additive change detection in nonlinear systems with unknown change parameters we study the change detection problem in partially observed nonlinear systems which satisfy the hidden markov model hmm property the change parameters are assumed unknown and the changes can be slow or sudden a partially observed system needs to be tracked first before changes can be detected sudden changes result in significant loss of track these can be detected easily using the increase in tracking error te or observation likelihood ol or using a cusum type method applied to either of these however slow changes which result in small loss of track often get missed we propose here a statistic that uses the tracked component of the change to detect it and hence detects slow changes faster than te or ol we show both analytically and through simulations that this statistic complements ol and te for change detection

adaptive approximation for multiple sensor fault detection and isolation of nonlinear uncertain systems this paper presents an adaptive approximation based design methodology and analytical results for distributed detection and isolation of multiple sensor faults in a class of nonlinear uncertain systems during the initial stage of the nonlinear system operation adaptive approximation is used for online learning of the modeling uncertainty then local sensor fault detection and isolation sfdi modules are designed using a dedicated nonlinear observer scheme the multiple sensor fault isolation process is enhanced by deriving a combinatorial decision logic that integrates information from local sfdi modules the performance of the proposed diagnostic scheme is analyzed in terms of conditions for ensuring fault detectability and isolability a simulation example of a single link robotic arm is used to illustrate the application of the adaptive approximation based sfdi methodology and its effectiveness in detecting and isolating multiple sensor faults

complex representations of finite monoids ii highest weight categories and quivers abstract in this paper we continue our study of complex representations of finite monoids we begin by showing that the complex algebra of a finite regular monoid is a quasi hereditary algebra and we identify the standard and costandard modules we define the concept of a monoid quiver and compute it in terms of the group characters of the standard and costandard modules we use our results to determine the blocks of the complex algebra of the full transformation semigroup we show that there are only two blocks when the degree 3 we also show that when the degree 5 the complex algebra of the full transformation semigroup is not of finite representation type answering negatively a conjecture of ponizovskii

nonlinear unknown input observability extension of the observability rank condition this paper provides an extension of the observability rank condition to nonlinear systems driven by both known and unknown inputs in particular the systems here considered are characterized by dynamics that are nonlinear in the state and linear in the inputs and characterized by a single unknown input or disturbance and multiple known inputs additionally it is assumed that the unknown input is a differentiable function of time up to a given order the goal of the paper is not to design new observers for these systems but to provide the analytic condition in order to check the weak local observability of the state this condition is simple and can be easily and automatically applied to the nonlinear systems mentioned above independently of their complexity and type of nonlinearity in particular the complexity of the analytic condition is comparable to the complexity of the standard method to check the state observability in the case without unknown inputs i e the observability rank condition this is a fundamental practical and unexpected advantage as for the observability rank condition the proposed analytic condition is based on the computation of the observable codistribution similarly to the case of only known inputs the observable codistribution is obtained by recursively computing the lie derivatives of the outputs along the vector fields that characterize the dynamics however in correspondence of the unknown input the corresponding vector field must be suitably rescaled additionally the lie derivatives of the outputs must also be computed along a new set of vector fields that are obtained by recursively performing suitable lie bracketing of the vector fields that define the dynamics in practice the entire observable codistribution is obtained by a very simple recursive algorithm finally it is shown that the recursive algorithm converges in a finite number of steps and the criterion to establish that the convergence has been reached is provided the proposed analytic extension of the observability rank condition is illustrated by checking the weak local observability of several nonlinear systems driven by known inputs and a single disturbance

