h sub spl infin control of discrete time uncertain systems this paper considers h sub spl infin control problems involving discrete time uncertain linear systems the uncertainty is supposed to belong to convex bounded domains and no additional assumptions are made as for instance matching conditions two h sub spl infin guaranteed cost control problems are solved the first one concerns the determination of a state feedback gain if one exists in such way the h sub spl infin norm of a certain transfer function remains bounded by a prespecified h sub spl infin level for all possible models the second one includes this bound as an additional variable to be minimized to achieve the smallest feasible limiting bound the results follow from the simple geometry of those problems which are shown to be convex in the particular parametric space under consideration an example illustrates the theory

bayesian approach with hidden markov modeling and mean field approximation for hyperspectral data analysis the main problems in hyperspectral image analysis are spectral classification segmentation and data reduction in this paper we propose a bayesian estimation approach which gives a joint solution for these problems the problem is modeled as a blind sources separation bss the data are m hyperspectral images and the sources are k m images which are composed of compact homogeneous regions and have mutually disjoint supports the set of all these regions cover the total surface of the observed scene to insure these properties we propose a hierarchical markov model for the sources with a common hidden classification field which is modeled via a potts markov field the joint bayesian estimation of the hidden variable sources and the mixing matrix of the bss gives a solution for all three problems spectra classification segmentation and data reduction of hyperspectral images the mean field approximation mfa algorithm for the posterior laws is proposed for the effective bayesian computation finally some results of the application of the proposed methods on simulated and real data are given to illustrate the performance of the proposed method compared to other classical methods such as pca and ica

characterization and computation of disturbance invariant sets for constrained switched linear systems with dwell time restriction this paper introduces the concept and characterization of disturbance dwell time invariance ddt invariance and constraint admissible ddt invariance caddt invariance for constrained systems with additive disturbance under dwell time switching using the characterization necessary and sufficient conditions for ddt invariance and algorithms for the computation of the minimal and maximal constraint admissible convex ddt invariant sets are provided numerical examples of such sets for several systems are also provided

supervisory control of families of linear set point controllers 2 robustness a simply structured high level controller called a supervisor has recently been proposed in part i of this article ibid vol 41 1996 for the purpose of orchestrating the switching of a sequence of candidate set point controllers into feedback with an imprecisely modeled siso process so as to cause the output of the process to approach and track a constant reference input the process is assumed to be modeled by an siso linear system whose transfer function is in the union of a number of subclasses each subclass being small enough so that one of the candidate controllers would solve the set point tracking problem if the process transfer function was to be one of the subclass members this paper proves that without any further modification the same supervisor described in part i can also perform this function in the face of norm bounded unmodeled dynamics and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance and noise inputs whether they are constant or not

robust stability and stabilization of linear switched systems with dwell time sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty a lyapunov function in quadratic form which is non increasing at the switching instants is assigned to each subsystem during the dwell time this function varies piecewise linearly in time after switching occurs it becomes time invariant afterwards this function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties the method proposed is then applied to stabilization via state feedback both for the nominal and the uncertain cases

on stability and h control of switched systems with random switching signals abstract in this paper the stability analysis and h control problems for a class of continuous time switched systems with a random switching signal are addressed the dwell time of the switched systems is characterized with a fixed part and a random part a new stability criterion which is equivalent to a necessary and sufficient condition developed previously is established first and then it is reformulated in terms of linear matrix inequalities based on the stability analysis result l 2 gain performance analysis and h control problems are studied several numerical examples are given to illustrate the effectiveness of our results

stabilization of switched continuous time systems with all modes unstable via dwell time switching stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems in this brief paper a sufficient condition ensuring the asymptotic stability of switched continuous time systems with all modes unstable is proposed the main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes then by using a discretized lyapunov function approach a computable sufficient condition for switched linear systems is proposed in the framework of dwell time it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability based on derived results an algorithm is proposed to compute the stability region of admissible dwell time a numerical example is proposed to illustrate our approach

