frequency domain approach to optimally robust residual generation and evaluation for model based fault diagnosis methods of residual generation and evaluation for model based fault diagnosis in uncertain linear dynamic systems are investigated with the aid of frequency domain approaches and h optimization techniques based on the factorization technique the construction of residual generators in terms of a parametrization concept is proposed with its help the fault detection and isolation problem with perfect model uncertainty decoupling is studied and moreover by its optimal approximation the problem of optimally robust residual generation is treated the optimization problem is solved by h techniques to increase the robustness of residual evaluation a frequency domain residual evaluation index is introduced and optimal input adaptive fault thresholds are derived with respect to the frequency domain evaluation index the results are illustrated in terms of an inverted pendulum example

quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions this paper deals with typical problems that arise when using wavelets in numerical analysis applications the first part involves the construction of quadrature formulae for the calculation of inner products of smooth functions and scaling functions several types of quadratures are discussed and compared for different classes of wavelets since their construction using monomials is ill conditioned also a modified well conditioned construction using chebyshev polynomials is presented the second part of the paper deals with pointwise asymptotic error expansions of wavelet approximations of smooth functions they are used to derive asymptotic interpolating properties of the wavelet approximation and to construct a convergence acceleration algorithm this is illustrated with numerical examples

the subgraph isomorphism problem for outerplanar graphs this paper deals with the subgraph isomorphism problem for outerplanar graphs suboutisom in general since trees and forests are outerplanar suboutisom is np complete we show that suboutisom remains np complete even when the strongest connectivity requirements are imposed on both graphs the same results holds for the induced subgraph isomorphism problem for outerplanar graphs except the case when both graphs are 2 connected for such graphs we give a polynomial algorithm which verifies whether a 2 connected outerplanar graph is an induced subgraph of another 2 connected outerplanar graph

parametrization of optimal fault detection filters this paper is concerned with the fault detection filter design problem for linear time invariant systems subject to disturbance and possible faults to make a tradeoff between fault sensitivity and disturbance sensitivity frameworks such as 2 and are considered it is shown that for and frameworks all optimal fault detection filters can be characterized by an envelope besieged by the special solutions serving as upper and lower bounds furthermore the explicit parametrization is given in terms of a free contractive system parameter this free parameter provides freedom to emphasize fault and disturbance sensitivities at different frequency ranges which can be used to construct new optimal fault detection filter the results are also extended to the optimization over finite frequency range for which the upper and or lower bound of the optimal solution set may not be rational on the other hand it is shown that the solution set of 2 problem is unique up to square inner system finally examples are given to illustrate the results

sampled data h h fault detection and isolation for nonlinear systems in t s form a direct discrete time design methodology for the sampled data fault detection and isolation fdi problem is proposed for a nonlinear system in takagi sugeno form the generalized observer scheme is adopted accompanied by a bank of the sensors number of observers a sufficient condition to find observer and residual gains based on an accessible approximate rather than unavailable exact discrete time model is proposed in terms of matrix inequalities so that it exhibits h h performance and asymptotic stability an algorithm involving a convex optimization is presented using the cone complementary linearization technique we show that the fdi observer ensures modified h h performance and lagrange stability when it is connected to the actual nonlinear system

on the complexity of submap isomorphism and maximum common submap problems generalized maps describe the subdivision of objects in cells and are widely used to model 2d and 3d images in this context several pattern recognition tasks involve solving submap isomorphism problems to decide if a map is included in another map or more generally computing maximum common submaps to measure the distance between two maps recently we have described a polynomial time algorithm for solving the submap isomorphism problem when the pattern map is connected in this paper we show that submap isomorphism is np complete when the pattern map is not connected then we characterize the inherent difficulty of submap isomorphism with respect to the number of connected components we show that it is fixed parameter tractable fpt and we give an fpt algorithm for submap isomorphism we experimentally compare this algorithm with a state of the art subgraph isomorphism algorithm for searching for patterns in an image and we show that it is both more accurate and more efficient finally we study the complexity of the maximum common submap problem and we show that it is np hard even though we restrict the problem to the search of common connected submaps highlightswe show that submap isomorphism is np complete we give a fixed parameter tractable algorithm for submap isomorphism we experimentally evaluate it to search for patterns in segmented images we show that maximum common connected submap is np hard