on numerical cubatures of singular surface integrals in boundary element methods we present and analyze methods for the accurate and efficient evaluation of weakly cauchy and hypersingular integrals over piecewise analytic curved surfaces in 3 the class of admissible integrands includes all kernels arising in the numerical solution of elliptic boundary value problems in three dimensional domains by the boundary integral equation method the possibly not absolutely integrable kernels of boundary integral operators in local coordinates are pseudohomogeneous with analytic characteristics depending on the local geometry of the surface at the source point this rules out weighted quadrature approaches with a fixed singular weight for weakly singular integrals it is shown that duffy s triangular coordinates leadalways to a removal of the kernel singularity also asymptotic estimates of the integration error are provided as the size of the boundary element patch tends to zero these are based on the rabinowitz richter estimates in connection with an asymptotic estimate of domains of analyticity in 2 it is further shown that the modified extrapolation approach due to lyness is in the weakly singular case always applicable corresponding error and asymptotic work estimates are presented for the weakly singular as well as for cauchy and hypersingular integrals which e g arise in the study of crack problems we analyze a family of product integration rules in local polar coordinates these rules are hierarchically constructed from finite part integration formulas in radial and gaussian formulas in angular direction again we show how the rabinowitz richter estimates can be applied providing asymptotic error estimates in terms of orders of the boundary element size

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

a fast poisson solver for complex geometries robust fast solvers for the poisson equation have generally been limited to regular geometries where direct methods based on fourier analysis or cyclic reduction and multigrid methods can be used while multigrid methods can be applied in irregular domains and to a broader class of partial differential equations they are difficult to implement in a robust fashion since they require an appropriate hierarchy of coarse grids which are not provided in many practical situations in this paper we present a new fast poisson solver based on potential theory rather than on direct discretization of the partial differential equation our method combines fast algorithms for computing volume integrals and evaluating layer potentials on a grid with a fast multipole accelerated integral equation solver the amount of work required is o m log m n where m is the number of interior grid points and n is the number of points on the boundary asymptotically the cost of our method is just twice that of a standard poisson solver on a rectangular domain in which the problem domain can be embedded independent of the complexity of the geometry

invariant subspaces for lpv systems and their applications the aim of this paper is to extend the notion of invariant subspaces known in the geometric control theory of the linear time invariant systems to the linear parameter varying lpv systems by introducing the concept of parameter varying invariant subspaces for lpv systems affine in their parameters algorithms are given to compute many parameter varying subspaces relevant in the solution of state feedback and observer design problems

electrostatic fields without singularities theory algorithms and error analysis the following problems that arise in the computation of electrostatic forces and in the boundary element method are considered given two convex interior disjoint polyhedra in 3 space endowed with a volume charge density which is a polynomial in the cartesian coordinates of r 3 compute the coulomb force acting on them given two interior disjoint polygons in 3 space endowed with a surface charge density which is polynomial in the cartesian coordinates of r 3 compute the normal component of the coulomb force acting on them for both problems adaptive gaussian approximation algorithms are given which for n gaussian points in time o n achieve absolute error o c n for a constant c 1 such a result improves upon previously known best asymptotic bounds this result is achieved by blending techniques from integral geometry computational geometry and numerical analysis in particular integral geometry is used in order to represent the forces as integrals whose kernal is free from singularities

representation theory of finite semigroups semigroup radicals and formal language theory in this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field generalizing results of rhodes for the field of complex numbers applications are given to obtain many new results as well as easier proofs of several results in the literature involving triangularizability of finite semigroups which semigroups have split basic semigroup algebras two sided semidirect product decompositions of finite monoids unambiguous products of rational languages products of rational languages with counter and cerny s conjecture for an important class of automata

new nonlinear residual feedback observer for fault diagnosis in nonlinear systems the increased complexity of plants and the development of sophisticated control systems have necessitated the parallel development of efficient fault detection and isolation fdi systems this paper discusses a model based technique viz observers for detecting and isolating parametric and sensor faults in this paper a novel diagonal nonlinear residual feedback observer is proposed which is valid for a certain class of nonlinear systems where subject to other conditions the state depends nonlinearly on the fault a number of typical chemical engineering systems can be represented by models of this form the structure of the observer ensures that the residuals are diagonally affected by the faults conditions for exact decoupling of residuals are presented and convergence of the observer in the presence of step faults is proved using lyapunov like analysis multiple observers and a decision logic module are used for fdi when there are un monitored faults results are presented from numerical simulations of an illustrative example and a typical chemical engineering system a counter current heat exchanger

