controlled invariance for discrete time nonlinear systems with an application to the disturbance decoupling problems invariant distributions are defined for discrete time nonlinear control systems and necessary and sufficient conditions are given for their controlled invariance this extends to discrete time systems the basic tool which has been so important in solving the various synthesis problems for continuous time systems to indicate their utility in the discrete time setting they are used to locally solve the disturbance decoupling problem

binary image comparison with local dissimilarity quantification in this paper we present a method for binary image comparison for binary images intensity information is poor and shape extraction is often difficult therefore binary images have to be compared without using feature extraction due to the fact that different scene patterns can be present in the images we propose a modified hausdorff distance hd locally measured in an adaptive way the resulting set of measures is richer than a single global measure the local hd measures result in a local dissimilarity map ldmap including the dissimilarity spatial layout a classification of the images in function of their similarity is carried out on the ldmaps using a support vector machine the proposed method is tested on a medieval illustration database and compared with other methods to show its efficiency

exact linearizations of input output systems the problem of transforming non linear systems to linear systems is receiving much attention in the literature in this paper we present necessary and sufficient conditions such that a non linear control system with output can be equivalent to a linear control system with linear output that is controllable and observable the conditions depend on certain lie derivatives of the output and can be verified in a finite number of steps for simplicity we consider only the single input single output case

remarks on linearization of discrete time autonomous systems and nonlinear observer design abstract this paper presents necessary and sufficient conditions under which a discrete time autonomous system with outputs is locally state equivalent to an observable linear system or a system in the nonlinear observer form krener and isidori 1983 in particular an open problem raised in lee and nam 1991 namely the observer linearization problem is solved for a nonlinear system which may not be invertible i e the mapping f may not be a local diffeomorphism as a consequence the nonlinear observer design problem is solved by means of exact linearization techniques

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

linearization of discrete time nonlinear systems and a canonical structure linearizable nonlinear discrete time systems are described as a composition of diffeomorphisms linearizability of a general nonlinear system is obtained as an extension of linearizability of the system expressed in terms of the diffeomorphisms

normal forms and approximated feedback linearization in discrete time abstract the paper discusses approximated feedback linearization of nonlinear discrete time dynamics which are controllable in first approximation and introduces two types of normal forms the study is set in the context of differential difference representations of discrete time dynamics proposed in monaco normand cyrot in normand cyrot ed perspectives in control a tribute to ioan dore landau springer londres 1998 pp 191 205

a constructive condition for dynamic feedback linearization the paper deals with dynamic feedback linearization of continuous time affine systems a constructive procedure based on prolongations is proposed based on necessary geometric conditions the algorithm computes a set of prolongation indices

shape matching of two dimensional objects in this paper we present results in the areas of shape matching of nonoccluded and occluded two dimensional objects shape matching is viewed as a segment matching problem unlike the previous work the technique is based on a stochastic labeling procedure which explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification to reduce the computation time the technique is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels this basic technique has been extended to the situation where various objects partially occlude each other to form an apparent object and our interest is to find all the objects participating in the occlusion in such a case several hierarchical processes are executed in parallel for every object participating in the occlusion and are coordinated in such a way that the same segment of the apparent object is not matched to the segments of different actual objects these techniques have been applied to two dimensional simple closed curves represented by polygons and the power of the techniques is demonstrated by the examples taken from synthetic aerial industrial and biological images where the matching is done after using the actual segmentation methods

the effect sampling on linear equivalence and feedback linearization we investigate the effect of sampling on linearization for continuous time systems it is shown that the discretized system is linearizable by state coordinate change for an open set of sampling times if and only if the continuous time system is linearizable by state coordinate change also it is shown that linearizability via digital feedback imposes highly nongeneric constraints on the structure of the plant even if this is known to be linearizable with continuous time feedback for n 2 we show under the assumption of completeness of adfg that if the discretized system is lineariable by state coordinate change and feedback then the continuous time affine complete analytic system is linearizable by state coordinate change only also we suggest a method of proof when n 3