a robust deconvolution scheme for fault detection and isolation of uncertain linear systems an lmi approach optimal h deconvolution filter theory is exploited for the design of robust fault detection and isolation fdi units for uncertain polytopic linear systems such a filter is synthesized under frequency domain conditions which ensure guaranteed levels of disturbance attenuation residual decoupling and deconvolution performance in prescribed frequency ranges by means of the projection lemma a quasi convex formulation of the problem is obtained via lmis a fdi logic based on adaptive thresholds is also proposed for reducing the generation of false alarms the effectiveness of the design technique is illustrated via a numerical example

a new fault detection scheme for networked control systems subject to uncertain time varying delay fault detection of networked control systems ncs subject to uncertain time varying delay is studied in this paper for the convenience of residual generator design influence caused by network induced delay is first transformed into time varying polytopic uncertainty which greatly facilitates further manipulation then design of the optimal residual generator is formulated as a model matching problem i e to design a residual generator best matching the optimal residual generator of ncs in the delay free case this procedure is assisted by parameter dependent lyapunov function matrix based bounded real lemma which has been proved to be much better than single constant lyapunov function matrix based results this approach not only can be used in conditions that the variation part of the delay is less than one sampling period but also can be applied to scenarios where the variation part of the delay is larger than one sampling period simulation results are also given to illustrate effectiveness of the proposed method

fault detection for t s fuzzy systems with unknown membership functions this paper is concerned with the fault detection fd problem for takagi sugeno t s fuzzy systems with unknown membership functions if the membership functions are unknown the linear fd filter designs with fixed gains have been considered in the literature to reduce the conservatism of the existing results a switching mechanism that depends on the lower and upper bounds of the unknown membership functions is provided to construct an fd filter with varying gains it is shown that the switching type fd filter with varying gains can achieve a better fd performance than the linear fd filter with fixed gains in addition based on some time domain inequalities a novel weighting matrix design approach is introduced to transform the fault sensitivity specification into an h constraint finally two examples are given to show the advantages of the proposed fd method

fault detection for fuzzy systems with intermittent measurements this paper investigates the problem of fault detection for takagi sugeno t s fuzzy systems with intermittent measurements the communication links between the plant and the fault detection filter are assumed to be imperfect i e data packet dropouts occur intermittently which appear typically in a network environment and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the unreliable communication links the aim is to design a fuzzy fault detection filter such that for all data missing conditions the residual system is stochastically stable and preserves a guaranteed performance the problem is solved through a basis dependent lyapunov function method which is less conservative than the quadratic approach the results are also extended to t s fuzzy systems with time varying parameter uncertainties all the results are formulated in the form of linear matrix inequalities which can be readily solved via standard numerical software two examples are provided to illustrate the usefulness and applicability of the developed theoretical results

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

planar formulae and their uses we define the set of planar boolean formulae and then show that the set of true quantified planar formulae is polynomial space complete and that the set of satisfiable planar formulae is np complete using these results we are able to provide simple and nearly uniform proofs of np completeness for planar node cover planar hamiltonian circuit and line geometric connected dominating set and of polynomial space completeness for planar generalized geography the np completeness of planar node cover and planar hamiltonian circuit and line were first proved elsewhere m r garey and d s johnson the rectilinear steiner tree is np complete siam j appl math 32 1977 pp 826 834 and m r garey d s johnson and r e tarjan the planar hamilton circuit problem is np complete siam j comp 5 1976 pp 704 714

