nonlinear state feedback for l 1 optimal control this paper considers l1 optimal control problems with full state feedback in contrast to h optimal control previous work has shown that linear l1 optimal controllers can be dynamic and arbitrarily high order however this paper shows that continuous memoryless nonlinear state feedback perform as well as dynamic linear state feedback the derivation which is nonconstructive relies on concepts from viability theory

consistency and convergence rates of one class svms and related algorithms we determine the asymptotic behaviour of the function computed by support vector machines svm and related algorithms that minimize a regularized empirical convex loss function in the reproducing kernel hilbert space of the gaussian rbf kernel in the situation where the number of examples tends to infinity the bandwidth of the gaussian kernel tends to 0 and the regularization parameter is held fixed non asymptotic convergence bounds to this limit in the l2 sense are provided together with upper bounds on the classification error that is shown to converge to the bayes risk therefore proving the bayes consistency of a variety of methods although the regularization term does not vanish these results are particularly relevant to the one class svm for which the regularization can not vanish by construction and which is shown for the first time to be a consistent density level set estimator

decentralized fuzzy observer based output feedback control for nonlinear large scale systems an lmi approach this paper presents a decentralized fuzzy control problem for asymptotic stabilization of a class of nonlinear large scale systems that use an observer based output feedback scheme a takagi sugeno t s fuzzy model is adopted for the nonlinear large scale system which has unknown interconnection terms and a fuzzy controller is separately considered for measurable and nonmeasurable premise variable cases sufficient conditions are derived for both asymptotic stabilization and optimization of a maximum bound of interconnection and are formulated in terms of linear matrix inequalities finally numerical examples are provided to verify the effectiveness of the proposed techniques

robust static output feedback stabilization for nonlinear discrete time systems with time delay via fuzzy control approach this paper addresses the problem of designing robust static output feedback controllers for nonlinear discrete time interval systems with time delays both in states and in control input in the approach we do not directly employ the lyapunov approach as do in most of traditional fuzzy control design approaches instead sufficient conditions for guaranteeing the robust stability for the considered systems are derived in terms of the matrix spectral norm of the closed loop fuzzy system the stability conditions are further formulated into linear matrix inequalities so that the desired controller can be easily obtained by using the matlab linear matrix inequality lmi toolbox finally an example is provided to illustrate the effectiveness of the proposed approach

fuzzy h sub spl infin output feedback control design for singularly perturbed systems with pole placement constraints an lmi approach this paper examines the problem of designing an h sub spl infin output feedback controller with pole placement constraints for singular perturbed takagi sugeno ts fuzzy models we propose a fuzzy h sub spl infin output feedback controller that not only guarantees the spl lscr sub 2 gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value but also ensures closed loop poles of each subsystem are in a prespecified linear matrix inequality lmi region in order to alleviate the numerical stiffness caused by the singular perturbation spl epsiv the design technique is formulated in terms of a family of spl epsiv independent linear matrix inequalities the proposed approach can be applied both standard and nonstandard singularly perturbed nonlinear systems a numerical example is provided to illustrate the design developed in this paper

time varying versus time invariant compensation for rejection of persistent bounded disturbances and robust stabilization it is shown that time varying compensation does not improve the optimal rejection of persistent bounded disturbances this result is obtained by exploiting a key observation that any time varying compensator which yields a given degree of disturbance rejection must do so uniformly over time thereby removing any advantage of time variation this key observation is exploited to show that time varying compensation does not improve the optimal rejection of disturbances regardless of the norm used to measure the disturbances thus absolutely summable finite energy or persistent bounded disturbances may be treated in the same manner it is shown that time varying compensation does not help in the bounded input bounded output robust stabilization of time invariant plants with unstructured uncertainty in doing so it is also shown that the small gain theorem is both necessary and sufficient for the bounded input bounded output stability of certain linear time varying plants subject to unstructured linear time varying perturbations

asymptotics and optimal bandwidth selection for highest density region estimation we study kernel estimation of highest density regions hdr our main contributions are twofold firstly we derive a uniform in bandwidth asymptotic approximation to a risk that is appropriate for hdr estimation this approximation is then used to derive a bandwidth selection rule for hdr estimation possessing attractive asymptotic properties we also present the results of numerical studies that illustrate the benefits of our theory and methodology

generalization error bounds in semi supervised classification under the cluster assumption we consider semi supervised classification when part of the available data is unlabeled these unlabeled data can be useful for the classification problem when we make an assumption relating the behavior of the regression function to that of the marginal distribution seeger 2000 proposed the well known cluster assumption as a reasonable one we propose a mathematical formulation of this assumption and a method based on density level sets estimation that takes advantage of it to achieve fast rates of convergence both in the number of unlabeled examples and the number of labeled examples

distribution free prediction bands for non parametric regression summary we study distribution free non parametric prediction bands with a focus on their finite sample behaviour first we investigate and develop different notions of finite sample coverage guarantees then we give a new prediction band by combining the idea of conformal prediction with non parametric conditional density estimation the proposed estimator called cops conformal optimized prediction set always has a finite sample guarantee under regularity conditions the estimator converges to an oracle band at a minimax optimal rate a fast approximation algorithm and a data driven method for selecting the bandwidth are developed the method is illustrated in simulated and real data examples

