problem and provide a systematic solution for linear type ilc consisting of the first order and higher order ilc schemes inherently relating to the first issue the second issue is concerned with the performance evaluation of various ilc schemes convergence speed is one of the most important factors in ilc a learning performance index q factor is introduced which provides a rigorous and quantified evaluation criterion for comparing the convergence speed of various ilc schemes we further explore a key issue how does the system dynamics affect the learning performance by associating the time weighted norm with the supreme norm we disclose the dynamics impact in ilc which can be assessed by global uniform bound and monotonicity in iteration domain finally we address a rather controversial issue in ilc can the higher order ilc outperform the lower order ilc in terms of convergence speed and robustness by applying the min max design which is robust and optimal and conducting rigorous analysis we reach the conclusion that the q factor of ilc sequences of lower order ilc is lower than that of higher order ilc in terms of the time weighted norm

an iterative learning controller with initial state learning in iterative learning control ilc a common assumption is that the initial states in each repetitive operation should be inside a given ball centred at the desired initial states which may be unknown this assumption is critical to the stability analysis and the size of the ball will directly affect the final output trajectory tracking errors in this paper this assumption is removed by using an initial state learning scheme together with the traditional d type ilc updating law both linear and nonlinear time varying uncertain systems are investigated uniform bounds for the final tracking errors are obtained and these bounds are only dependent on the system uncertainties and disturbances yet independent of the initial errors furthermore the desired initial states can be identified through learning iterations

on a direct method for proving the hyers ulam stability of functional equations abstract we study the stability of an equation in a single variable of the form f x a f h x b f h x with some conditions imposed on constants a b and function h the results are later applied for proving the stability by use of a direct method of a couple of functional equations in several variables they let us not only shorten various approaches obtained during the last years but also improve the approximating constants

a necessary and sufficient condition for consensus over random networks we consider the consensus problem for stochastic discrete time linear dynamical systems the underlying graph of such systems at a given time instance is derived from a random graph process independent of other time instances for such a framework we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments this easily verifiable condition uses the spectrum of the average weight matrix finally we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1

selections of set valued maps satisfying a linear inclusion in a single variable abstract we prove that a set valued map satisfying a linear functional inclusion in a single variable admits in appropriate conditions a unique selection satisfying a linear functional equation in a single variable as a consequence there follow results on the hyers ulam stability of the linear functional equation in a single variable and the equation of homomorphism of square symmetric groupoids

fast anisotropic gauss filtering we derive the decomposition of the anisotropic gaussian in a one dimensional 1 d gauss filter in the x direction followed by a 1 d filter in a nonorthogonal direction spl phi so also the anisotropic gaussian can be decomposed by dimension this appears to be extremely efficient from a computing perspective an implementation scheme for normal convolution and for recursive filtering is proposed also directed derivative filters are demonstrated for the recursive implementation filtering an 512 spl times 512 image is performed within 40 msec on a current state of the art pc gaining over 3 times in performance for a typical filter independent of the standard deviations and orientation of the filter accuracy of the filters is still reasonable when compared to truncation error or recursive approximation error the anisotropic gaussian filtering method allows fast calculation of edge and ridge maps with high spatial and angular accuracy for tracking applications the normal anisotropic convolution scheme is more advantageous with applications in the detection of dashed lines in engineering drawings the recursive implementation is more attractive in feature detection applications for instance in affine invariant edge and ridge detection in computer vision the proposed computational filtering method enables the practical applicability of orientation scale space analysis

fast space variant elliptical filtering using box splines the efficient realization of linear space variant non convolution filters is a challenging computational problem in image processing in this paper we demonstrate that it is possible to filter an image with a gaussian like elliptic window of varying size elongation and orientation using a fixed number of computations per pixel the associated algorithm which is based upon a family of smooth compactly supported piecewise polynomials the radially uniform box splines is realized using preintegration and local finite differences the radially uniform box splines are constructed through the repeated convolution of a fixed number of box distributions which have been suitably scaled and distributed radially in an uniform fashion the attractive features of these box splines are their asymptotic behavior their simple covariance structure and their quasi separability they converge to gaussians with the increase of their order and are used to approximate anisotropic gaussians of varying covariance simply by controlling the scales of the constituent box distributions based upon the second feature we develop a technique for continuously controlling the size elongation and orientation of these gaussian like functions finally the quasi separable structure along with a certain scaling property of box distributions is used to efficiently realize the associated space variant elliptical filtering which requires o 1 computations per pixel irrespective of the shape and size of the filter

