state estimation with partially observed inputs a unified kalman filtering approach for linear stochastic time varying state space models with gaussian noises this paper investigates state estimation for the scenario where the input variables of the state equation are not fully observed but rather the input data are available only at an aggregate level unlike the existing filters for unknown inputs that are based on the approach of minimum variance unbiased estimation this paper does not impose the unbiasedness condition for state estimation instead it incorporates a bayesian approach to derive a modified kalman filter by pooling the prior knowledge about the state vector at the aggregate level with the measurements on the output variables at the original level of interest the estimated state vector is shown to be a minimum mean square error estimator the developed filter provides a unified approach to state estimation it includes the existing filters obtained under two extreme scenarios as its special cases i e the classical kalman filter where all the inputs are observed and the filter for unknown inputs

exact 3d boundary representation in finite element analysis based on cartesian grids independent of the geometry summary this paper proposes a novel immersed boundary method where the embedded domain is exactly described by using its computer aided design cad boundary representation with non uniform rational b splines nurbs or t splines the common feature with other immersed methods is that the current approach substantially reduces the burden of mesh generation in contrast the exact boundary representation of the embedded domain allows to overcome the major drawback of existing immersed methods that is the inaccurate representation of the physical domain a novel approach to perform the numerical integration in the region of the cut elements that is internal to the physical domain is presented and its accuracy and performance evaluated using numerical tests the applicability performance and optimal convergence of the proposed methodology is assessed by using numerical examples in three dimensions it is also shown that the accuracy of the proposed methodology is independent on the cad technology used to describe the geometry of the embedded domain copyright 2015 john wiley sons ltd

inexact schwarz algebraic multigrid preconditioners for crack problems modeled by extended finite element methods summary traditional algebraic multigrid amg preconditioners are not well suited for crack problems modeled by extended finite element methods xfem this is mainly because of the unique xfem formulations which embed discontinuous fields in the linear system by addition of special degrees of freedom these degrees of freedom are not properly handled by the amg coarsening process and lead to slow convergence in this paper we proposed a simple domain decomposition approach that retains the amg advantages on well behaved domains by avoiding the coarsening of enriched degrees of freedom the idea was to employ a multiplicative schwarz preconditioner where the physical domain was partitioned into healthy or unfractured and cracked subdomains first the healthy subdomain containing only standard degrees of freedom was solved approximately by one amg v cycle followed by concurrent direct solves of cracked subdomains this strategy alleviated the need to redesign special amg coarsening strategies that can handle xfem discretizations numerical examples on various crack problems clearly illustrated the superior performance of this approach over a brute force amg preconditioner applied to the linear system copyright 2011 john wiley sons ltd

a non gaussian kalman filter with application to the estimation of vehicular speed single inductive loop detectors ilds which provide online measurements of traffic volume and occupancy are widely used devices in road systems because of the nature of traffic flow fast estimation and forecasting of vehicular speed using the data collected by an ild are crucial to online road traffic management here we formulate statistical inference for vehicular speed as a dynamic generalized linear model with a reciprocal inverse gaussian observational distribution the formulation motivates us to extend the gaussian kalman filter to this non gaussian scenario this results in a set of simple recursive formulas in which the current estimate of the parameter of interest is updated as a weighted harmonic average of the previous estimate and the current observation by applying the developed non gaussian kalman filter to analyze traffic data collected by an ild we provide a competitive alternative for estimating vehicular speed at a minimum computational cost

h_inf functional filtering for linear systems with unknown inputs a new method for the h1 functional filtering for systems with unknown inputs is presented first a functional filtering technique is presented then we show that the dynamic of the estimation error can be modeled in the descriptor system form this formulation makes it possible to describe the dynamic estimation error free of the derivative of the disturbances the filter parameters are obtained from the bounded real lemma of descriptor systems the developed approach unifies the design of functional reduced order and full order filters necessary and sufficient conditions for the solvability of the problem are obtained in terms of a set of bilinear matrix inequalities bmi under certain conditions these inequalities can be transformed to a set of linear matrix inequalities lmi two numerical examples are presented to illustrate the approach described in the paper the first example concerns the estimation of the state of charge soc of the the lithium ion battery and the second example highlights the reduced nature of the proposed functional filter