support vector data descriptions and k means clustering one class we present clustersvdd a methodology that unifies support vector data descriptions svdds and k means clustering into a single formulation this allows both methods to benefit from one another i e by adding flexibility using multiple spheres for svdds and increasing anomaly resistance and flexibility through kernels to k means in particular our approach leads to a new interpretation of k means as a regularized mode seeking algorithm the unifying formulation further allows for deriving new algorithms by transferring knowledge from one class learning settings to clustering settings and vice versa as a showcase we derive a clustering method for structured data based on a one class learning scenario additionally our formulation can be solved via a particularly simple optimization scheme we evaluate our approach empirically to highlight some of the proposed benefits on artificially generated data as well as on real world problems and provide a python software package comprising various implementations of primal and dual svdd as well as our proposed clustersvdd

density level sets asymptotics inference and visualization abstractwe study the plug in estimator for density level sets under hausdorff loss we derive asymptotic theory for this estimator and based on this theory we develop two bootstrap confidence regions for level sets we introduce a new technique for visualizing density level sets even in multidimensions which is easy to interpret and efficient to compute supplementary materials for this article are available online

further studies on h observer design for continuous time takagi sugeno fuzzy model abstract this brief paper is concerned with the problem of observer based h control for nonlinear systems presented by t s takagi sugeno fuzzy models the aim is to reduce the conservatism of finding a smaller h performance index by applying the non quadratic lyapunov function the one step lmis linear matrix inequalities method is applied to design the controller gains and observer gains in addition the initial positions of the observer states are also discussed and an optimization problem is solved to obtain new stable region in the end three examples are given to demonstrate the effectiveness of the proposed approach

asymptotics in empirical risk minimization in this paper we study a two category classification problem we indicate the categories by labels y 1 and y 1 we observe a covariate or feature x x d consider a collection ha of classifiers indexed by a finite dimensional parameter a and the classifier ha that minimizes the prediction error over this class the parameter a is estimated by the empirical risk minimizer n over the class where the empirical risk is calculated on a training sample of size n we apply the kim pollard theorem to show that under certain differentiability assumptions n converges to a with rate n 1 3 and also present the asymptotic distribution of the renormalized estimator for example let v0 denote the set of x on which given x x the label y 1 is more likely than the label y 1 if x is one dimensional the set v0 is the union of disjoint intervals the problem is then to estimate the thresholds of the intervals we obtain the asymptotic distribution of the empirical risk minimizer when the classifiers have k thresholds where k is fixed we furthermore consider an extension to higher dimensional x assuming basically that v0 has a smooth boundary in some given parametric class we also discuss various rates of convergence when the differentiability conditions are possibly violated here we again restrict ourselves to one dimensional x we show that the rate is n 1 in certain cases and then also obtain the asymptotic distribution for the empirical prediction error

bootstrapping regression models the regression and correlation models are considered it is shown that the bootstrap approximation to the distribution of the least squares estimates is valid and some error bounds are given

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

bootstrap confidence region estimation of the motion of rigid bodies abstract this article deals with statistical inference of the motion of rigid bodies using bootstrap methodology we consider two types of motion motion in p dimensional euclidean space and motion on a p dimensional sphere this article is motivated by problems of interest to polar scientists understanding the motion of ice pack at the north pole and those to geoscientists studying the motion of tectonic plates in addition to obtaining the point estimates for various parameters describing the motion of rigid bodies we also perform confidence region estimation and testing of certain hypotheses we consider two types of situations when homologous data are available and when the data consists of nonhomologous points we illustrate the methodology by analyzing two data sets a data set on the motion of arctic sea ice and a data set from plate tectonics

robust h sub spl infin control for uncertain discrete time delay fuzzy systems via output feedback controllers this work investigates the problem of robust output feedback h sub spl infin control for a class of uncertain discrete time fuzzy systems with time delays the state space takagi sugeno fuzzy model with time delays and norm bounded parameter uncertainties is adopted the purpose is the design of a full order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h sub spl infin norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities lmis a sufficient condition for the solvability of this problem is presented explicit expressions of a desired output feedback controller are proposed when the given lmis are feasible the effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust h sub spl infin control for a class of uncertain nonlinear discrete delay systems

new fuzzy control model and dynamic output feedback parallel distributed compensation a new fuzzy modeling based on fuzzy linear fractional transformations model is introduced this new representation is shown to be a flexible tool for handling complicated nonlinear models particularly the new fuzzy model provides an efficient and tractable way to handle the output feedback parallel distributed compensation problem we demonstrate that this problem can be given a linear matrix inequality characterization and hence is immediately solvable through available semidefinite programming codes the capabilities of the new fuzzy modeling is illustrated through numerical examples