robust h sub spl infin disturbance attenuation for a class of uncertain discrete time fuzzy systems the paper is concerned with robust stabilization and h sub spl infin control of a class of uncertain discrete time fuzzy systems the class of uncertain systems is described by state space takagi sugeno ts fuzzy models with linear nominal parts and norm bounded parameter uncertainties in the state and output equations first a sufficient condition on robust stability of the fuzzy models is proposed then h sub spl infin disturbance attenuation performance of the fuzzy models is analyzed some sufficient conditions are derived on robust h sub spl infin disturbance attenuation in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties a numerical example shows the use of the results on the stabilization and h sub spl infin disturbance attenuation of a class of discrete time nonlinear systems via fuzzy switch

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

an extension of the standard mixture model for image segmentation standard gaussian mixture modeling gmm is a well known method for image segmentation however the pixels themselves are considered independent of each other making the segmentation result sensitive to noise to reduce the sensitivity of the segmented result with respect to noise markov random field mrf models provide a powerful way to account for spatial dependences between image pixels however their main drawback is that they are computationally expensive to implement and require large numbers of parameters based on these considerations we propose an extension of the standard gmm for image segmentation which utilizes a novel approach to incorporate the spatial relationships between neighboring pixels into the standard gmm the proposed model is easy to implement and compared with mrf models requires lesser number of parameters we also propose a new method to estimate the model parameters in order to minimize the higher bound on the data negative log likelihood based on the gradient method experimental results obtained on noisy synthetic and real world grayscale images demonstrate the robustness accuracy and effectiveness of the proposed model in image segmentation as compared to other methods based on standard gmm and mrf models

switching stabilizability for continuous time uncertain switched linear systems this paper investigates the switching stabilizability problem for a class of continuous time switched linear systems with time variant parametric uncertainties first a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived under the assumption that the closed loop switched system does not generate sliding motions then an additional condition is introduced to exclude the possibility of unstable sliding motions finally a necessary and sufficient for the asymptotic stabilizability of such continuous time uncertain switched linear systems is presented this result improves upon conditions found in the literature which are either sufficient only or necessary only

infinite horizon switched lqr problems in discrete time a suboptimal algorithm with performance analysis this paper studies the quadratic regulation problem for discrete time switched linear systems dslqr problem on an infinite time horizon a general relaxation framework is developed to simplify the computation of the value iterations based on this framework an efficient algorithm is developed to solve the infinite horizon dslqr problem with guaranteed closed loop stability and suboptimal performance due to these guarantees the proposed algorithm can be used as a general controller synthesis tool for switched linear systems

triplet markov fields for the classification of complex structure data we address the issue of classifying complex data we focus on three main sources of complexity namely the high dimensionality of the observed data the dependencies between these observations and the general nature of the noise model underlying their distribution we investigate the recent triplet markov fields and propose new models in this class designed for such data and in particular allowing very general noise models in addition our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework one advantage of our models is that whatever the initial complexity of the noise model parameter estimation can be carried out using state of the art bayesian clustering techniques under the usual simplifying assumptions as generative models they can be seen as an alternative in the supervised case to discriminative conditional random fields identifiability issues underlying the models in the nonsupervised case are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity

output reachable set estimation for switched linear systems and its application in safety verification this paper addresses the output reachable set estimation problem for continuous time switched linear systems consisting of hurwtiz stable subsystems based on a common lyapunov function approach the output reachable set is estimated by a union of bounding ellipsoids then multiple lyapunov functions with time scheduled structure are employed to estimate the output reachable set for switched systems under dwell time constraint furthermore the safety verification problem of uncertain switched systems is investigated based on the result of output reachable set estimation first a sufficient condition ensuring the existence of an approximate bisimulation relation between two switched linear systems with a prescribed precision is proposed then the safety verification for an uncertain switched system can be performed through an alternative safety verification for a switched system with exact parameters numerical examples are provided to illustrate our results