parity equations based unknown input reconstruction for mimo stochastic systems with an application in this paper an approach for reconstructing an unknown input for multiple input multiple output systems is presented it is assumed that the system is affected by process noise whereas the available system inputs are contaminated by measurement noise the novel approach is based on a parity equations concept and forms an extension of the idea developed previously by the authors a modification of the algorithm is also provided which allows the approach to deal with systems whose zero is close to unity the order of the parity space can be treated as a tuning parameter allowing for a trade off between the smoothness of the reconstructed unknown input and a phase lag an analytical solution of the overall problem is obtained by making use of a lagrange multiplier method the utility of the scheme is demonstrated when applied to a practical hydrological system

linear filtering for bilinear stochastic differential systems with unknown inputs investigates the problem of state estimation for bilinear stochastic multivariable differential systems in the presence of an additional disturbance whose statistics are completely unknown a linear filter is proposed based on a suitable decomposition of the state of the bilinear system into two components the first one is a computable function of the observations while the second component is estimated via a suitable linear filtering algorithm no a priori information on the disturbance is required for the filter implementation the proposed filter is robust with respect to the unknown input in that the covariance of the estimation error is not affected by such input numerical simulations show the effectiveness of the proposed filter

numerical analysis of interface hybrid difference methods for elliptic interface equations abstract we propose an extension of the hybrid difference method called the interface hybrid difference methods for solving elliptic interface equations the hybrid difference method is composed of two types of approximations one is the finite difference approximation of pdes within cells cell fd and the other is the intercell finite difference intercell fd on edges of cells the intercell finite difference is derived from continuity of normal fluxes for the interface problems a new intercell condition is introduced when the cell interface and the problem interface are coincident the domain is decomposed into cells so that each cell is contained exclusively in one of the subregions complete convergence analysis in the discrete energy norm is presented and numerical examples are provided to confirm the theoretical results

a preconditioner for substructuring based on constrained energy minimization a preconditioner for substructuring based on constrained energy minimization concepts is presented the preconditioner is applicable to both structured and unstructured meshes and offers a straightforward approach for the iterative solution of second and fourth order structural mechanics problems the approach involves constraints associated with disjoint sets of nodes on substructure boundaries these constraints provide the means for preconditioning at both the substructure and global levels numerical examples are presented that demonstrate the good performance of the method in terms of iterations compute time and condition numbers of the preconditioned equations

dual primal feti methods for three dimensional elliptic problems with heterogeneous coefficients in this paper certain iterative substructuring methods with lagrange multipliers are considered for elliptic problems in three dimensions the algorithms belong to the family of dual primal finite element tearing and interconnecting feti methods which recently have been introduced and analyzed successfully for elliptic problems in the plane the family of algorithms for three dimensions is extended and a full analysis is provided for the new algorithms particular attention is paid to finding algorithms with a small primal subspace since that subspace represents the only global part of the dual primal preconditioner it is shown that the condition numbers of several of the dual primal feti methods can be bounded polylogarithmically as a function of the dimension of the individual subregion problems and that the bounds are otherwise independent of the number of subdomains the mesh size and jumps in the coefficients these results closely parallel those of other successful iterative substructuring methods of primal as well as dual type

event based state estimation of linear dynamic systems with unknown exogenous inputs in this work an event based optimal state estimation problem for linear time varying systems with unknown inputs is investigated by treating the unknown input as a process with a non informative prior the event based minimum mean square error mmse estimator is obtained in a recursive form it is shown that for the general time varying case the closed loop matrix of the optimal event based estimator is exponentially stable and the estimation error covariance matrix is asymptotically bounded for each sample path of the event triggering process the results are also extended to the multiple sensor scenario where each sensor is allowed to have its own event triggering condition the efficiency of the proposed results is illustrated by a numerical example and comparative simulation with the mmse estimators obtained based on time triggered measurements the results are potentially applicable to event based secure state estimation of cyber physical systems