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

diagnosis of unknown parametric faults in non linear stochastic dynamical systems a new detection and isolation scheme for unknown parametric faults in non linear stochastic systems is presented that is particularly suited for small parametric changes the proposed residual is the moving angle between two stochastic processes the error derived from the reference model and the expected error in case a certain fault has occurred since the fault is unknown fault classes are defined most of the faults that belong to such a fault class can be detected and isolated by just testing one representative of this fault class as the moving angle itself is a stochastic process an estimator is designed and characterised conditions for the detectability and isolability of fault classes are given for this estimator based on hypotheses tests finally the theoretical results are confirmed by simulations and monte carlo tests

the representation theory of the monoid of all partial functions on a set and related monoids as ei category algebras the ordinary quiver of an algebra a is a graph that contains information about the algebra s representations we give a description of the quiver of cptn the algebra of the monoid of all partial functions on n elements our description uses an isomorphism between cptn and the algebra of the epimorphism category en whose objects are the subsets of 1 n and morphism are all total epimorphisms this is an extension of a well known isomorphism of the algebra of isn the monoid of all partial injective maps on n elements and the algebra of the groupoid of all bijections between subsets of an n element set the quiver of the category algebra is described using results of margolis steinberg and li on the quiver of ei categories we use the same technique to compute the quiver of other natural transformation monoids we also show that the algebra cptn has three blocks for n 1 and we give a natural description of the descending loewy series of cptn in the category form

sensor fault reconstruction and observability for unknown inputs with an application to wastewater treatment plants in this article we propose a general methodology for identifying and reconstructing sensor faults on dynamical processes this methodology is issued from the general identification theory developed in the previous papers busvelle e and gauthier j p 2003 on determining unknown functions in differential systems with an application to biological reactor esaim control optimisation and calculus of variations 9 509 553 busvelle e and gauthier j p 2004 new results on identifiability of nonlinear systems in 2nd symposium on systems structure and control oaxaca mexico busvelle e and gauthier j p 2005 observation and identification tools for non linear systems application to a fluid catalytic cracker international journal of control 78 208 234 in fact this identification theory also provides a general framework for the problem of observability with unknown inputs indeed many problems of fault detection can be formulated as such observability problems the e

on the effect of numerical integration in the galerkin boundary element method we discuss the effect of cubature errors when using the galerkin method for approximating the solution of fredholm integral equations in three dimensions the accuracy of the cubature method has to be chosen such that the error resulting from this further discretization does not increase the asymptotic discretization error we will show that the asymptotic accuracy is not influenced provided that polynomials of a certain degree are integrated exactly by the cubature method this is done by applying the bramble hilbert lemma to the boundary element method

fault detection and isolation of linear discrete time periodic systems using the geometric approach this technical note solves the problem to detect and isolate faults in linear periodic discrete time systems a residual generator is designed through a suitable unknown input observer with the requirement that each residual should be sensitive only to one fault and simultaneously insensitive to the other faults that can affect the system and with the additional requirement of detectability that is the transition matrix of its relative error system has all eigenvalues smaller than in modulus for a given positive p 1 the solution is based on geometric tools and it makes use of the outer observable subspace notion

unknown input observer for state affine systems a necessary and sufficient condition the problem of designing an unknown input observer for linear systems and its application to fault detection is widely studied in the literature for nonlinear systems only subclasses of nonlinear systems and sufficient conditions have been stated in this paper an unknown input observer design for state affine systems is considered based on the geometric approach a necessary and sufficient condition is given for the existence of an unknown input observer

functional unknown input reconstruction of descriptor systems the problem of finding conditions for the reconstruction of a linear combination of the vector of unknown inputs is tackled appropriate definitions are given in order to address formally the analysis thus necessary and sufficient conditions are obtained for two cases when the reconstruction may be achieved in finite time and when it is possible to do it asymptotically the results are applied for the fault detection with the respective deduction of analogous conditions