stability analysis of switched systems using variational principles an introduction many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode switched systems provide a suitable mathematical model for such processes and their stability analysis is important for both theoretical and practical reasons we review a specific approach for stability analysis based on using variational principles to characterize the most unstable solution of the switched system we also discuss a link between the variational approach and the stability analysis of switched systems using lie algebraic considerations both approaches require the use of sophisticated tools from many different fields of applied mathematics the purpose of this paper is to provide an accessible and self contained review of these topics emphasizing the intuitive and geometric underlying ideas

a novel lyapunov function for a non weighted l2 gain of asynchronously switched linear systems abstract in this paper a novel lyapunov function is proposed to study switched linear systems with a switching delay between activation of system modes and activation of candidate controller modes the novelty consists in continuity of the lyapunov function at the switching instants and discontinuity when the system modes and controller modes are matched this structure is exploited to construct a time varying lyapunov function that is non increasing at time instants of discontinuity stability criteria based on the novel lyapunov function are developed to guarantee global asymptotic stability in the noiseless case most importantly when exogenous disturbances are considered the proposed lyapunov function can be used to guarantee a finite non weighted l 2 gain for asynchronously switched systems for which lyapunov functions proposed in literature are inconclusive a numerical example illustrates the effectiveness of the proposed method

approximate maximum likelihood hyperparameter estimation for gibbs priors the parameters of the prior the hyperparameters play an important role in bayesian image estimation of particular importance for the case of gibbs priors is the global hyperparameter spl beta which multiplies the hamiltonian here we consider maximum likelihood ml estimation of spl beta from incomplete data i e problems in which the image which is drawn from a gibbs prior is observed indirectly through some degradation or blurring process important applications include image restoration and image reconstruction from projections exact ml estimation of spl beta from incomplete data is intractable for most image processing here we present an approximate ml estimator that is computed simultaneously with a maximum a posteriori map image estimate the algorithm is based on a mean field approximation technique through which multidimensional gibbs distributions are approximated by a separable function equal to a product of one dimensional 1 d densities we show how this approach can be used to simplify the ml estimation problem we also show how the gibbs bogoliubov feynman gbf bound can be used to optimize the approximation for a restricted class of problems we present the results of a monte carlo study that examines the bias and variance of this estimator when applied to image restoration

fuzzy control of model car this paper discusses fuzzy control of a model car fuzzy control rules are derived by modelling an expert s driving actions experiments are performed using a model car with a sensing unit and a micro computer

uniformly stabilizing sets of switching sequences for switched linear systems a set of switching sequences of a discrete time switched linear system is said to be uniformly stabilizing if the system is uniformly exponentially stable over all switching sequences that belong to the set based on the recent result that a switched linear system is uniformly stable if and only if an increasing countable union of linear matrix inequality conditions is satisfied we characterize all uniformly stabilizing sets of switching sequences a discrete time hybrid automaton of the automobile engine is considered to illustrate the result

assessing a mixture model for clustering with the integrated completed likelihood we propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood for this purpose the observed data are assigned to unknown clusters using a maximum a posteriori operator then the integrated completed likelihood icl is approximated using the bayesian information criterion bic numerical experiments on simulated and real data of the resulting icl criterion show that it performs well both for choosing a mixture model and a relevant number of clusters in particular icl appears to be more robust than bic to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data

stability and stabilization of discrete time switched systems this paper addresses two strategies for stabilization of discrete time linear switched systems the first one is of open loop nature trajectory independent and is based on the determination of an upper bound of the minimum dwell time by means of a family of quadratic lyapunov functions the relevant point on dwell time calculation is that the proposed stability condition does not require the lyapunov function be uniformly decreasing at every switching time the second one is of closed loop nature trajectory dependent and is designed from the solution of what we call lyapunov metzler inequalities from which the stability condition is expressed being non convex a more conservative but simpler to solve version of the lyapunov metzler inequalities is provided the theoretical results are illustrated by means of examples