linearization of discrete time systems abstract we characterize the equivalence of single input single output discrete time nonlinear systems to linear ones via a state coordinate change and with or without feedback four cases are distinguished by allowing or disallowing feedback as well as by including the output map or not the interdependence of these problems is analyzed an important feature that distinguishes these discrete time problems from the corresponding problem in continuous time is that the state coordinate transformation is here directly computable as a higher composition of the system and output maps finally certain connections are made with the continuous time case

fast algorithm for robust template matching with m estimators we propose a fast algorithm for speeding up the process of template matching that uses m estimators for dealing with outliers we propose a particular image hierarchy called the p pyramid that can be exploited to generate a list of ascending lower bounds of the minimal matching errors when a nondecreasing robust error measure is adopted then the set of lower bounds can be used to prune the search of the p pyramid and a fast algorithm is thereby developed in this paper this fast algorithm ensures finding the global minimum of the robust template matching problem in which a nondecreasing m estimator serves as an error measure experimental results demonstrate the effectiveness of our method

global state and feedback equivalence of nonlinear systems the problem of finding global state space transformations and global feedback of the form u t x t to transform a given nonlinear system xdot f x g x u to a controllable linear system on rn or on an open subset of rn is considered here we give a complete set of differential geometric conditions which are equivalent to the existence of a solution to the above problem

on dynamic input output linearization of discrete time nonlinear systems this paper studies the problem of linearizing the input output map of an analytic discrete time nonlinear system locally around a given trajectory necessary and sufficient conditions are given for the existence of a regular dynamic state feedback control law under which the input dependent part of the response of a nonlinear system becomes linear in the input and independent of the initial state the proposed conditions are less restrictive than those obtained by lee and marcus for linearizing the input output map via a static state feedback instrumental in the problem solution is the inversion structure algorithm for a discrete time nonlinear system firstly the solvability conditions are expressed in terms of the inversion algorithm secondly the proof of the existence and construction of the dynamic state feedback compensator relies on this algorithm

a functional equations approach to nonlinear discrete time feedback stabilization through pole placement abstract the present work proposes a new approach to the nonlinear discrete time feedback stabilization problem with pole placement the problem s formulation is realized through a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived using tools from functional equations theory one can prove that the solution to the above system of nonlinear functional equations is locally analytic and an easily programmable series solution method can be developed under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear discrete time state feedback control law that are both computed through the solution of the system of nonlinear functional equations the feedback stabilization with pole placement design objective can be attained under rather general conditions the key idea of the proposed single step design approach is to bypass the intermediate step of transforming the original system into a linear controllable one with an external reference input associated with the classical exact feedback linearization approach however since the proposed method does not involve an external reference input it cannot meet other control objectives such as trajectory tracking and model matching

necessary and sufficient conditions for state equivalence to a nonlinear discrete time observer canonical form in this technical note we obtain necessary and sufficient conditions for a multi input multi output discrete time nonlinear system to be state equivalent to a nonlinear observer form and for an uncontrolled multi output system to be state equivalent to a linear observer form we adopt a geometric approach and the proofs are constructive with respect to the required coordinate change

the immersion under feedback of a multidimensional discrete time non linear system into a linear system this paper deals with the problem of finding conditions which ensure the reproducibility of the input output behaviour of a linear analytic discrete time system by means of a linear discrete time system on this basis the problem of modifying the system by feedback in order for it to enjoy such a property is posed and solved

spatially eigen weighted hausdorff distances for human face recognition abstract hausdorff distance is an efficient measure of the similarity of two point sets in this paper we propose a new spatially weighted hausdorff distance measure for human face recognition the weighting function used in the hausdorff distance measure is based on an eigenface which has a large value at locations of importance facial features and can reflect the face structure more effectively two modified hausdorff distances namely spatially eigen weighted hausdorff distance sewhd and spatially eigen weighted doubly hausdorff distance sew2hd are proposed which incorporate the information about the location of important facial features such as eyes mouth and face contour so that distances at those regions will be emphasized experimental results based on a combination of the orl mit and yale face databases show that sew2hd can achieve recognition rates of 83 90 and 92 for the first one the first three and the first five likely matched faces respectively while the corresponding recognition rates of sewhd are 80 83 and 88 respectively