feti dp methods with an adaptive coarse space a coarse space is constructed for the dual primal finite element tearing and interconnecting feti dp domain decomposition method applied to highly heterogeneous problems by solving local generalized eigenvalue problems for certain problems with highly varying coefficients e g from multiscale simulations the coefficient jump will appear in the condition number bound even if standard techniques such as scaling and the weighting of constraints are used the feti dp theory is revisited and two central estimates are identified where the dependency on the coefficient contrast can enter the condition number bound the first is a poincare inequality and the second an extension theorem these estimates are replaced by local eigenvalue problems enriching the feti dp coarse space by a few numerically computed eigenvectors yields independence of the contrast of the coefficients even in challenging situations

brief extension of minimum variance estimation for systems with unknown inputs in this paper we address the problem of minimum variance estimation for discrete time time varying stochastic systems with unknown inputs the objective is to construct an optimal filter in the general case where the unknown inputs affect both the stochastic model and the outputs it extends the results of darouach and zasadzinski automatica 33 1997 717 where the unknown inputs are only present in the model the main difficulty in treating this problem lies in the fact that the estimation error is correlated with the systems noises this fact leads generally to suboptimal filters necessary and sufficient conditions for the unbiasedness of this filter are established then conditions under which the estimation error and the system noises are uncorrelated are presented and an optimal estimator and a predictor filters are derived sufficient conditions for the existence of these filters are given and sufficient conditions for their stability are obtained for the time invariant case a numerical example is given in order to illustrate the proposed method

riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices until recently it was believed that a necessary and sufficient condition for convergence of the riccati difference equation of optimal filtering was that the system be both delectable and stabilizable recently it has been shown that the stabilizability condition can be removed but convergence has only established under restrictive assumptions including the requirement that the state transition matrix be nonsingular the present paper generalizes these results in several directions first properties of the algebraic riccati equation are established for the case of singular state transition matrix second several assumptions previously imposed in establishing convergence of the riccati difference equation for systems with unreachable modes on the unit circle are relaxed including replacing observability by detectability weakening the conditions on the initial covariance and allowing the state transition matrix to be singular third results on the convergence and properties of the riccati equations are expressed as both necessary and sufficient conditions whereas previous results were only sufficient these extensions mean that the results have wider applicability including fixed lag smoothing problems and filtering for systems with time delays the implications of the results in the dual problem of optimal control are also studied

on existence optimality and asymptotic stability of the kalman filter with partially observed inputs for linear stochastic time varying systems we investigate the properties of the kalman filter with partially observed inputs we first establish the existence condition of a general linear filter when the unknown inputs are partially observed then we examine the optimality of the kalman filter with partially observed inputs finally on the basis of the established existence condition and optimality result we investigate asymptotic stability of the filter for the corresponding time invariant systems it is shown that the results on existence and asymptotic stability obtained in this paper provide a unified approach to accommodating a variety of filtering scenarios as its special cases including the classical kalman filter and state estimation with unknown inputs

estimation of systems with statistically constrained inputs abstract this paper discusses the estimation of a class of discrete time linear stochastic systems with statistically constrained unknown inputs ui which can represent an arbitrary combination of a class of un modeled dynamics random ui with unknown covariance matrix and deterministic ui in filter design an upper bound filter is explored to compute recursively and adaptively the upper bounds of covariance matrices of the state prediction error innovation and state estimate error furthermore the minimum upper bound filter mubf is obtained via online scalar parameter convex optimization in pursuit of the minimum upper bounds two examples a system with multiple piecewise uis and a continuous stirred tank reactor cstr are used to illustrate the proposed mubf scheme and verify its performance

brief paper unbiased minimum variance state estimation for linear systems with unknown input the problem of state estimation for a linear system with unknown input which affects both the system and the output is discussed in this paper a recursive optimal filter with global optimality in the sense of unbiased minimum variance over all linear unbiased estimators is provided the necessary and sufficient condition for the convergence and stability is also given which is milder than existing approaches

network coding capacity with a constrained number of coding nodes we study network coding capacity under a constraint on the total number of network nodes that can perform coding that is only a certain number of network nodes can produce coded outputs whereas the remaining nodes are limited to performing routing we prove that every nonnegative monotonically nondecreasing eventually constant rational valued function on the nonnegative integers is equal to the capacity as a function of the number of allowable coding nodes of some directed acyclic network