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

stochastic approximation algorithms for partition function estimation of gibbs random fields we present an analysis of previously proposed monte carlo algorithms for estimating the partition function of a gibbs random field we show that this problem reduces to estimating one or more expectations of suitable functionals of the gibbs states with respect to properly chosen gibbs distributions as expected the resulting estimators are consistent certain generalizations are also provided we study computational complexity with respect to grid size and show that monte carlo partition function estimation algorithms can be classified into two categories e type algorithms that are of exponential complexity and p type algorithms that are of polynomial complexity turing reducible to the problem of sampling from the gibbs distribution e type algorithms require estimating a single expectation whereas p type algorithms require estimating a number of expectations with respect to gibbs distributions which are chosen to be sufficiently close to each other in the latter case the required number of expectations is of polynomial order with respect to grid size we compare computational complexity by using both theoretical results and simulation experiments we determine the most efficient e type and p type algorithms and conclude that p type algorithms are more appropriate for partition function estimation we finally suggest a practical and efficient p type algorithm for this task

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

mixture of regression models for large spatial datasets abstractwhen a spatial regression model that links a response variable to a set of explanatory variables is desired it is unlikely that the same regression model holds throughout the domain when t

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

testing a point null hypothesis the irreconcilability of p values and evidence abstract the problem of testing a point null hypothesis or a small interval null hypothesis is considered of interest is the relationship between the p value or observed significance level and conditional and bayesian measures of evidence against the null hypothesis although one might presume that a small p value indicates the presence of strong evidence against the null such is not necessarily the case expanding on earlier work especially edwards lindman and savage 1963 and dickey 1977 it is shown that actual evidence against a null as measured say by posterior probability or comparative likelihood can differ by an order of magnitude from the p value for instance data that yield a p value of 05 when testing a normal mean result in a posterior probability of the null of at least 30 for any objective prior distribution objective here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null other definiti

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

the infinite hidden markov random field model hidden markov random field hmrf models are widely used for image segmentation as they appear naturally in problems where a spatially constrained clustering scheme is asked for a major limitation of hmrf models concerns the automatic selection of the proper number of their states i e the number of region clusters derived by the image segmentation procedure existing methods including likelihood or entropy based criteria and reversible markov chain monte carlo methods usually tend to yield noisy model size estimates while imposing heavy computational requirements recently dirichlet process dp infinite mixture models have emerged in the cornerstone of nonparametric bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori infinite mixture models based on the original dp or spatially constrained variants of it have been applied in unsupervised image segmentation applications showing promising results under this motivation to resolve the aforementioned issues of hmrf models in this paper we introduce a nonparametric bayesian formulation for the hmrf model the infinite hmrf model formulated on the basis of a joint dirichlet process mixture dpm and markov random field mrf construction we derive an efficient variational bayesian inference algorithm for the proposed model and we experimentally demonstrate its advantages over competing methodologies

mode identifying time estimation and switching delay tolerant control for switched systems in this paper an elementary time unit etu method is proposed to study the problem of estimating the admissible delay in the identification of the active mode in the analysis and design of switched systems the activation interval of a subsystem is considered to consist of a finite time number of segments called etus by which a novel class of time scheduled lyapunov function is used to estimate the admissible delay in mode identification for switched systems further the etu method is applied for switching delay tolerant control problem and a class of time scheduled state feedback controllers are designed to achieve the exponentially stability several numerical examples are presented to validate the theoretic findings