stability of density based clustering high density clusters can be characterized by the connected components of a level set l x p x of the underlying probability density function p generating the data at some appropriate level 0 the complete hierarchical clustering can be characterized by a cluster tree t l in this paper we study the behavior of a density level set estimate l and cluster tree estimate t based on a kernel density estimator with kernel bandwidth h we define two notions of instability to measure the variability of l and t as a function of h and investigate the theoretical properties of these instability measures

a nonparametric approach to the estimation of lengths and surface areas fil cuevas antonio universidad de san andres departamento de matematica y ciencias argentina

output feedback robust h sup spl infin control of uncertain fuzzy dynamic systems with time varying delay this paper presents an output feedback robust h sup spl infin control problem for a class of uncertain fuzzy dynamic systems with time varying delayed state the takagi sugeno fuzzy model is employed to represent an uncertain nonlinear systems with time varying delayed state using a single quadratic lyapunov function the globally exponential stability and disturbance attenuation of the closed loop fuzzy control system are discussed sufficient conditions for the existence of robust h sup spl infin controllers are given in terms of matrix inequalities constructive algorithm for design of robust h sup spl infin controller is also developed the resulting controller is nonlinear and automatically tuned based on fuzzy operation

robust fuzzy h_ infty estimator based stabilization design for nonlinear parabolic partial differential systems with different boundary conditions in this paper a new robust fuzzy h infty estimator based stabilization design for a class of n dimensional nonlinear parabolic partial differential systems pdss with either the dirichlet or neumann boundary conditions is proposed first an n dimensional parabolic takagi sugeno t s fuzzy pds is used to approximate the n dimensional nonlinear parabolic pds via the knowledge based t s fuzzy system technique second based on the n dimensional parabolic t s fuzzy pds a robust fuzzy estimator based controller is employed not only to stabilize the pds but also to attenuate the effects of external and measurement noises on the pds in the spatiotemporal domain below a prescribed attenuation level the robust fuzzy h infty estimator based stabilization design problem can be formulated as a diffusion matrix inequality dmi problem to solve dmis via the traditional algebraic matrix techniques we utilize the divergence theorem and the poincare inequality to transform the dmis into bilinear matrix inequalities with a poincare constant defined according to the spatial domain of the corresponding pds finally the robust fuzzy h infty estimator based stabilization design problem can be effectively solved by a set of linear matrix inequalities instead of the bmis with the help of the proposed decoupled method additionally an optimal robust fuzzy h infty estimator based stabilization design can be realized via minimizing the noise attenuation level a simulation example is provided to illustrate the design procedure and verify the performance of the proposed optimal design

smooth discrimination analysis ties f and g can be based on the estimation of the set g x fx gx we consider applications where it is appropriate to assume that the region g has a smooth boundary or belongs to another nonparametric class of sets in particular this assumption makes sense if discrimination is used as a data analytic tool decision rules based on minimization of empirical risk over the whole class of sets and over sieves are considered their rates of convergence are obtained we show that these rules achieve optimal rates for estimation of g and optimal rates of convergence for bayes risks an interesting conclusion is that the optimal rates for bayes risks can be very fast in particular faster than the parametric root n rate these fast rates cannot be guaranteed for plug in rules

h sub spl infin fuzzy output feedback control design for nonlinear systems an lmi approach addresses the problem of stabilizing a class of nonlinear systems by using an h sub spl infin fuzzy output feedback controller first a class of nonlinear systems is approximated by a takagi sugeno ts fuzzy model then based on a well known lyapunov functional approach we develop a technique for designing an h sub spl infin fuzzy output feedback control law which guarantees the l sub 2 gain from an exogenous input to a regulated output is less or equal to a prescribed value a design algorithm for constructing an h sub spl infin fuzzy output feedback controller is given in contrast to the existing results the premise variables of the h sub spl infin fuzzy output feedback controller are not necessarily to be the same as the premise variables of the ts fuzzy model of the plant a numerical simulation example is presented to illustrate the theory development

convergence rates for persistence diagram estimation in topological data analysis computational topology has recently seen an important development toward data analysis giving birth to the field of topological data analysis topological persistence or persistent homology appears as a fundamental tool in this field in this paper we study topological persistence in general metric spaces with a statistical approach we show that the use of persistent homology can be naturally considered in general statistical frameworks and that persistence diagrams can be used as statistics with interesting convergence properties some numerical experiments are performed in various contexts to illustrate our results

concentration of the empirical level sets of tukey s halfspace depth tukey s halfspace depth has attracted much interest in data analysis because it is a natural way of measuring the notion of depth relative to a cloud of points or more generally to a probability measure given an i i d sample we investigate the concentration of upper level sets of the tukey depth relative to that sample around their population version we show that under some mild assumptions on the underlying probability measure concentration occurs at a parametric rate and we deduce moment inequalities at that same rate in a computational prospective we study the concentration of a discretized version of the empirical upper level sets