condition number analysis and preconditioning of the finite cell method the isogeometric finite cell method in which a domain is immersed in a structured background mesh suffers from conditioning problems when cells with small volume fractions occur in this contribution we establish a rigorous scaling relation between the condition number of i fcm system matrices and the smallest cell volume fraction ill conditioning stems either from basis functions being small on cells with small volume fractions or from basis functions being nearly linearly dependent on such cells based on these two sources of ill conditioning an algebraic preconditioning technique is developed which is referred to as symmetric incomplete permuted inverse cholesky sipic a detailed numerical investigation of the effectivity of the sipic preconditioner in improving i fcm condition numbers and in improving the convergence speed and accuracy of iterative solvers is presented for the poisson problem and for two and three dimensional problems in linear elasticity in which nitche s method is applied in either the normal or tangential direction the accuracy of the preconditioned iterative solver enables mesh convergence studies of the finite cell method

simultaneous input and state estimation for nonlinear systems with applications to flow field estimation this paper studies the problem of simultaneous input and state estimation sise for nonlinear dynamical systems with and without direct input output feedthrough we take a bayesian perspective to develop a sequential joint input and state estimation approach our scheme gives rise to a nonlinear maximum a posteriori optimization problem which we solve using the classical gauss newton method the proposed approach generalizes a number of sise methods presented in the literature we illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously

technical communique on the asymptotic stability of minimum variance unbiased input and state estimation in this note we investigate the asymptotic stability of the filter for minimum variance unbiased input and state estimation developed by gillijns and de moor sufficient conditions for the stability are proposed and proven with inspiration from the kalman filter stability analysis

extension of friedland s separate bias estimation to randomly time varying bias of nonlinear systems by extending b friedland s 1969 separate bias estimation algorithm for linear systems to nonlinear systems and combining the result with the suboptimal fading extended kalman filter proposed by d h zhou 1990 and by d h zhou et al a pseudo separate bias estimation algorithm for randomly time varying bias of a class of nonlinear time varying stochastic systems is obtained a simulation example is presented to illustrate the effectiveness of the algorithm

toward extremely scalable nonlinear domain decomposition methods for elliptic partial differential equations the solution of nonlinear problems e g in material science requires fast and highly scalable parallel solvers finite element tearing and interconnecting dual primal feti dp domain decomposition methods are parallel solution methods for implicit problems discretized by finite elements recently nonlinear versions of the well known feti dp methods for linear problems have been introduced in these methods the nonlinear problem is decomposed before linearization this approach can be viewed as a strategy to further localize computational work and to extend the parallel scalability of feti dp methods toward extreme scale supercomputers here a recent nonlinear feti dp method is combined with an approach that allows an inexact solution of the feti dp coarse problem we combine the nonlinear feti dp domain decomposition method with an algebraic multigrid amg method and thus obtain a hybrid nonlinear domain decomposition multigrid method we consider scalar nonlinear problems as well as nonlinear hyp

state estimation for descriptor systems via the unknown input filtering method this paper addresses the optimal unbiased minimum variance state estimation of descriptor systems in the framework of unknown input filtering it is shown that any descriptor system can be equivalently transformed into a standard state space system with unknown inputs the existing globally optimal state estimators can then be readily used to facilitate the optimal filter design this research highlights the relationship between descriptor state estimation and unknown input filtering for standard state space systems with unknown inputs a direct application to the state estimation of descriptor systems with unknown inputs via the proposed results is also addressed an illustrative example is given to show the novelty of the proposed results

technical communique reduced order kalman filter with unknown inputs this paper presents an optimal reduced order kalman filter for discrete time dynamic stochastic linear systems with unknown inputs the problem is to estimate a part of the state vector in the case where none of the observations are assumed to be noise free the proposed filter is obtained by minimizing the trace of the estimation error covariance matrix with respect to the remaining degrees of freedom after noninteresting state and unknown inputs decoupling the necessary and sufficient conditions for stability and convergence of the filter are established