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

estimating the granularity coefficient of a potts markov random field within a markov chain monte carlo algorithm this paper addresses the problem of estimating the potts parameter jointly with the unknown parameters of a bayesian model within a markov chain monte carlo mcmc algorithm standard mcmc methods cannot be applied to this problem because performing inference on requires computing the intractable normalizing constant of the potts model in the proposed mcmc method the estimation of is conducted using a likelihood free metropolis hastings algorithm experimental results obtained for synthetic data show that estimating jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of on the other hand choosing an incorrect value of can degrade estimation performance significantly to illustrate the interest of this method the proposed algorithm is successfully applied to real bidimensional sar and tridimensional ultrasound images

a fuzzy clustering approach toward hidden markov random field models for enhanced spatially constrained image segmentation hidden markov random field hmrf models have been widely used for image segmentation as they appear naturally in problems where a spatially constrained clustering scheme taking into account the mutual influences of neighboring sites is asked for fuzzy c means fcm clustering has also been successfully applied in several image segmentation applications in this paper we combine the benefits of these two approaches by proposing a novel treatment of hmrf models formulated on the basis of a fuzzy clustering principle we approach the hmrf model treatment problem as an fcm type clustering problem effected by introducing the explicit assumptions of the hmrf model into the fuzzy clustering procedure our approach utilizes a fuzzy objective function regularized by kullback leibler divergence information and is facilitated by application of a mean field like approximation of the mrf prior we experimentally demonstrate the superiority of the proposed approach over competing methodologies considering a series of synthetic and real world image segmentation applications

robust state dependent switching of linear systems with dwell time a state dependent switching law that obeys a dwell time constraint and guarantees the stability of a switched linear system is designed sufficient conditions are obtained for the stability of the switched systems when the switching law is applied in presence of polytopic type parameter uncertainty a lyapunov function in quadratic form is assigned to each subsystem such that it is non increasing at the switching instants during the dwell time this function varies piecewise linearly in time after the dwell the system switches if the switching results in a decrease in the value of the lf the method proposed is also applicable to robust stabilization via state feedback it is further extended to guarantee a bound on the l2 gain of the switching system it is also used in deriving state feedback control law that robustly achieves a prescribed l2 gain bound

em procedures using mean field like approximations for markov model based image segmentation this paper deals with markov random field model based image segmentation this involves parameter estimation in hidden markov models for which one of the most widely used procedures is the em algorithm in practice difficult ies arise due to the dependence structure in the models and approximations are required to make the algorithm tractable we propose a class of algorithms in which the idea is to deal with systems of independent variables this corresponds to approximations of the pixels interactions similar to the mean field approximation it follows algorithms that have the advantage of taking the markovian structure into account while preserving the good features of em in addition this class that includes new and already known procedures is presented in a unified framework showing that apparently distant algorithms come from similar approximation principles we illustrate the algorithms performance on synthetic and real images these experiments point out the ability of our procedures to take the spatial information into account our algorithms often show significant improvement when comparing with the em algorithm applied with no account of the spatial structure and with the icm algorithm based on maximization of the pseudo likelihood and commonly used in image segmentation

robust student s t mixture model with spatial constraints and its application in medical image segmentation finite mixture model based on the student s t distribution which is heavily tailed and more robust than gaussian has recently received great attention for image segmentation a new finite student s t mixture model smm is proposed in this paper existing models do not explicitly incorporate the spatial relationships between pixels first our model exploits dirichlet distribution and dirichlet law to incorporate the local spatial constrains in an image secondly we directly deal with the student s t distribution in order to estimate the model parameters whereas the student s t distributions in previous models are represented as an infinite mixture of scaled gaussians that lead to an increase in complexity finally instead of using expectation maximization em algorithm the proposed method adopts the gradient method to minimize the higher bound on the data negative log likelihood and to optimize the parameters the proposed model is successfully compared to the state of the art finite mixture models numerical experiments are presented where the proposed model is tested on various simulated and real medical images

practical bayesian density estimation using mixtures of normals abstract mixtures of normals provide a flexible model for estimating densities in a bayesian framework there are some difficulties with this model however first standard reference priors yield improper posteriors second the posterior for the number of components in the mixture is not well defined if the reference prior is used third posterior simulation does not provide a direct estimate of the posterior for the number of components we present some practical methods for coping with these problems finally we give some results on the consistency of the method when the maximum number of components is allowed to grow with the sample size