existence of similarity transformation converting bmis to lmis under a mild condition we investigate the existence of a similarity transformation regarding robust hinfin stability analysis and observer controller synthesis problems the observer based controller is capable of disturbance rejection in the presence of unknown but bounded disturbance we present results which illustrate plainly the role of the similarity transformation in converting a bmi problem into an lmi problem in a unified fashion applicable to both continuous and discrete time problems with or without uncertainty finally the validity and applicability of the approach are illuminated by examples

a robust h observer based controller design for uncertain t s fuzzy systems with unknown premise variables via lmi this paper addresses the problem of robust h fuzzy observer based controller design for the takagi sugeno t s fuzzy systems with unmeasurable premise variables the proposed design method considers uncertainty for such a problem for the first time using some linear transformations for the output matrices of each local model of the t s fuzzy system and employing finsler s lemma the robust stability conditions in the form of linear matrix inequalities lmis are derived two numerical simulations are provided to show the validity of the proposed method

ranking the best instances we formulate a local form of the bipartite ranking problem where the goal is to focus on the best instances we propose a methodology based on the construction of real valued scoring functions we study empirical risk minimization of dedicated statistics which involve empirical quantiles of the scores we first state the problem of finding the best instances which can be cast as a classification problem with mass constraint next we develop special performance measures for the local ranking problem which extend the area under an roc curve auc criterion and describe the optimal elements of these new criteria we also highlight the fact that the goal of ranking the best instances cannot be achieved in a stage wise manner where first the best instances would be tentatively identified and then a standard auc criterion could be applied eventually we state preliminary statistical results for the local ranking problem

bootstrap confidence regions for directional data abstract methods are proposed for constructing bootstrap confidence regions for the mean direction of a random p dimensional unit vector x with an arbitrary unimodal distribution on the p sphere the approach of this article differs from that of other authors in that it is based on pivotal statistics a general pivotal method is introduced that produces a wide variety of confidence regions on general p dimensional spheres included are confidence cones and likelihood based regions it can readily be modified to incorporate extra assumptions about the underlying distribution such as rotational symmetry the general method leads to confidence pictures which present information about the estimated posterior likelihood of mean orientation by shading spherical surfaces an application is given to a sample of spherical cross bed measurements the methods extend to the case where x has random length and to calculation of confidence regions for reference directions of axial bipolar or girdle distributions

minimax optimal level set estimation this paper describes a new methodology and associated theoretical analysis for rapid and accurate extraction of level sets of a multivariate function from noisy data the identification of the boundaries of such sets is an important theoretical problem with applications for digital elevation maps medical imaging and pattern recognition this problem is significantly different from classical segmentation because level set boundaries may not correspond to singularities or edges in the underlying function as a result segmentation methods which rely upon detecting boundaries would be potentially ineffective in this regime this issue is addressed in this paper through a novel error metric sensitive to both the error in the location of the level set estimate and the deviation of the function from the critical level hoeffding s inequality is used to derive a novel regularization term that is distinctly different from regularization methods used in conventional image denoising settings building upon this foundation it is possible to derive error performance bounds for the proposed estimator and demonstrate that it exhibits near minimax optimal error decay rates for large classes of level set problems the proposed method automatically adapts to the spatially varying regularity of both the boundary of the level set and the underlying function

a weighted procrustes criterion the procrustes criterion is a common measure for the distance between two matricesx andy and can be interpreted as the sum of squares of the euclidean distances between their respective column vectors often a weighted procrustes criterion using for example a weighted sum of the squared distances between the column vectors is called for this paper describes and analyzes the performance of an algorithm for rotating a matrixx such that the column weighted procrustes distance toy is minimized the problem of rotatingx intoy such that an aggregate measure of tucker s coefficient of congruence is maximized is also discussed

estimation of high density regions using one class neighbor machines in this paper we investigate the problem of estimating high density regions from univariate or multivariate data samples we estimate minimum volume sets whose probability is specified in advance known in the literature as density contour clusters this problem is strongly related to one class support vector machines ocsvm we propose a new method to solve this problem the one class neighbor machine ocnm and we show its properties in particular the ocnm solution asymptotically converges to the exact minimum volume set prespecified finally numerical results illustrating the advantage of the new method are shown

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

minimax bounds for active learning this paper analyzes the potential advantages and theoretical challenges of active learning algorithms active learning involves sequential sampling procedures that use information gleaned from previous samples in order to focus the sampling and accelerate the learning process relative to passive learning algorithms which are based on nonadaptive usually random samples there are a number of empirical and theoretical results suggesting that in certain situations active learning can be significantly more effective than passive learning however the fact that active learning algorithms are feedback systems makes their theoretical analysis very challenging this paper aims to shed light on achievable limits in active learning using minimax analysis techniques we study the achievable rates of classification error convergence for broad classes of distributions characterized by decision boundary regularity and noise conditions the results clearly indicate the conditions under which one can expect significant gains through active learning furthermore we show that the learning rates derived are tight for boundary fragment classes in d dimensional feature spaces when the feature marginal density is bounded from above and below