brief paper unbiased minimum variance input and state estimation for linear discrete time systems this paper addresses the problem of simultaneously estimating the state and the input of a linear discrete time system a recursive filter optimal in the minimum variance unbiased sense is developed where the estimation of the state and the input are interconnected the input estimate is obtained from the innovation by least squares estimation and the state estimation problem is transformed into a standard kalman filtering problem necessary and sufficient conditions for the existence of the filter are given and relations to earlier results are discussed

framework for state and unknown input estimation of linear time varying systems the design of unknown input decoupled observers and filters requires the assumption of an existence condition in the literature this paper addresses an unknown input filtering problem where the existence condition is not satisfied instead of designing a traditional unknown input decoupled filter a double model adaptive estimation approach is extended to solve the unknown input filtering problem it is proved that the state and the unknown inputs can be estimated and decoupled using the extended double model adaptive estimation approach without satisfying the existence condition numerical examples are presented in which the performance of the proposed approach is compared to methods from literature

fluid structure partitioned procedures based on robin transmission conditions in this article we design new partitioned procedures for fluid structure interaction problems based on robin type transmission conditions the choice of the coefficient in the robin conditions is justified via simplified models the strategy is effective whenever an incompressible fluid interacts with a relatively thin membrane as in hemodynamics applications we analyze theoretically the new iterative procedures on a model problem which represents a simplified blood vessel system in particular the robin neumann scheme exhibits enhanced convergence properties with respect to the existing partitioned procedures the theoretical results are checked using numerical experimentation

a robust preconditioning technique for the extended finite element method the extended finite element method enhances the approximation properties of the finite element space by using additional enrichment functions but the resulting stiffness matrices can become ill conditioned in that case iterative solvers need a large number of iterations to obtain an acceptable solution in this paper a procedure is described to obtain stiffness matrices whose condition number is close to the one of the finite element matrices without any enrichments a domain decomposition is employed and the algorithm is very well suited for parallel computations the method was tested in numerical experiments to show its effectiveness the experiments have been conducted for structures containing cracks and material interfaces we show that the corresponding enrichments can result in arbitrarily ill conditioned matrices the method proposed here however provides well conditioned matrices and can be applied to any sort of enrichment the complexity of this approach and its relation to the domain decomposition is discussed computation times have been measured for a structure containing multiple cracks for this structure the computation times could be decreased by a factor of 2

insufficiency of linear coding in network information flow it is known that every solvable multicast network has a scalar linear solution over a sufficiently large finite field alphabet it is also known that this result does not generalize to arbitrary networks there are several examples in the literature of solvable networks with no scalar linear solution over any finite field however each example has a linear solution for some vector dimension greater than one it has been conjectured that every solvable network has a linear solution over some finite field alphabet and some vector dimension we provide a counterexample to this conjecture we also show that if a network has no linear solution over any finite field then it has no linear solution over any finite commutative ring with identity our counterexample network has no linear solution even in the more general algebraic context of modules which includes as special cases all finite rings and abelian groups furthermore we show that the network coding capacity of this network is strictly greater than the maximum linear coding capacity over any finite field exactly 10 greater so the network is not even asymptotically linearly solvable it follows that even for more general versions of linearity such as convolutional coding filter bank coding or linear time sharing the network has no linear solution

deadbeat unknown input state estimation and input reconstruction for linear discrete time systems abstract this paper considers discrete time input reconstruction and state estimation assuming that the system has no invariant zeros without assuming that the initial condition is known and without assuming that at least one markov parameter has full column rank algorithms based on the generalized inverse of a block toeplitz matrix are given for unknown input state estimation and simultaneous input reconstruction and state estimation in both cases the unknown input is an arbitrary signal both algorithms are deadbeat which means that exact input reconstruction and state estimation are achieved in a finite number of steps

simultaneous input and state estimation for stochastic nonlinear systems with additive unknown inputs abstract this paper investigates simultaneous input and state estimation for a class of nonlinear stochastic systems we propose a recursive filter to concurrently estimate system states and unknown inputs we show that the estimation errors of the proposed filter are practically exponentially stable in probability and the estimation error covariance matrices are uniformly bounded