a geometric approach to the synthesis of failure detection filters a geometric formulation of beard s failure detection filter problem is stated using the concepts of c a invariant and unobservability subspaces the notions of output separable and mutually detectable families of subspaces introduced by beard are also clarified it is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum moreover it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions finally the complete duality between a generalization of beard s detection filter problem and the restricted control decoupling problem is illustrated

robust inversion based fault estimation for discrete time lpv systems the article presents a state space based fault diagnosis fd method for discrete time affine linear parameter varying lpv systems the goal of the technical note is to develop a robust and dynamic inversion based technique for systems with parameter varying representations when an additive exogenous disturbance signal perturbs the system after applying geometric concepts for explicit fault inversion a robust strategy is proposed to attenuate the effect of the unknown disturbance input signal on the fault estimation error the proposed robust observer is derived as a solution of off line linear matrix inequality lmi conditions the technical note demonstrates the viability of the novel methodology through a numerical example

a mathematical framework for new fault detection schemes in nonlinear stochastic continuous time dynamical systems in this work a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous time dynamical systems is developed these schemes are based on a stochastic process called the residual which reflects the system behavior and whose changes are to be detected a quickest detection scheme for the residual is proposed which is based on the computed likelihood ratios for time varying statistical changes in the ornstein uhlenbeck process several expressions are provided depending on a priori knowledge of the fault which can be employed in a proposed cusum type approximated scheme this general setting gathers different existing fault detection schemes within a unifying framework and allows for the definition of new ones a comparative simulation example illustrates the behavior of the proposed schemes

on observer based fault detection for nonlinear systems abstract this paper addresses analysis and integrated design of observer based fault detection fd for nonlinear systems to gain a deeper insight into the observer based fd framework definitions and existence conditions for nonlinear observer based fd systems are studied first then a scheme for an integrated design of observer based fd systems for affine nonlinear systems is proposed our work is considerably inspired by the study on input output stability and stabilization of nonlinear systems examples are given at the end of the paper to illustrate the theoretical results

on the observability codistributions of a nonlinear system abstract the purpose of this is to introduce the notion of observability codistribution for a nonlinear system which extends the dual of the notion of unobservability subspace then we study its properties which bear important similarities with a number of properties which render the notion of unobservability subspace powerful in the solution of certain design problems

lowering orders of derivatives in non linear residual generation using realization theory consistency relations are often used to design residual generators based on non linear process models a main difficulty is that they generally include time differentiated versions of known signals which are difficult to estimate in a noisy environment the main results of this paper show how to lower the need to estimate derivatives of known signals in order to compute a residual necessary and sufficient conditions for lowering the order of the derivatives in one step are presented and a main step in the approach is to obtain a state space realization of the residual generator an attractive feature of the approach is that general differential algebraic system descriptions can be handled in the same way as for example ordinary differential equations and also that stability of the residual generator is always guaranteed

detection filter design for lpv systems a geometric approach this paper investigates fault detection and isolation of linear parameter varying lpv systems by using parameter varying c a invariant subspace and parameter varying unobservability subspaces the so called detection filter approach formulated as the fundamental problem of residual generation fprg for linear time invariant lti systems is extended for a class of lpv systems the question of stability is addressed in the terms of lyapunov quadratic stability by using linear matrix inequalities the results are applied to the model of a generic small commercial aircraft

global observability and detectability analysis of uncertain reaction systems and observer design observation issues are of fundamental importance for reaction systems due to the limited availability of on line sensors and the uncertainties related to the mathematical model the objective of this work is to propose a methodology to make a global analysis of observability and detectability of such systems with a particular concern about the design of robust observers for this the uncertainties of the reaction system are modelled as arbitrary unknown inputs these results include and generalize the standard asymptotic observers well known in the biotechnology moreover the observability properties required for the existence of such observers and for the assignability of their convergence dynamics are clarified