algebraic bethe ansatz for 19 vertex models with reflection conditions in this work we solve the 19 vertex models with the use of algebraic bethe ansatz for diagonal reflection matrices sklyanin k matrices the eigenvectors eigenvalues and bethe equations are given in a general form quantum spin chains of spin one derived from the 19 vertex models were also discussed

control systems in neural networks with local memory abstract based on a new paradigm of neural networks consisting of neurons with local memory nnlm we discuss the representation of a control system by neural networks using this representation the basic issues of complete controllability and observability for the system are addressed a separation principle of learning and control is presented for nnlm the result shows that the weights of the network will not affect its dynamics some results about local linearization via a regular static feedback and nonlinear transformation are also given

layered graph matching with composite cluster sampling this paper presents a framework of layered graph matching for integrating graph partition and matching the objective is to find an unknown number of corresponding graph structures in two images we extract discriminative local primitives from both images and construct a candidacy graph whose vertices are matching candidates i e a pair of primitives and whose edges are either negative for mutual exclusion or positive for mutual consistence then we pose layered graph matching as a multicoloring problem on the candidacy graph and solve it using a composite cluster sampling algorithm this algorithm assigns some vertices into a number of colors each being a matched layer and turns off all the remaining candidates the algorithm iterates two steps 1 sampling the positive and negative edges probabilistically to form a composite cluster which consists of a few mutually conflicting connected components ccps in different colors and 2 assigning new colors to these ccps with consistence and exclusion relations maintained and the assignments are accepted by the markov chain monte carlo mcmc mechanism to preserve detailed balance this framework demonstrates state of the art performance on several applications such as multi object matching with large motion shape matching and retrieval and object localization in cluttered background

an endmember based distance for content based hyperspectral image retrieval we propose a specific content based image retrieval cbir system for hyperspectral images exploiting its rich spectral information the cbir image features are the endmember signatures obtained from the image data by endmember induction algorithms eias endmembers correspond to the elementary materials in the scene so that the pixel spectra can be decomposed into a linear combination of endmember signatures eia search for points in the high dimensional space of pixel spectra defining a convex polytope often a simplex covering the image data this paper introduces a dissimilarity measure between hyperspectral images computed over the image induced endmembers proving that it complies with the axioms of a distance we provide a comparative discussion of dissimilarity functions and quantitative evaluation of their relative performances on a large collection of synthetic hyperspectral images and on a dataset extracted from a real hyperspectral image alternative dissimilarity functions considered are the hausdorff distance and robust variations of it we assess the cbir performance sensitivity to changes in the distance between endmembers the eia employed and some other conditions the proposed hyperspectral image distance improves over the alternative dissimilarities in all quantitative performance measures the visual results of the cbir on the real image data demonstrate its usefulness for practical applications

losslessness feedback equivalence and the global stabilization of discrete time nonlinear systems in this paper a necessary and sufficient condition for a nonlinear system of the form spl sigma given by x k 1 f x k g x k u k y k h x k j x k u k to be lossless is given and it is shown that a lossless system can be globally asymptotically stabilized by output feedback if and only if the system is zero state observable then we investigate conditions under which spl sigma can be rendered lossless via smooth state feedback in particular we show that this is possible if and only if the system in question has relative degree spl lcub 0 0 spl rcub and has lossless zero dynamics under suitable controllability like rank conditions we prove that nonlinear systems having relative degree spl lcub 0 0 spl rcub and lossless zero dynamics can be globally stabilized by smooth state feedback as a consequence we obtain sufficient conditions for a class of cascaded systems to be globally stabilizable the global stabilization problem of the nonlinear system spl sigma without output is also investigated in this paper by means of feedback equivalence some of the results are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

quadratic forms and approximate feed back linearization in discrete time quadratic feedback linearization is discussed for discrete time systems i e approximate feedback linearization up to the second order with respect to input and state variables after introducing in discrete time two equivalence classes invariant under quadratic static state feedback and diffeomorphism two canonical quadratic representations are proposed then it is shown that any nonlinear discrete time dynamics which are controllable in their first approximations can be linearized up to the second order under dynamic feedback the results stated here can be considered as the general discrete time analogues of the continuous time ones kang and krener 1992