alldifferent based filtering for subgraph isomorphism the subgraph isomorphism problem involves deciding if there exists a copy of a pattern graph in a target graph this problem may be solved by a complete tree search combined with filtering techniques that aim at pruning branches that do not contain solutions we introduce a new filtering algorithm based on local all different constraints we show that this filtering is stronger than other existing filterings i e it prunes more branches and that it is also more efficient i e it allows one to solve more instances quicker

h sub 2 and h sub spl infin robust filtering for convex bounded uncertain systems investigates robust filtering design problems in h sub 2 and h sub spl infin spaces for continuous time systems subjected to parameter uncertainty belonging to a convex bounded polyhedral domain it is shown that by a suitable change of variables both designs can be converted into convex programming problems written in terms of linear matrix inequalities the results generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured then assuming the order of the uncertain system is known the optimal guaranteed performance h sub 2 and h sub spl infin filters are proven to be of the same order as the order of the system a numerical example illustrate the theoretical results

a robust fault detection filter for polynomial nonlinear systems via sum of squares decompositions abstract a novel diagnostic framework is discussed for fault detection of nonlinear systems whose structure is described by multivariate polynomials the trade off between disturbance rejection and fault sensitivity prescriptions is characterized via algebraic geometry conditions and the unknown input observer design problem is formulated via sum of squares sos technicalities by exploiting the results of the positivstellensatz theorem an adaptive threshold logic is proposed to reduce the generation of false alarms and the diagnostic filter capabilities are illustrated via a numerical example taken from the literature

wavelet transform domain filters a spatially selective noise filtration technique wavelet transforms are multiresolution decompositions that can be used to analyze signals and images they describe a signal by the power at each scale and position edges can be located very effectively in the wavelet transform domain a spatially selective noise filtration technique based on the direct spatial correlation of the wavelet transform at several adjacent scales is introduced a high correlation is used to infer that there is a significant feature at the position that should be passed through the filter the authors have tested the technique on simulated signals phantom images and real mr images it is found that the technique can reduce noise contents in signals and images by more than 80 while maintaining at least 80 of the value of the gradient at most edges the authors did not observe any gibbs ringing or significant resolution loss on the filtered images artifacts that arose from the filtration are very small and local the noise filtration technique is quite robust there are many possible extensions of the technique the authors see its applications in spatially dependent noise filtration edge detection and enhancement image restoration and motion artifact removal they have compared the performance of the technique to that of the weiner filter and found it to be superior

improving bipartite graph edit distance approximation using various search strategies recently the authors of the present paper introduced an approximation framework for the graph edit distance problem the basic idea of this approximation is to first build a square cost matrix c c ij where each entry cij reflects the cost of a node substitution deletion or insertion plus the matching cost arising from the local edge structure based on c an optimal assignment of the nodes and their local structure can be established in polynomial time since this approach considers local rather than the global structural properties of the graphs only the graph edit distance derived from the optimal node assignment generally overestimates the true edit distance the present paper pursues the idea of applying additional search strategies that build upon the initial assignment in order to reduce this overestimation to this end six different search strategies are investigated in this paper in an exhaustive experimental evaluation on five real world graph data sets we empirically verify a substantial gain of distance accuracy by means of all search methods while run time remains remarkably low highlightswe show how the well known bipartite graph edit distance approximation can substantially be improved with respect to distance accuracy to this end we introduce and compare six different methodologies for extending the graph matching framework we empirically verify a substantial gain of distance accuracy by means of all methods while run time remains remarkably low the benefit of improved distance quality is also verified in a clustering application

wavelet simultaneous approximation from samples affected by noise the authors recently introduced a pth order wavelet regularization method together with the gcv criterion for approximating a function from a finite sample affected by noise convergence results of the method were proven for the l2 norm the present paper addresses the problem of simultaneous approximation which is of interest in applications where derivatives are useful for extracting several features from a signal it is proved that it is not needed to devise a special method to this purpose since the convergence of the method devised by the authors also works for the hq norm 0 q p