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

conditioned invariant and locally conditioned invariant distributions abstract we define the concepts of conditioned invariant and locally conditioned invariant distributions for nonlinear system and show how they can be used to solve the problem of tracking an output signal of a nonlinear system in spite of unknown disturbances

fault reconstruction for takagi sugeno fuzzy systems via learning observers abstractthis paper addresses the problem of observer based fault reconstruction for takagi sugeno fuzzy systems two types of fuzzy learning observers are constructed to achieve simultaneous reconstruction of system states and actuator faults stability and convergence of the proposed observers are proved using lyapunov stability theory and necessary conditions for the existence of the observers are further discussed the design of fuzzy learning observers can be formulated in terms of a series of linear matrix inequalities that can be conveniently solved using convex optimisation technique a single link flexible manipulator is employed to verify the effectiveness of the proposed fault reconstructing approaches

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

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

on the origin of a trace inequality numerous authors are apparently unaware that bounds on the trace of a matrix product presented in 1995 were originally published in 1990

nonlinear system fault diagnosis based on adaptive estimation an approach to fault diagnosis for a class of nonlinear systems is proposed in this paper it is based on a new adaptive estimation algorithm for recursive estimation of the parameters related to faults this algorithm is designed in a constructive manner through a nontrivial combination of a high gain observer and a recently developed linear adaptive observer without resort to any linearization its global exponential convergence is ensured by an easy to check persistent excitation condition a numerical example is presented for illustration

mobius functions and semigroup representation theory ii character formulas and multiplicities abstract we generalize the character formulas for multiplicities of irreducible constituents from group theory to semigroup theory using rota s theory of mobius inversion the technique works for a large class of semigroups including inverse semigroups semigroups with commuting idempotents idempotent semigroups and semigroups with basic algebras using these tools we are able to give a complete description of the spectra of random walks on finite semigroups admitting a faithful representation by upper triangular matrices over the complex numbers these include the random walks on chambers of hyperplane arrangements studied by bidigare hanlon rockmore brown and diaconis applications are also given to decomposing tensor powers and exterior products of rook matrix representations of inverse semigroups generalizing and simplifying earlier results of solomon for the rook monoid

observer based residual generation for fault diagnosis for non affine non linear polynomial systems this paper proposes an observer based residual generator obrg for diagnosing faults in a continuous non affine system with polynomial non linearities up to any finite degree where the fault and an unknown input affect both the system and part of the output firstly given certain assumptions and the use of defined extended vectors a parameterized polynomial system is considerred for which a compact set of sufficient conditions is given for the existence of a candidate obrg conditions for error stability by a lyapunov method and detectability are given the calculation steps in the design of the obrg are shown to involve the solution of three linear equations with parameterizations and the calculation of a set of constant matrices for detectability of faults a result is then given establishing that the design holds for a much wider class of systems the residual design is applied to a real three tank system

numerical quadratures for layer potentials over curved domains in r 3 numerical quadratures for calculating simple and double layer potentials over curved domains in mathbb r 3 are given more generally these numerical quadratures are shown to be useful for evaluating surface integral involving kernels which are pseudohomogeneous of degree 1 in addition to potential flow problems such kernels are encountered when dealing with helmholtz problem stokes flow problems or linear elasticity problems

a graph theoretic approach to fault detection and isolation for structured bilinear systems in this paper using a graph theoretic approach we address some issues related to the fault detection and isolation for structured bilinear systems considering a structured bilinear system submitted to faults and disturbances we give necessary and sufficient conditions to the solvability of the so called bilinear fundamental problem of residual generation we also treat the cases where the system is submitted to multiple failures occurring simultaneously or only one at a time one of the main advantages of the proposed analysis tool is that all the given conditions are easy to check because they deal with finding paths in a digraph this makes our approach well suited to studying large scale systems