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

rejection of persistent spl lscr sub spl infin bounded disturbances for nonlinear systems a nonlinear spl lscr sup 1 control problem which deals with the rejection of persistent bounded disturbances for nonlinear systems is investigated the concept of invariance plays an important role in the spl lscr sup 1 performance analysis and synthesis the main idea is to construct an invariant subset in the state space such that achieving disturbance rejection is equivalent to restricting the state dynamics to the subset the relation between the spl lscr sup 1 control of a continuous time system and the l sup 1 control of its euler approximated discrete time system is established

a plug in approach to support estimation we suggest a new approach based on the use of density estimators for the problem of estimating the compact support of a multivariate density this subject motivated in terms of pattern analysis by grenander has interesting connections with detection and clustering a natural class of density based estimators is defined universal consistency results and convergence rates are established for these estimators with respect to the usual measure based metric d between sets further convergence rates with respect to both d and the hausdorff metric d h are also obtained under some fairly intuitive shape restrictions

robustness design of nonlinear dynamic systems via fuzzy linear control this study introduces a fuzzy linear control design method for nonlinear systems with optimal h sup spl infin robustness performance first the takagi and sugeno fuzzy linear model 1985 is employed to approximate a nonlinear system next based on the fuzzy linear model a fuzzy controller is developed to stabilize the nonlinear system and at the same time the effect of external disturbance on control performance is attenuated to a minimum level thus based on the fuzzy linear model h sup spl infin performance design can be achieved in nonlinear control systems in the proposed fuzzy linear control method the fuzzy linear model provides rough control to approximate the nonlinear control system while the h sup spl infin scheme provides precise control to achieve the optimal robustness performance linear matrix inequality lmi techniques are employed to solve this robust fuzzy control problem in the case that state variables are unavailable a fuzzy observer based h sup spl infin control is also proposed to achieve a robust optimization design for nonlinear systems a simulation example is given to illustrate the performance of the proposed design method

on nonparametric estimation of density level sets let x 1 x n be independent identically distributed observations from an unknown probability density f consider the problem of estimating the level set g g f x r 2 f x from the sample x 1 x n under the assumption that the boundary of g has a certain smoothness we propose piecewise polynomial estimators of g based on the maximization of local empirical excess masses we show that the estimators have optimal rates of convergence in the asymptotically minimax sense within the studied classes of densities we find also the optimal convergence rates for estimation of convex level sets a generalization to the n dimensional case where n 2 is given

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

fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances to date nonlinear l gain control problems have not been solved by the conventional control methods for the nonlinear dynamic systems with persistent bounded disturbances this study introduces a fuzzy control design to deal with the nonlinear l gain output feedback control problem first the takagi and sugeno t s fuzzy model is employed to approximate the nonlinear dynamic system next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to minimize the upper bound of l gain of the closed loop system under some linear matrix inequality lmi constraints therefore the nonlinear l gain control problem is transformed into a suboptimal control problem i e to minimize the upper bound of the l gain of the closed loop system subject to some lmi constraints in this situation the nonlinear l gain output feedback control problem can be easily solved by a lmi based optimization method the proposed methods which efficiently attenuate the peak of perturbation due to persistent bounded disturbances extend the l gain control problems from linear dynamic systems to nonlinear dynamic systems

conditional minimum volume predictive regions for stochastic processes abstract motivated by interval region prediction in nonlinear time series we propose a minimum volume mv predictor for a strictly stationary process the mv predictor varies with respect to the current position in the state space and has the minimum lebesgue measure among all regions with the nominal coverage probability we have established consistency convergence rates and asymptotic normality for both coverage probability and lebesgue measure of the estimated mv predictor under the assumption that the observations are from a strong mixing process applications with both real and simulated datasets illustrate the proposed methods

piecewise integral sliding mode control for t s fuzzy systems this paper addresses the issue of piecewise integral sliding mode control ismc for the takagi sugeno t s fuzzy systems ismc is chosen to stabilize the t s fuzzy system because of its superior capability in treating uncertainties individual integral sliding surfaces are designed in different operating regions of the t s fuzzy system conditions on the existence of the sliding mode in the associated region are given the chattering phenomenon around region boundaries is analyzed and the prevention of such chattering is discussed an illustrative example is finally given to show the efficiency of the proposed method

a robust h_ infty non pdc design scheme for singularly perturbed t s fuzzy systems with immeasurable state variables this paper addresses an observer based robust h infty fuzzy controller design method for singularly perturbed nonlinear systems with external disturbances which are represented by uncertain takagi sugeno t s fuzzy models for a practical output feedback design the premise variables of the fuzzy controller and the fuzzy observer are considered unknown in general a fuzzy lyapunov function is utilized for the synthesis of the nonparallel distributed compensation based controller the closed loop singularly perturbed t s fuzzy system is asymptotically robustly stable in the absence of disturbances and satisfies an h infty norm condition in the presence of disturbances for all positive values of the singular perturbation parameter within the given desired bound using the descriptor redundancy approach some strict linear matrix inequality lmi conditions are derived for the h infty robustness of the closed loop system when uncertainties are simultaneously considered in all state space matrices of each fuzzy subsystem the main disadvantage of a fuzzy lyapunov function based design is that the bounds on the derivatives of the membership functions must be known a priori inspired by a recent work that provides the bounds of the membership derivatives for a given arbitrary compact set on the state space a new method is proposed that guarantees that the closed loop observer based uncertain singularly perturbed t s fuzzy system remains robustly stable in the compact set using finsler s lemma the resulting design conditions are converted to lmis two numerical examples are provided to show the effectiveness of the proposed method