an efficient solution to multi objective control problems with lmi objectives we revisit a technique for solving multi objective control problems through affinely parameterizing the closed loop system with the youla parameterization and confining the search of the youla parameter to finite dimensional subspaces it is pretty well known how to solve such problems if the closed loop specifications are formulated in terms of the solvability of linear matrix inequalities however all approaches proposed so far suffer from a substantial inflation of size of the resulting optimization problems if improving the approximation accuracy on the basis of a novel state space approach to solving static output feedback control problems by convex optimization for a specific class of plants we reveal how the growth of the size of the optimization problems can be considerably reduced to arrive at more efficient algorithms as an additional ingredient we discuss how to use the so called mixed controller as a starting point for a genuine multi objective design in order to improve the algorithms

optimal quadratic time isomorphism of ordered graphs in this paper we introduce the concept of ordered graph and ordered graph isomorphism that provides a natural representation of many objects in applications such as computer vision and pattern recognition while no efficient polynomial bound isomorphism algorithm for general graphs exists today we show that the ordered graph isomorphism problem can be optimally solved in quadratic time an experimental evaluation demonstrates the superior performance of the new method our ordered graph isomorphism algorithm is simple and can be easily implemented it is therefore expected to be practically useful in many applications

finite frequency h_ infty deconvolution with application to approximated bandlimited signal recovery this paper investigates a finite frequency h infty deconvolution problem for single input single output discrete time systems motivated by the fact that many practical signals are located in a finite frequency range this paper is focused on developing a design method for achieving better deconvolution performance over a finite frequency range first a finite frequency h infty deconvolution problem is formulated such that the deconvolution specification is characterized by a modified h mathbf infty index associated with the corresponding finite frequency range by an adapted generalized kalman yakubovich popov lemma and an auxiliary vector approach a matrix inequality condition is obtained for parameterizing a required deconvolution filter based on which a simple iterative algorithm is then constructed for optimizing the filter performance multiobjective deconvolution is further discussed in the same framework compared with the traditional frequency weighting strategy the proposed method can directly analyze and synthesize the deconvolution performance within finite frequency ranges the advantage of which is demonstrated in a bandlimited signal recovery example

technical communique robust fault detection of uncertain linear systems via quasi lmis a novel h deconvolution filter design method is discussed for fault detection of uncertain polytopic linear systems subject to unknown inputs the enhancement of fault sensitivity is characterized in terms of an h index by means of the projection lemma and congruence transformations a quasi convex lmi formulation of the design problem is obtained the effectiveness of the filter is illustrated via a numerical example

approximation of graph edit distance based on hausdorff matching graph edit distance is a powerful and flexible method for error tolerant graph matching yet it can only be calculated for small graphs in practice due to its exponential time complexity when considering unconstrained graphs in this paper we propose a quadratic time approximation of graph edit distance based on hausdorff matching in a series of experiments we analyze the performance of the proposed hausdorff edit distance in the context of graph classification and compare it with a cubic time algorithm based on the assignment problem investigated applications include nearest neighbor classification of graphs representing letter drawings fingerprints and molecular compounds as well as hidden markov model classification of vector space embedded graphs representing handwriting in many cases a substantial speedup is achieved with only a minor loss in accuracy or in one case even with a gain in accuracy overall the proposed hausdorff edit distance shows a promising potential in terms of flexibility efficiency and accuracy highlightsquadratic time approximation of graph edit distance based on hausdorff matching error tolerant graph matching method without constraints on node and edge labels experimental evaluation for classification of graphs representing letter drawings fingerprints and molecules experimental evaluation for hidden markov model recognition of vector space embedded graphs representing handwriting promising potential in terms of flexibility efficiency and accuracy