a fault detection approach for nonlinear systems based on data driven realizations of fuzzy kernel representations this paper is devoted to the data driven fault detection of nonlinear systems for our purpose the definition of takagi sugeno fuzzy data driven forms of kernel representations for nonlinear systems is introduced first which builds the basis of our work the major contributions consist of two parts in the first part a data driven method for fuzzy process modeling is proposed and associated with it some modeling issues are addressed with the aid of the so called randomized algorithm technique in the probabilistic framework it is followed by a data driven realization of fuzzy kernel representation and its implementation in the fault detection system design to link the data driven methods to the well established observer based fault detection approaches the recursive form of the fuzzy kernel representation is proposed in the second part the fuzzy observer based fault detection design scheme is investigated based on the recursive fuzzy kernel representation the main results of our study are illustrated by an experimental study on the laboratory setup of a three tank system

a geometric approach to nonlinear fault detection and isolation we present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems a necessary condition for the problem to be solvable is derived in terms of an unobservability distribution which is computable by means of suitable algorithms the existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an observable quotient subsystem unaffected by all fault signals but one for this subsystem a fault detection filter is designed

a game theoretic fault detection filter the fault detection process is approximated with a disturbance attenuation problem the solution to this problem for both linear time varying and time invariant systems leads to a game theoretic filter which bounds the transmission of all exogenous signals except the fault to be detected in the limit when the disturbance attenuation bound is brought to zero a complete transmission block is achieved by embedding the nuisance inputs into an unobservable invariant subspace since this is the same invariant subspace structure seen in some types of detection filters we can claim that the asymptotic game filter is itself a detection filter one can also make use of this subspace structure to reduce the order of the limiting game theoretic filter by factoring this invariant subspace out of the state space the resulting lower dimensional filter will then be sensitive only to the failure to be detected a pair of examples given at the end of the paper demonstrate the effectiveness of the filter for time invariant and time varying problems in both full order and reduced order forms

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

a decomposition of multidimensional point sets with applications to k nearest neighbors and n body potential fields we define the notion of a well separated pair decomposition of points in d dimensional space we then develop efficient sequential and parallel algorithms for computing such a decomposition we apply the resulting decomposition to the efficient computation of k nearest neighbors and n body potential fields

fault detection schemes for continuous time stochastic dynamical systems in this paper the fault detection fd task in stochastic continuous time dynamical systems is addressed a new family of fd approaches is presented which is based on the application of hypothesis testing on continuous time estimators the given fd schemes are widely analyzed in the framework of their characteristics such as fault detectability false alarms and missed detection a collection of sufficient detectability conditions are given for a class of faults referred here as generic characterizing the faults which can be detected with certain formalized guarantee by the given fd schemes and providing also an upper bound for the detection time in a probabilistic sense the application and comparative performance of these fd approaches is illustrated for different faults in a simulation example

on the approximation of fault directions for mutual detectability an invariant zero approach this note is concerned with the approximation of fault directions in relation to mutual detectability in detection filter problems as an efficient system representation for analysis of detection order we utilize the observer canonical form by which we show that the invariant zero and the detection order can be analytically calculated by a set of polynomials associated with fault directions noting that this approach clearly shows the condition for the detection order to be plural we propose a fault direction approximation method which increases its detection order for obtaining a mutually detectable system regarding the resulting degradation of fault isolation performance as a disturbance we present its quantitative analysis and propose a method of selecting a threshold in order to guarantee proper fault isolation

ℋ ℋ fault detection filter for a class of nonlinear descriptor systems this article addresses the problem of designing a robust fault detection filter rfdf for a class of nonlinear descriptor systems whose nonlinear term is globally lipschitz and linear term is described by a linear parameter varying form the effect of perturbations on the residuals is minimised using the norm while the sensitivity performance is guaranteed using the index thanks to a particular lyapunov function which depends on the faults and the filter design problem is formulated as a convex optimisation problem solved via linear matrix inequality techniques performances of the proposed filter are shown through the application of an activated sludge process model

efficient automatic quadrature in 3 d galerkin bem we present cubature methods approximating the surface integrals arising by galerkin discretization of boundary integral equations on surfaces in r3 this numerical integrator does not depend on the explicit form of the kernel function the trial and test space or the surface parametrization thus it is possible to generate the system matrix for a broad class of integral equations just by replacing the sub routine for evaluating the kernel function we will present formulae to determine the minimal order of the cubature methods for a required accuracy emphasis is laid on numerical experiments confirming the theoretical results