fast o 1 bilateral filtering using trigonometric range kernels it is well known that spatial averaging can be realized in space or frequency domain using algorithms whose complexity does not scale with the size or shape of the filter these fast algorithms are generally referred to as constant time or o 1 algorithms in the image processing literature along with the spatial filter the edge preserving bilateral filter involves an additional range kernel this is used to restrict the averaging to those neighborhood pixels whose intensity are similar or close to that of the pixel of interest the range kernel operates by acting on the pixel intensities this makes the averaging process nonlinear and computationally intensive particularly when the spatial filter is large in this paper we show how the o 1 averaging algorithms can be leveraged for realizing the bilateral filter in constant time by using trigonometric range kernels this is done by generalizing the idea presented by porikli i e using polynomial kernels the class of trigonometric kernels turns out to be sufficiently rich allowing for the approximation of the standard gaussian bilateral filter the attractive feature of our approach is that for a fixed number of terms the quality of approximation achieved using trigonometric kernels is much superior to that obtained by porikli using polynomials

comments on the core of the direct method for proving hyers ulam stability of functional equations in this short paper the core of the direct method for proving stability of functional equations is described in a clear way and in a quite general form

on approximate solutions of the linear functional equation of higher order abstract we show that under some assumptions every approximate solution of the linear functional equation of higher order in single variable generates a solution of the equation that is close to it we also give a description of a procedure that yields such a solution estimate the distance between those approximate and exact solutions to the equation and discuss the problem of uniqueness moreover as a consequence we obtain some results concerning the hyers ulam stability of the equation

optimal iterative learning control design for multi agent systems consensus tracking abstract under a repeatable operation environment this paper proposes an iterative learning control scheme that can be applied to multi agent systems to perform consensus tracking under the fixed communication topology the agent dynamics are modeled by time varying nonlinear equations which satisfy the global lipschitz continuous condition in addition the desired consensus trajectory is only accessible to a subset of the followers by using the concept of the graph dependent matrix norm the convergence conditions can be specified at the agent level which depend on a set of eigenvalues that are associated with the communication topology the results are first derived for homogeneous agent systems and then extended to heterogeneous systems next optimal controller gain design methods are proposed in the sense that the norm of tracking error converges at the fastest rate which imposes a tightest bounding function for the actual tracking error in the norm analysis framework in the end an illustrative example of a group of heterogeneous agents is provided to demonstrate the effectiveness of the proposed design methods

synchronization of coupled harmonic oscillators with local interaction this paper studies synchronization of coupled second order linear harmonic oscillators with local interaction we analyze convergence conditions over respectively directed fixed and switching network topologies by using tools from algebraic graph theory matrix theory and nonsmooth analysis it is shown that the coupled harmonic oscillators can be synchronized under mild network connectivity conditions examples are given to validate the convergence conditions the theoretical result is also applied to synchronized motion coordination of multi agent systems as a proof of concept

stability of functional equations in single variable abstract this paper discusses hyers ulam stability for functional equations in single variable including the forms of linear functional equation nonlinear functional equation and iterative equation surveying many known and related results we clarify the relations between hyers ulam stability and other senses of stability such as iterative stability continuous dependence and robust stability which are used for functional equations applying results of nonlinear functional equations we give the hyers ulam stability of bottcher s equation we also prove a general result of hyers ulam stability for iterative equations

an iterative learning approach to formation control of multi agent systems abstract in this paper an efficient framework is proposed to the formation control problem of multiple agents with unknown nonlinear dynamics by means of the iterative learning approach in particular a distributed d type iterative learning scheme is developed for the multi agent system with switching topology whose switching time and sequence are allowed to be varied at different iterations according to the actual trajectories of agents and a sufficient condition is derived to ensure that the desired formation can be always preserved from the initial starting location to the final one after some iterations simulation results are provided to verify the effectiveness of the proposed approach

consensus problems on networks with antagonistic interactions in a consensus protocol an agreement among agents is achieved thanks to the collaborative efforts of all agents expresses by a communication graph with nonnegative weights the question we ask in this paper is the following is it possible to achieve a form of agreement also in presence of antagonistic interactions modeled as negative weights on the communication graph the answer to this question is affirmative on signed networks all agents can converge to a consensus value which is the same for all agents except for the sign necessary and sufficient conditions are obtained to describe cases in which this is possible these conditions have strong analogies with the theory of monotone systems linear and nonlinear laplacian feedback designs are proposed