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

robust filtering for uncertain nonlinearly parameterized plants we address the robust filtering problem for a wide class of systems whose state space data assume a very general nonlinear dependence in the uncertain parameters our resolution methods rely on new linear matrix inequality characterizations of spl hscr sub 2 and spl hscr sub spl infin performances which in conjunction with suitable linearization transformations of the variables give rise to practical and computationally tractable formulations for the robust filtering problem

enumerating all connected maximal common subgraphs in two graphs we represent a new method for finding all connected maximal common subgraphs in two graphs which is based on the transformation of the problem into the clique problem we have developed new algorithms for enumerating all cliques that represent connected maximal common subgraphs these algorithms are based on variants of the bron kerbosch algorithm in this paper we explain the transformation of the maximal common subgraph problem into the clique problem we give a short summary of the variants of the bron kerbosch algorithm in order to explain the modification of that algorithm such that the detected cliques represent connected maximal common subgraphs after introducing and proving several variants of the modified algorithm we discuss the runtimes for all variants by means of random graphs the results show the drastical reduction of the runtimes for the new algorithms

optimal linear filtering under parameter uncertainty this paper addresses the problem of designing a guaranteed minimum error variance robust filter for convex bounded parameter uncertainty in the state output and input matrices the design procedure is valid for linear filters that are obtained from the minimization of an upper bound of the error variance holding for all admissible parameter uncertainty the results provided generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured assuming the order of the uncertain system is known the optimal robust linear filter is proved to be of the same order as the order of the system in the present case of convex bounded parameter uncertainty the basic numerical design tools are linear matrix inequality lmi solvers instead of the riccati equation solvers used for the design of robust filters available in the literature to date the paper that contains the most important and very recent results on robust filtering is used for comparison purposes in particular it is shown that under the same assumptions our results are generally better as far as the minimization of a guaranteed error variance is considered some numerical examples illustrate the theoretical results

fault detection for discrete time linear systems based on descriptor observer approach this paper investigates the problem of actuator fault detection filter design for discrete time linear systems with output disturbance by using the descriptor observer method an h fault detection filter is designed to guarantee the residual system is admissible and satisfies the h performance by utilizing lyapunov function approach a sufficient condition for the admissible of the residual system is obtained in the form of linear matrix inequality lmi the desired fault detection filter can be designed by solving a set of lmis finally a numerical example is proposed to illustrate the effectiveness of the developed method

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

regions adjacency graph applied to color image segmentation this paper presents different algorithms based on a combination of two structures of a graph and of two color image processing methods in order to segment color images the structures used in this study are the region adjacency graph and the associated line graph we see how these structures can enhance segmentation processes such as region growing or watershed transformation the principal advantage of these structures is that they give more weight to the adjacency relationships between regions than the usual methods we note nevertheless that this advantage leads the adjustment of more parameters than other methods to best refine the result of the segmentation we show that this adjustment is necessarily image dependent and observer dependent

robust fault detection with missing measurements this paper investigates the problem of robust fault detection for uncertain systems with missing measurements the parameter uncertainty is assumed to be of polytopic type and the measurement missing phenomenon which appears typically in a network environment is modelled by a stochastic variable satisfying the bernoulli random binary distribution the focus is on the design of a robust fault detection filter or a residual generation system which is stochastically stable and satisfies a prescribed disturbance attenuation level this problem is solved in the parameter dependent framework which is much less conservative than the quadratic approach both full order and reduced order designs are considered and formulated via linear matrix inequality lmi based convex optimization problems which can be efficiently solved via standard numerical software a continuous stirred tank reactor cstr system is utilized to illustrate the design procedures

brief an lmi approach to design robust fault detection filter for uncertain lti systems in this paper the robust fault detection filter design problem for uncertain linear time invariant lti systems with both unknown inputs and modelling errors is studied the basic idea of our study is to use an optimal residual generator assuming no modelling errors as the reference residual model of the robust fault detection filter design for uncertain lti systems with modelling errors and based on it to formulate the robust fault detection filter design as an h model matching problem by using some recent results of h optimization a solution of the optimization problem is then presented via a linear matrix inequality lmi formulation the main results include the development of an optimal reference residual model the formulation of robust fault detection filter design problem the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the lmi solution parameters the determination of adaptive threshold for fault detection an illustrative design example is employed to demonstrate the effectiveness of the proposed approach