parameterization of nonlinear observer based fault detection systems this note addresses parameterization issues of nonlinear observer based fault detection fd systems which are composed of a residual generator a residual evaluator and a threshold our study consists of two steps in the first step with the aid of nonlinear factorization and input output operator techniques we prove that any stable residual generator can be parameterized by a cascade connection of the process kernel representation and a post filter that represents the parameter system in the second step based on the state space representation of the parameterized residual generators we investigate the so called mathcal l infty and mathcal l 2 classes of observer based fd systems this leads to the parameterization of the threshold settings for both classes of fd systems and associated with them to the characterization of the existence conditions

weighted fuzzy observer based fault detection approach for discrete time nonlinear systems via piecewise fuzzy lyapunov functions the main focus of this paper is on the analysis and integrated design of mathcal l 2 observer based fault detection fd systems for discrete time nonlinear industrial processes to gain a deeper insight into this fd framework the existence condition is introduced first then an integrated design of mathcal l 2 observer based fd approach is realized by solving the proposed existence condition with the aid of takagi sugeno fuzzy dynamic modeling technique and piecewise fuzzy lyapunov functions most importantly a weighted piecewise fuzzy observer based residual generator is proposed aiming at achieving an optimal integration of residual evaluation and threshold computation into fd systems the core of this approach is to make use of the knowledge provided by fuzzy models of each local region and then to weight the local residual signal by means of different weighting factors in comparison with the standard norm based fuzzy observer based fd methods the proposed scheme may lead to a significant improvement of the fd performance in the end the effectiveness of the proposed method is verified by a numerical example and a case study on the laboratory setup of continuous stirred tank heater plant

observability and observers for nonlinear systems this paper deals with observability and observers for general nonlinear systems in the non control affine case we characterize systems that are observable independently of the inputs an exponential observer for these systems is also exhibited

technical communique an observation algorithm for nonlinear systems with unknown inputs this paper deals with the design of unknown input observers for nonlinear systems an algorithm which determines if the state and the unknown input of the system can be recovered in finite time is introduced this algorithm leads to the transformation of the system into an extended block triangular observable form suitable for the design of finite time observers the proposed method is useful to relax some restrictive conditions of the existing nonlinear unknown input observer design procedures

a characterization of finite ei categories with hereditary category algebras abstract in this paper we give an explicit algorithm to construct the ordinary quiver of a finite ei category for which the endomorphism groups of all objects have orders invertible in the field k we classify all finite ei categories with hereditary category algebras characterizing them as free ei categories in a sense which we define for which all endomorphism groups of objects have invertible orders some applications on the representation types of finite ei categories are derived

fault detection observers for continuous non linear polynomial systems of general degree this paper proposes a robust fault detection observer rfdo for a continuous non linear system with polynomial non linearities up to any finite degree the observer error and residual are robust with respect to unknown inputs sufficient conditions are given in an efficient algebraic compact form for a rfdo observer and residual to exist useable results on detectablility conditions are proved numerical prodedures for the design of a rfdo and a sub optimal rfdo sorfdo are given the theory is illustrated with an application to a benchmark three tank system one linear and three non linear models are considered with corresponding rdfos including a sub optimal rfdo and the performances of the corresponding residuals are compared under two initial conditions for a scenario consisting of a leak fault and a disturbance

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature

the rapid evaluation of volume integrals of potential theory on general regions abstract we present a new method for the rapid high order accurate evaluation of certain volume integrals in potential theory on general irregular regions the kernels of the integrals are either a fundamental solution or a linear combination of the derivatives of a fundamental solution of a second order linear elliptic differential equation instead of using a standard quadrature formula or the exact evaluation of any integral the methods rely on rapid methods of solving the differential equation which the kernel is the solution of therefore the number of operations needed to evaluate the volume integral is essentially equal to the number of operations needed to solve the differential equation on a rectangular region with a regular grid and the method requires no evaluation of the kernel