linear dynamics hidden by input output linearization abstract the input output linearization method has been quite useful in determining the linear input output responses of non linear systems however research has shown that this technique can often hide part of the non linear system which is linearizable we prove sufficient conditions that a non linear system contain a k dimensional linear system after the input output linearization control is applied here p k n where p is the relative degree of the system and n is the dimension of the non linear system the results for k n are known from the literature

reversible linear and nonlinear discrete time dynamics it is shown that any causal discrete time system can be realized with a reversible or invertible state variable representation this bridges the gap with continuous time where flows always satisfy this property and settles an old debate on the relevance of invertibility in nonlinear discrete dynamics as the result applies to the linear case it is shown how the classic approach should be slightly modified and several examples of the benefits that can be obtained are given difference algebra is employed for nonlinear systems it leads to a most elegant characterization of causality which enables reversibility to be demonstrated module theory suffices in the linear case which is supplemented by elementary matrix manipulations

feedback linearizing control of discrete time nonlinear systems with input constraints a feedback linearizing control strategy for discrete time nonlinear systems subject to input constraints is proposed the control system comprises i a feedback linearizing controller ii a constraint mapping algorithm that transforms the actual input constraints into constraints on the feedback linearized system and iii a linear model predictive controller that regulates the resulting constrained linear system closed loop stability analysis is a challenging problem because the transformed constraints are state dependent sufficient conditions for asymptotic stability are presented for fully and partially feedback linearizable systems as part of the analysis a new stability result for unconstrained discrete time nonlinear systems which parallels a well known continuous time result is derived

on sampled data models for nonlinear systems models for deterministic continuous time nonlinear systems typically take the form of ordinary differential equations to utilize these models in practice invariably requires discretization in this paper we show how an approximate sampled data model can be obtained for deterministic nonlinear systems such that the local truncation error between the output of this model and the true system is of order spl delta sup r 1 where spl delta is the sampling period and r is the system relative degree the resulting model includes extra zero dynamics which have no counterpart in the underlying continuous time system the ideas presented here generalize well known results for the linear case we also explore the implications of these results in nonlinear system identification

extended lie brackets for nonlinear time delay systems in this note the extended lie bracket operator is introduced for the analysis and control of nonlinear time delay systems nltds this tool is used to characterize the integrability conditions of a given submodule the obtained results have two fundamental outcomes first they define the necessary and sufficient conditions under which a given set of nonlinear one forms in the n dimensional delayed variables x t x t sd with d constant but unknown are integrable thus generalizing the well known fundamental frobenius theorem to delay systems secondly they set the basis for the extension to this context of the geometric approach used for delay free systems the effectiveness of the results is shown by solving the problem of the equivalence of a nltds to an accessible linear time delay system ltds by bicausal change of coordinates

on the linear equivalents of nonlinear systems this paper studies feedback equivalence of nonlinear systems an equivalence relation is established for the systems x f x u a complete characterization of the class of nonlinear systems which are equivalent to controllable linear systems is obtained

some numerical aspects of approximate linearization of single input non linear systems we characterize approximate linearization to order m of a single input non linear system in terms of the existence of an integrating factor to order m 2 which is equivalent to the well known condition that a system of vector fields be order m 1 involutive we present a constructive method to obtain the required transformation for approximate linearization which results in substantial computational savings

on the synthesis of linear input output responses for nonlinear systems necessary and sufficient conditions are given for the existence of a feedback control law under which the input dependent part of the response of a given nonlinear system becomes linear in the input and independent of the initial state

linearization of discrete time systems by exogenous dynamic feedback it is shown that a discrete time system may be linearizable by exogenous dynamic feedback even if it cannot be linearized by endogenous feedback this property is completely unexpected and constitutes a fundamental difference with respect to the continuous time case the notion of exogenous linearizing output is introduced it is shown that existence of an exogenous linearizing output is a sufficient condition for dynamic linearizability necessary and sufficient conditions for the existence of an exogenous linearizing output are provided the results of the paper are obtained using transformal operator matrices the properties of such operators are studied the theory is applied to the exact discrete time model of a mobile robot showing that the above mentioned property concerns not only academic examples but also physical systems