a robust estimator for stochastic systems under unknown persistent excitation a robust estimator for uncertain stochastic systems under unknown persistent disturbance is presented the given discrete time stochastic formulation neither requires a known bound on the magnitude of the unknown excitation nor assumes stability of the system however the proposed estimator assumes certain structural conditions on system uncertainties though the proposed estimator is developed based on stochastic lyapunov analysis its structure and performance are comparable to that of unbiased minimum variance filters based on the disturbance decoupling technique unlike unbiased minimum variance filters implementation of the developed estimator only requires adding an auxiliary term to the nominal steady state kalman filter and it does not involve any similarity transformation or propagation of matrix difference equations

state estimation for stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels abstract this paper deals with robust state estimation problem for a class of stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels an unbiased unknown input insensitive filter is designed such that the variance of the estimation error is minimized in the sense of the so called p estimation the filter gain matrix is derived through solving a recursive riccati equation and a generalized lyapunov equation a necessary and sufficient condition that guarantees the existence of the filter is given which establishes a fundamental limit on the mean square capacity of each fading channel unknown input estimation and finite horizon stability of the proposed filter are also discussed to illustrate the effectiveness of the proposed approach the proposed algorithm is applied to a faulty remote controlled uninterruptible power system where both the state and the fault are estimated

cutfem discretizing geometry and partial differential equations we discuss recent advances on robust unfitted finite element methods on cut meshes these methods are designed to facilitate computations on complex geometries obtained for example from computer

a unified filter for simultaneous input and state estimation of linear discrete time stochastic systems in this paper we present a unified optimal and exponentially stable filter for linear discrete time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum variance sense without making any assumptions on the direct feedthrough matrix we also provide the connection between the stability of the estimator and a system property known as strong detectability and discuss the global optimality of the proposed filter finally an illustrative example is given to demonstrate the performance of the unified unbiased minimum variance filter

polynomial time algorithms for multicast network code construction the famous max flow min cut theorem states that a source node s can send information through a network v e to a sink node t at a rate determined by the min cut separating s and t recently it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to re encode the information they receive we demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed we give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity we extend these algorithms to integer capacities and to codes that are tolerant to edge failures

optimal filtering for systems with unknown inputs via the descriptor kalman filtering method this paper addresses globally optimal unbiased minimum variance state estimation for systems with unknown inputs that affect both the system and the output with the descriptor kalman filtering method it is shown that directly applying the conventional descriptor kalman filter dkf to the considered problem may not yield the globally optimal solution because the unknown input vector may not be estimable to remedy this problem three approaches are proposed to facilitate optimal filter design the transformed approach uses some input and output transformations the untrammeled approach does not require any transformations and the augmented approach reconstructs the unknown input dynamics then three 5 block forms of the extended dkf 5 block edkf are derived as globally optimal state estimators in the sense that the first two filters are equivalent to the recently developed extended recursive three step filter and the third is equivalent to the conventional augmented state kalman filter the relationship between the proposed edkfs and the existing results in the literature is addressed simulation results are given to illustrate the usefulness of the proposed filters

technical communique extension of unbiased minimum variance input and state estimation for systems with unknown inputs this paper extends the existing results on joint input and state estimation to systems with arbitrary unknown inputs the objective is to derive an optimal filter in the general case where not only unknown inputs affect both the system state and the output but also the direct feedthrough matrix has arbitrary rank the paper extends both the results of gillijns and de moor gillijns s de moor b 2007b unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough automatica 43 934 937 and darouach zasadzinski and boutayeb darouach m zasadzinski m boutayeb m 2003 extension of minimum variance estimation for systems with unknown inputs automatica 39 867 876 the resulting filter is an extension of the recursive three step filter ertsf and serves as a unified solution to the addressed unknown input filtering problem the relationship between the ertsf and the existing literature results is also addressed