morphometric tools for landmark data geometry and biology 1 introduction 2 preliminaries 3 landmarks 4 distance measures 5 shape coordinates 6 principal axes of shape change for triangles 7 features of shape comparison 8 retrospect and prospect

robust fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances a novel decoupled approach unlike the l 2 gain h control case the l gain control problem is dealing with persistent bounded disturbances this study introduces l gain fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer for nonlinear systems via t s fuzzy models the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables do not depend on the state variables estimated by a fuzzy observer a novel decoupled method is proposed in this study to transform the non lmi conditions into some lmi forms by the proposed decoupled method and the genetic algorithm the l gain fuzzy observer based fuzzy control problem can be easily solved by an lmi based method

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

estimating the relative rotation of two tectonic plates from boundary crossings abstract let 1 s be unknown vectors on the sphere and ao be an unknown rotation suppose that uij are estimates of points lying on the great circle normal to i and ik are estimates of points lying on the great circle normal to ao i this article discusses a method to construct a confidence region for ao this problem arises in the reconstruction of the relative motion of two tectonic plates on opposing sides of a rift the boundary on each side is represented by a collection of great circle segments and ao is the rotation that takes one boundary into the other the data consist of measured crossing points uij and ik of the various segments on the opposing boundaries the analysis completes an analysis of hellinger 1981 the errors in tectonic data are quite concentrated and the problem reduces to linear regression once this is realized many interesting problems such as triple junctions or multiple time periods can be examined the analysis is aided substantially by a parameterization of t

kronecker products unitary matrices and signal processing applications discrete unitary transforms are extensively used in many signal processing applications and in the development of fast algorithms kronecker products have proved quite useful in this semitutorial paper we briefly review properties of kronecker products and direct sums of matrices which provide a compact notation in treating patterned matrices a generalized matrix product which inherits some useful algebraic properties from the standard kronecker product and allows a large class of discrete unitary transforms to be generated from a single recursion formula is then introduced the notation is intimately related to sparse matrix factorizations and examples are included illustrating the utility of the new notation in signal processing applications finally some novel characteristics of hadamard transforms and polyadic permutations are derived in the framework of kronecker products

further results on the optimal rejection of persistent bounded disturbances the problem of designing controllers that optimally reject persistent disturbances is studied the focus is on the case where the plant to be controlled has either zeros or poles on the stability boundary i e the unit circle in the discrete time case and the extended j omega axis in the continuous time case for the discrete time case the problem of minimizing a cost functional of the form f rg sub 1 where the transform g of g has some unit circle zeros is studied a previously published dual problem formulation is extended and it is shown that an optimal controller need not exist the construction of a sequence of suboptimal controllers whose performance approaches the unattainable infimum of the cost function is studied it is shown that two results which hold in the case of h sub infinity optimization do not hold in the presented situation specifically the introduction of unit circle zeros can increase the value of the infimum even when every unit circle zero of g is also a zero of f and a sequence of controllers constructed in an obvious fashion fails to be an optimizing sequence similar results are obtained for the continuous time case

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

properties of euclidean and non euclidean distance matrices abstract a distance matrix d of order n is symmetric with elements 1 2 d ij 2 where dii 0 d is euclidean when the 1 2 n n 1 quantities dij can be generated as the distances between a set of n points x n p in a euclidean space of dimension p the dimensionality of d is defined as the least value of p rank x of any generating x in general p 1 and p 2 are also acceptable but may include imaginary coordinates even when d is euclidean basic properties of euclidean distance matrices are established in particular when rank d it is shown that depending on whether etd e is not or is zero the generating points lie in either p 1 dimensions in which case they lie on a hypersphere or in p 2 dimensions in which case they do not the notation e is used for a vector all of whose values are one when d is non euclidean its dimensionality p r s will comprise r real and s imaginary columns of x and r s are invariant for all generating x of minimal rank higher ranking representations can arise only from p 1 r 1 s or p 1 r s 1 or p 2 r 1 s 1 so that not only are r s invariant but they are both minimal for all admissible representations x

distribution free prediction sets this article introduces a new approach to prediction by bringing together two different nonparametric ideas distribution free inference and nonparametric smoothing specifically we consider the problem of constructing nonparametric tolerance prediction sets we start from the general conformal prediction approach and we use a kernel density estimator as a measure of agreement between a sample point and the underlying distribution the resulting prediction set is shown to be closely related to plug in density level sets with carefully chosen cutoff values under standard smoothness conditions we get an asymptotic efficiency result that is near optimal for a wide range of function classes but the coverage is guaranteed whether or not the smoothness conditions hold and regardless of the sample size the performance of our method is investigated through simulation studies and illustrated in a real data example