model selection via multifold cross validation a natural extension of the simple leave one out cross validation cv method is to allow the deletion of more than one observations in this article several notions of the multifold cross validation mcv method have been discussed in the context of variable selection under a linear regression model we show that the delete d mcv criterion is asymptotically equivalent to the well known fpe criterion two computationally more feasible methods the r fold cross validation and the repeated learning testing criterion are also studied the performance of these criteria are compared with the simple leave one out cross validation method simulation results are obtained to gain some understanding on the small sample properties of these methods

hidden markov random field model selection criteria based on mean field like approximations hidden markov random fields appear naturally in problems such as image segmentation where an unknown class assignment has to be estimated from the observations at each pixel choosing the probabilistic model that best accounts for the observations is an important first step for the quality of the subsequent estimation and analysis a commonly used selection criterion is the bayesian information criterion bic of schwarz 1978 but for hidden markov random fields its exact computation is not tractable due to the dependence structure induced by the markov model we propose approximations of bic based on the mean field principle of statistical physics the mean field theory provides approximations of markov random fields by systems of independent variables leading to tractable computations using this principle we first derive a class of criteria by approximating the markov distribution in the usual bic expression as a penalized likelihood we then rewrite bic in terms of normalizing constants also called partition functions instead of markov distributions it enables us to use finer mean field approximations and to derive other criteria using optimal lower bounds for the normalizing constants to illustrate the performance of our partition function based approximation of bic as a model selection criterion we focus on the preliminary issue of choosing the number of classes before the segmentation task experiments on simulated and real data point out our criterion as promising it takes spatial information into account through the markov model and improves the results obtained with bic for independent mixture models

an approach to h control of fuzzy dynamic systems this paper presents an approach to h control of a class of continuous time nonlinear systems which can be represented by a fuzzy dynamic model a suitable piecewise differentiable quadratic lyapunov function is used to establish asymptotic stability and h performance of the closed loop fuzzy control system a constructive algorithm is developed to obtain the h feedback control law which involves solving a set of suitable algebraic riccati equations an example is given to illustrate the application of the method

discussion on stability l _ 2 gain and asynchronous h _ infty control of discrete time switched systems with average dwell time this note addresses a defect occurring in in which the desired l 2 gain should be replaced by weighted l 2 gain performance the corrected results and proof are presented

parallel and deterministic algorithms from mrfs surface reconstruction deterministic approximations to markov random field mrf models are derived one of the models is shown to give in a natural way the graduated nonconvexity gnc algorithm proposed by a blake and a zisserman 1987 this model can be applied to smooth a field preserving its discontinuities a class of more complex models is then proposed in order to deal with a variety of vision problems all the theoretical results are obtained in the framework of statistical mechanics and mean field techniques a parallel iterative algorithm to solve the deterministic equations of the two models is presented together with some experiments on synthetic and real images

stability and stabilization of nonlinear switched systems under average dwell time in this paper the problems of stability and stabilization of nonlinear discrete time switched systems is investigated firstly in order to implement the lower bound of minimum average dwell time adt of discrete time switched nonlinear systems the open chain and quasi cyclic switching signals are introduced secondly the problem of these underlying nonlinear discrete time switched systems are solved by using the interval type 2 it2 fuzzy modeling approach thirdly a novel delayed it2 fuzzy controller is devised to guarantee the asymptotically stable of the resulting systems finally a numerical simulation example is given to show the merit and effectiveness of the proposed approach

generating functions of switched linear systems analysis computation and stability applications in this paper a unified framework is proposed to study the exponential stability of discrete time switched linear systems and more generally the exponential growth rates of their trajectories under three types of switching rules arbitrary switching optimal switching and random switching it is shown that the maximum exponential growth rates of system trajectories over all initial states under these three switching rules are completely characterized by the radii of convergence of three suitably defined families of functions called the strong the weak and the mean generating functions respectively in particular necessary and sufficient conditions for the exponential stability of the switched linear systems are derived based on these radii of convergence various properties of the generating functions are established and their relations are discussed algorithms for computing the generating functions and their radii of convergence are also developed and illustrated through examples