information flow decomposition for network coding we propose a method to identify structural properties of multicast network configurations by decomposing networks into regions through which the same information flows this decomposition allows us to show that very different networks are equivalent from a coding point of view and offers a means to identify such equivalence classes it also allows us to divide the network coding problem into two almost independent tasks one of graph theory and the other of classical channel coding theory this approach to network coding enables us to derive the smallest code alphabet size sufficient to code any network configuration with two sources as a function of the number of receivers in the network but perhaps the most significant strength of our approach concerns future network coding practice namely we propose deterministic algorithms to specify the coding operations at network nodes without the knowledge of the overall network topology such decentralized designs facilitate the construction of codes that can easily accommodate future changes in the network e g addition of receivers and loss of links

unbiased minimum variance linear state estimation abstract a method is developed for linear estimation in the presence of unknown or highly non gaussian system inputs the state update is determined so that it is unaffected by the unknown inputs the filter may not be globally optimum in the mean square error sense however it performs well when the unknown inputs take extreme or unexpected values in many geophysical and environmental applications it is performance during these periods which counts the most the application of the filter is illustrated in the real time estimation of mean areal precipitation

delayed unknown input observers for discrete time linear systems with guaranteed performance abstract in this paper we propose a state and unknown input observer for discrete time linear systems with bounded unknown inputs and measurement disturbances the design procedure is formulated using a set of linear matrix inequalities and leverages delayed or fixed lag estimates the observer error states and or user defined performance outputs are guaranteed to operate at certain performance bounds furthermore by employing sufficiently large delays the observer is guaranteed to provide exact asymptotic state and input estimates for minimum phase systems we demonstrate via numerical examples that the proposed observer can be used for a wider class of systems than those satisfying matching conditions

robust and scalable domain decomposition solvers for unfitted finite element methods abstract unfitted finite element methods e g extended finite element techniques or the so called finite cell method have a great potential for large scale simulations since they avoid the generation of body fitted meshes and the use of graph partitioning techniques two main bottlenecks for problems with non trivial geometries however the linear systems that arise from these discretizations can be much more ill conditioned due to the so called small cut cell problem the state of the art approach is to rely on sparse direct methods which have quadratic complexity and are thus not well suited for large scale simulations in order to solve this situation in this work we investigate the use of domain decomposition preconditioners balancing domain decomposition by constraints for unfitted methods we observe that a straightforward application of these preconditioners to the unfitted case has a very poor behavior as a result we propose a customization of the classical bddc methods based on the stiffness weighting operator and an improved definition of the coarse degrees of freedom in the definition of the preconditioner these changes lead to a robust and algorithmically scalable solver able to deal with unfitted grids a complete set of complex 3d numerical experiments shows the good performance of the proposed preconditioners

pairwise intersession network coding on directed networks when there exists only a single multicast session in a directed acyclic cyclic network the existence of a network coding solution is characterized by the classic min cut max flow theorem for the case of more than one coexisting sessions network coding also demonstrates throughput improvement over noncoded solutions this paper proposes pairwise intersession network coding which allows for arbitrary directed networks but restricts the coding operations to being between two symbols for acyclic networks or between two strings of symbols for cyclic networks a graph theoretic characterization of pairwise intersession network coding is proven based on paths with controlled edge overlap this new characterization generalizes the edge disjoint path characterization of noncoded network communication and includes the well studied butterfly graph as a special case based on this new characterization various aspects of pairwise intersession network coding are studied including the sufficiency of linear codes the complexity of identifying coding opportunities its topological analysis and bandwidth and coding efficiency

kalman filter for discrete time stochastic linear systems subject to intermittent unknown inputs state estimation of stochastic discrete time linear systems subject to persistent unknown inputs has been widely studied but only few works have been dedicated to the case where unknown inputs may be simultaneously or sequentially active or inactive in this technical note a kalman filter approach is proposed for state estimation of systems with unknown intermittent inputs the design is based on the minimisation of the trace of the state estimation error covariance matrix under the constraint that the state estimation error is decoupled from the unknown inputs corrupting the system at the current time the necessary and sufficient stability conditions are established considering the upper bound of the prediction error covariance matrix

a quasi algebraic multigrid approach to fracture problems based on extended finite elements the modeling of discontinuities arising from fracture of materials poses a number of significant computational challenges the extended finite element method provides an attractive alternative to standard finite elements in that they do not require fine spatial resolution in the vicinity of discontinuities nor do they require repeated remeshing to properly address propagation of cracks they do however give rise to linear systems requiring special care within an iterative solver method an algebraic multigrid method is proposed that is suitable for the linear systems associated with modeling fracture via extended finite elements the new method follows naturally from an energy minimizing algebraic multigrid framework the key idea is the modification of the prolongator sparsity pattern to prevent interpolation across cracks this is accomplished by accessing the standard levelset functions used during the discretization process numerical experiments illustrate that the resulting method converges in a fashion that is relatively insensitive to mesh resolution and to the number of cracks or their location