some linear models for estimating the motion of rigid bodies with applications to geometric quality assurance abstract a geometrical method to assess the quality of a part is to sample points on the surface of the part and to bring an ideal computer representation of the part as close as possible to the sampled locations the points are sampled with a coordinate measuring machine cmm that gives the coordinates with respect to the machine s own three dimensional system of axis of the sampled locations computer assisted design cad gives the ideal representation of the part the matching involves estimating a rotation and a translation vector characterizing the rigid body transformation needed to go from the computer model to the sampled locations the sum of the squared residual distances between the sampled locations and the fitted computer part is a measure of the quality of the part this article investigates the statistical properties of this method when the surface of the part is made of planar regions estimating the translation vector and the rotation matrix is shown to be locally equivalent to fitt

conditions of output stabilization for nonlinear models in the takagi sugeno s form this paper deals with the control law design with an observer for models in the takagi sugeno s ts form in the general case where the nonlinearities and the variables involved are not measurable the results presented in this paper give sufficient conditions of stabilization for the global loop i e ts model stabilized with a state feedback and a fuzzy observer conditions are given in the form of linear matrix inequalities lmi problem

consistent procedures for cluster tree estimation and pruning for a density f on mathbb r d a high density cluster is any connected component of x f x geq lambda for some lambda 0 the set of all high density clusters forms a hierarchy called the cluster tree of f we present two procedures for estimating the cluster tree given samples from f the first is a robust variant of the single linkage algorithm for hierarchical clustering the second is based on the k nearest neighbor graph of the samples we give finite sample convergence rates for these algorithms which also imply consistency and we derive lower bounds on the sample complexity of cluster tree estimation finally we study a tree pruning procedure that guarantees under milder conditions than usual to remove clusters that are spurious while recovering those that are salient

fully adaptive density based clustering the clusters of a distribution are often defined by the connected components of a density level set however this definition depends on the user specified level we address this issue by proposing a simple generic algorithm which uses an almost arbitrary level set estimator to estimate the smallest level at which there are more than one connected components in the case where this algorithm is fed with histogram based level set estimates we provide a finite sample analysis which is then used to show that the algorithm consistently estimates both the smallest level and the corresponding connected components we further establish rates of convergence for the two estimation problems and last but not least we present a simple yet adaptive strategy for determining the width parameter of the involved density estimator in a data depending way

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

robust stabilization design for nonlinear stochastic system with poisson noise via fuzzy interpolation method because the noise for a real dynamical system may be poisson process due to discontinuous random fluctuation the h robust control designs for nonlinear stochastic systems with external disturbance and poisson noise are studied the h robust control designs need to solve hamilton jacobi inequality hji for these nonlinear stochastic systems to efficiently attenuate the effect of the external disturbance and poisson noise since it is difficult to solve the hji directly the fuzzy approach is developed to simplify the design procedure of the h robust control designs for nonlinear stochastic systems with external disturbance and poisson noise the asymptotic stability in probability of the proposed nonlinear stochastic control systems under disturbance free condition is also discussed if the system state variables are unavailable then the h robust estimator based output feedback control design is also proposed for nonlinear stochastic systems with external disturbance and poisson noise finally an example of robust control of nervous system with poisson stimulation in parkinsonism patients is given to confirm the performance of the proposed method

a classification framework for anomaly detection one way to describe anomalies is by saying that anomalies are not concentrated this leads to the problem of finding level sets for the data generating density we interpret this learning problem as a binary classification problem and compare the corresponding classification risk with the standard performance measure for the density level problem in particular it turns out that the empirical classification risk can serve as an empirical performance measure for the anomaly detection problem this allows us to compare different anomaly detection algorithms empirically i e with the help of a test set furthermore by the above interpretation we can give a strong justification for the well known heuristic of artificially sampling labeled samples provided that the sampling plan is well chosen in particular this enables us to propose a support vector machine svm for anomaly detection for which we can easily establish universal consistency finally we report some experiments which compare our svm to other commonly used methods including the standard one class svm

error analysis of coefficient based regularized algorithm for density level detection in this letter we consider a density level detection dld problem by a coefficient based classification framework with regularizer and data dependent hypothesis spaces although the data dependent characteristic of the algorithm provides flexibility and adaptivity for dld it leads to difficulty in generalization error analysis to overcome this difficulty an error decomposition is introduced from an established classification framework on the basis of this decomposition the estimate of the learning rate is obtained by using rademacher average and stepping stone techniques in particular the estimate is independent of the capacity assumption used in the previous literature

optimal disturbance rejection for nonlinear control systems the problem of optimal disturbance rejection for a general class of multiinput multioutput mimo nonlinear systems achieved over a set of stabilizing compensator operators is formulated in a banach space setting conditions on the operators are imposed on the basis of the inputs as well as the outputs an existence theorem for optimal solutions is established under some realistic and verifiable conditions for solving the optimization problem a generalized recursive nonlinear programming algorithm is passed and a simple example of nonlinear optimal feedback design is given to show that the problem can be reduced to standard min max optimization and is hence solvable