feedback equivalence for a class of nonlinear singularly perturbed systems the feedback equivalence for a class of nonlinear singularly perturbed systems is studied this is accomplished by reducing the full order problem into a lower order exact problem using the slow manifold theory this facilitates development of an approximate and simpler linearizing control strategy achievable to an arbitrary degree of accuracy it is shown that in contradistinction to systems with unobservable parasitics where a state dependent transformation and a static feedback controller are required for systems with observable parasitics a state and control dependent transformation and a dynamic feedback controller should be used to transform the exact system into a linear system in controller and observer form

stable inversion for nonlinear discrete time systems we solve the exact output tracking problem for square nonlinear discrete time systems through stable inversion this stable inversion problem involves finding a bounded solution of a dynamical system driven by a bounded signal such a solution is given by a difference representation formula whose existence under the proper assumptions can be proven using a picard process

immersion and immersion by nonsingular feedback of a discrete time nonlinear system into a linear system an analytic discrete time nonlinear system is considered necessary and sufficient conditions for immersion of the system into a linear system are given local immersion is defined by nonsingular feedback into a linear system and given necessary and sufficient conditions for this problem it is shown that a similar approach can also be applied to continuous time affine nonlinear systems

feedback control of linear systems by multirate pulse width modulation in this note sampled data methods for modeling and control design of pulse width modulated systems are examined both single rate and multirate approaches are considered local controllability and observability analyses of the sampled data models are performed and feedback linearizability conditions for the sampled data models are derived multirate nonlinear state and output feedback designs are presented that permit asymptotic regulation or tracking

partial shape classification using contour matching in distance transformation an algorithm is presented to recognize and locate partially distorted 2d shapes without regard to their orientation location and size the algorithm first calculates the curvature function from the digitized image of an object the points of local maxima and minima extracted from the smooth curvature are used as control points to segment the boundary and to guide the boundary matching procedure the boundary matching procedure considers two shapes at a time one shape from the template databank and the other from the object being classified the procedure tries to match the control points in the unknown shape to those of a shape from the template databank and estimates the translation rotation and scaling factors to be used to normalize the boundary of the unknown shape the chamfer 3 4 distance transformation and a partial distance measurement scheme constitute the final step in measuring the similarity between the two shapes the unknown shape is assigned to the class corresponding to the minimum distance the algorithm has been successfully tested on partial shapes using two sets of data one with sharp corners and the other with curve segments this algorithm not only is computationally simple but also works reasonably well in the presence of a moderate amount of noise

input output linearization with state equivalence and decoupling the authors attempt to characterize the whole class of nonlinear systems that can be linearized to controllable and decouplable linear systems the authors present the necessary and sufficient conditions for their problem to be solvable more importantly they explicitly characterize the nonlinear system satisfying these conditions by a set of parameters which are invariant under the group action of state feedback and transformation this set of parameters can be calculated without solving a set of partial differential equations using this set of parameters one can directly determine which of the canonical forms of decouplable and controllable linear systems is feedback equivalent to the nonlinear system for the design of decoupled systems with linear input output dynamic characteristics it is more convenient to deal with the canonical form which is the simplest representation of the original system

object matching algorithms using robust hausdorff distance measures a hausdorff distance hd is one of commonly used measures for object matching this work analyzes the conventional hd measures and proposes two robust hd measures based on m estimation and least trimmed square lts which are more efficient than the conventional hd measures by computer simulation the matching performance of the conventional and proposed hd measures is compared with synthetic and real images

on the problem of feedback linearization the paper studies and solves in a geometric framework the problem of partial feedback linearization for discrete time dynamics an algorithm for computing the largest linearizable subsystem is proposed this approach can be considered as dual to the one already proposed in literature in an algebraic context

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

canonical forms of decouplable and controllable linear systems in this paper we present the canonical forms of decouplable and controllable linear systems some of the non zero elements in gilbert s canonically decoupled structure which remain undetermined are explicitly determined by a complete set of invariances our result constitutes the key step to characterization of the whole class of nonlinear systems that are feedback equivalent to decouplable and controllable linear systems