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

on the equivalence between the unbiased minimum variance estimation and the infinity augmented kalman filter in this paper the augment kalman filter akf approach is discussed under the infinity condition it is proved that the akf in infinity condition is equivalent to the minimum variance unbiased mv

unbiased minimum variance estimation for systems with unknown exogenous inputs a new method is developed for the state estimation of linear discrete time stochastic systems in the presence of an unknown disturbance the filter obtained is optimal in the unbiased minimum variance sense the necessary and sufficient conditions for the existence and the stability of the filter are given

technical communique two stage kalman estimator with unknown exogenous inputs this paper presents a two stage estimator for bias and state filtering in discrete time stochastic linear systems affected by unknown inputs or disturbances we show that the state estimate can be expressed as x k k x k k b k kb k k where x k k is a bias free state estimate and b k k the optimal estimate of constant bias the proposed two stage estimator is based on an alternate derivation of the unbiased minimum variance estimator with unknown exogenous inputs developed by darouach and zasadzinski 1997 automatica 33 717 719

brief paper on the global optimality of unbiased minimum variance state estimation for systems with unknown inputs in this paper a globally optimal filtering framework is developed for unbiased minimum variance state estimation for systems with unknown inputs that affect both the system state and the output the resulting optimal filters are globally optimal within the unbiased minimum variance filtering over all linear unbiased estimators globally optimal state estimators with or without output and or input transformations are derived through the global optimality evaluation of this research the performance degradation of the filter proposed by darouach zasadzinski and boutayeb darouach m zasadzinski m boutayeb m 2003 extension of minimum variance estimation for systems with unknown inputs automatica 39 867 876 is clearly illustrated and the global optimality of the filter proposed by gillijns and de moor gillijns s de moor b 2007b unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough automatica 43 934 937 is further verified the relationship with the existing literature results is addressed a unified approach to design a specific globally optimal state estimator that is based on the desired form of the distribution matrix from the unknown input to the output is also presented a simulation example is given to illustrate the proposed results

bddc and feti dp preconditioners with adaptive coarse spaces for three dimensional elliptic problems with oscillatory and high contrast coefficients abstract bddc and feti dp algorithms are developed for three dimensional elliptic problems with adaptively enriched coarse components it is known that these enriched components are necessary in the development of robust preconditioners to form the adaptive coarse components carefully designed generalized eigenvalue problems are introduced for each faces and edges and the coarse components are formed by using eigenvectors with their corresponding eigenvalues larger than a given tolerance t o l upper bounds for condition numbers of the preconditioned systems are shown to be c t o l with the constant c depending only on the maximum number of edges and faces per subdomain and the maximum number of subdomains sharing an edge numerical results are presented to test the robustness of the proposed approach

technical communique on the optimality of recursive unbiased state estimation with unknown inputs for system models with unknown inputs state estimates may be obtained using linear minimum variance unbiased estimation here a proof is presented showing that the optimal solution over the class of all linear unbiased estimates may be written in the form of a linear recursive filter thereby validating previous work in this area

unbiased minimum variance fault and state estimation for linear discrete time varying two dimensional systems the fault and state estimation problem is addressed for a class of linear discrete time varying two dimensional systems subject to state and measurement noises two estimators are proposed to compute the estimation of the system state and or fault recursively both of which are unbiased with minimum variance through formulating the estimation problem as the solvability problem of the corresponding matrix equations of estimator gains and system constraint the necessary and sufficient condition of the existence and the solution for the proposed estimators are given an example is used to demonstrate the effectiveness of the proposed estimators