stability of time delay feedback switched linear systems we address stability of state feedback switched linear systems in which delays are present in both the feedback state and the switching signal of the switched controller for switched systems with average dwell time switching signals we provide a condition in terms of upper bounds on the delays and in terms of a lower bound on the average dwell time to guarantee asymptotic stability of the closed loop the condition also implies that in general feedback switched linear systems are robust with respect to both small state delays and small switching delays our approach combines existing multiple lyapunov function techniques with the merging switching signal technique which gives relationships between the average dwell times of two mismatched switching signals and their mismatched times a methodology for numerical solution based on linear matrix inequality is also included

entropic criterion for model selection abstract model or variable selection is usually achieved through ranking models according to the increasing order of preference one of methods is applying kullback leibler distance or relative entropy as a selection criterion yet that will raise two questions why use this criterion and are there any other criteria besides conventional approaches require a reference prior which is usually difficult to get following the logic of inductive inference proposed by caticha relative entropy and inductive inference in g erickson y zhai eds bayesian inference and maximum entropy methods in science and engineering aip conference proceedings vol 707 2004 available from arxiv org abs physics 0311093 we show relative entropy to be a unique criterion which requires no prior information and can be applied to different fields we examine this criterion by considering a physical problem simple fluids and results are promising

h sub infinity control and filtering for sampled data systems h sub infinity control and filtering problems for sampled data systems are studied necessary and sufficient conditions are obtained for the existence of controllers and filters that satisfy a specified h sub infinity performance bound when these conditions hold explicit formulas for a controller and a filter satisfying the h sub infinity performance bound are also given

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

a nonconservative lmi condition for stability of switched systems with guaranteed dwell time ensuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems several methods have been proposed in the literature to address this problem but unfortunately they provide sufficient conditions only this technical note proposes the use of homogeneous polynomial lyapunov functions in the non restrictive case where all the subsystems are hurwitz showing that a sufficient condition can be provided in terms of an lmi feasibility test by exploiting a key representation of polynomials several properties are proved for this condition in particular that it is also necessary for a sufficiently large degree of these functions as a result the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well some examples illustrate the proposed approach

an approach to h control of a class of nonlinear systems this paper considers robust h control of a class of nonlinear systems that can be represented by a heterogeneous model a new controller design method using both state feedback is proposed based on quadratic stability theory a number of necessary and sufficient conditions are derived for quadratic stabilizability with disturbance attenuation of the control system concerned an example is also given to demonstrate the performance of the proposed controller design methods

convex lifted conditions for robust l 2 stability analysis and l 2 stabilization of linear discrete time switched systems with minimum dwell time constraint stability analysis of discrete time switched systems under minimum dwell time is studied using a new type of lmi conditions these conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions proposed in geromel and colaneri 2006b the convexification of the conditions is performed by a lifting process which introduces a moderate number of additional decision variables the convexity of the conditions can be exploited to extend the results to uncertain systems control design and 2 gain computation without introducing additional conservatism several examples are presented to show the effectiveness of the approach

a spatially constrained generative model and an em algorithm for image segmentation in this paper we present a novel spatially constrained generative model and an expectation maximization em algorithm for model based image segmentation the generative model assumes that the unobserved class labels of neighboring pixels in the image are generated by prior distributions with similar parameters where similarity is defined by entropic quantities relating to the neighboring priors in order to estimate model parameters from observations we derive a spatially constrained em algorithm that iteratively maximizes a lower bound on the data log likelihood where the penalty term is data dependent our algorithm is very easy to implement and is similar to the standard em algorithm for gaussian mixtures with the main difference that the labels posteriors are smoothed over pixels between each e and m step by a standard image filter experiments on synthetic and real images show that our algorithm achieves competitive segmentation results compared to other markov based methods and is in general faster