estimation of extreme risk regions under multivariate regular variation when considering d possibly dependent random variables one is often interested in extreme risk regions with very small probability p we consider risk regions of the form z rd f z where f is the joint density and a small number estimation of such an extreme risk region is difficult since it contains hardly any or no data using extreme value theory we construct a natural estimator of an extreme risk region and prove a refined form of consistency given a random sample of multivariate regularly varying random vectors in a detailed simulation and comparison study the good performance of the procedure is demonstrated we also apply our estimator to financial data

optimal rejection of persistent bounded disturbances in this paper we formulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude but is otherwise arbitrary the objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance mathematically this corresponds to requiring uniformly good disturbance rejection over all time since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used see 7 sect 5 6 the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose l 2 norm is small as is the case with the currently popular h infty theory the present theory is a natural counterpart to the existing theory of optimal disturbance rejection the so called h infty theory which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square integrable and has unit energy it is shown that the problem studied here has quite different features from its predecessor complete solutions to the problem are given in several important cases including those where the plant is minimum phase or when it has only a single unstable zero in other cases procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers

nonlinear l 1 optimal controllers for linear systems in this paper we study the l sub 1 optimal control problem for linear systems we show that by allowing the class of controllers to include nonlinear controllers we can make the closed loop l sub 1 norm strictly smaller than we could do using only linear controllers

sequential anomaly detection in the presence of noise and limited feedback this paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data the proposed approach consists of two main elements 1 filtering or assigning a belief or likelihood to each successive measurement based upon our ability to predict it from previous noisy observations and 2 hedging or flagging potential anomalies by comparing the current belief against a time varying and data adaptive threshold the threshold is adjusted based on the available feedback from an end user our algorithms which combine universal prediction with recent work on online convex programming do not require computing posterior distributions given all current observations and involve simple primal dual parameter updates at the heart of the proposed approach lie exponential family models which can be used in a wide variety of contexts and applications and which yield methods that achieve sublinear per round regret against both static and slowly varying product distributions with marginals drawn from the same exponential family moreover the regret against static distributions coincides with the minimax value of the corresponding online strongly convex game we also prove bounds on the number of mistakes made during the hedging step relative to the best offline choice of the threshold with access to all estimated beliefs and feedback signals we validate the theory on synthetic data drawn from a time varying distribution over binary vectors of high dimensionality as well as on the enron email dataset

estimation of a convex density contour in two dimensions abstract if a density in two dimensions has a convex contour containing probability the contour may be estimated from a sample by finding the convex polygon of smallest area containing a proportion of the sample points an algorithm for finding a particular contour is given that takes o n 2 space and o n 3 time for n sample points

confidence regions for spatial excursion sets from repeated random field observations with an application to climate abstractthe goal of this article is to give confidence regions for the excursion set of a spatial function above a given threshold from repeated noisy observations on a fine grid of fixed locations given an asymptotically gaussian estimator of the target function a pair of data dependent nested excursion sets are constructed that are sub and super sets of the true excursion set respectively with a desired confidence asymptotic coverage probabilities are determined via a multiplier bootstrap method not requiring gaussianity of the original data nor stationarity or smoothness of the limiting gaussian field the method is used to determine regions in north america where the mean summer and winter temperatures are expected to increase by mid 21st century by more than 2 degrees celsius

on relaxed lmi based designs for fuzzy regulators and fuzzy observers relaxed conditions for stability of nonlinear continuous and discrete time systems given by fuzzy models are presented a theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature numerical results exemplify this fact these results are also used for fuzzy regulators and observers designs the nonlinear systems are represented by fuzzy models proposed by takagi and sugeno 1985 the stability analysis and the design of controllers are described by linear matrix inequalities that can be solved efficiently using convex programming techniques the specification of the decay rate constrains on control input and output are also discussed

l 1 optimal compensators for continuous time systems previous work has been concerned with minimizing the l 1 norm of an error pulse response for discrete time siso 1 and mimo 2 systems in this paper we study the problem of minimizing the l1 norm of the error impulse response for siso continuous time systems this problem is quite different from the discrete time problem in that irrational solutions are obtained even when the problem data are rational two methods are suggested for the solution of the continuous time problem an exact method which leads to a finite dimensional nonlinear programming problem and an approximate method which leads to a linear programming problem

the geometry of shape spaces kendall introduced shape spaces which classified n tuples of points in r k and explained their role for statistics the aim of this paper is to study such shape spaces and in particular to explore the corresponding spaces for points on spheres the ultimate purpose of the work is to be able to apply statistical techniques to observations where only the shape of the observations is significant the geometry of the shape space is critical in determining the type of statistical technique which one should use therefore the major part of this paper is devoted to an examination of the geometry and the statistics is only introduced in a simple case when considering random processes on the shape space