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

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

classical refined and component wise analysis of reinforced shell structures this paper compares early and very recent approaches to the static analysis of reinforced shell wing structures early approaches were those based on the pure semimonocoque theory along with the beam assumptions of the euler bernoulli and timoshenko type the recent approaches are based on a hierarchical one dimensional formulation these are obtained by adopting various polynomial expansions of the displacement field above the cross section of the structure according to the unified formulation which was recently proposed by the first author two classes were developed in the unified formulation framework in the first class taylor expansion models were developed by exploiting n order taylor like polynomials classical beam theories euler bernoulli and timoshenko were obtained as special cases of taylor expansion in the second class lagrange expansion models were built by means of four and nine point lagrange type polynomials over the cross section of the wing the component wise approach was obtai

the unified structure of unbiased minimum variance reduced order filters a unified two stage functional filter utsff is proposed serving as a unified structure of unbiased minimum variance reduced order filters for linear time varying discrete time systems the utsff includes two parts one is for the main functional estimate which defines the main computing structure of the filter and the other is for the complementary functional estimate which is added to the former in order to further enhance the filtering performance the relationships between the utsff and existing reduced order filters are explored through the utsff a general procedure for applying a suitable unbiased minimum variance reduced order filter is given simulation examples are also given to illustrate the proposed results

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

kalman filtering and riccati equations for descriptor systems a general formulation of a discrete time filtering problem for descriptor systems is considered it is shown that the nature of descriptor systems leads directly to the need to examine singular estimation problems using a dual approach to estimation the authors derive a so called 3 block form for the optimal filter and a corresponding 3 block riccati equation for a general class of time varying descriptor models which need not represent a well posed system in that the dynamics may be either over or under constrained specializing in the time invariant case they examine the asymptotic properties of the 3 block filter and in particular analyze in detail the resulting 3 block algebraic riccati equation the noncausal nature of discrete time descriptor dynamics implies that future dynamics may provide some information about the present state a modified form for the descriptor kalman filter that takes this information into account is presented

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

optimal filtering in stochastic discrete time systems with unknown inputs in this note we derive a recursive filtering algorithm for the linear discrete time dynamic system with indeterminate stochastic inputs the algorithm is based on the minimax optimal method of parameter estimation in the linear regression model with parameters of two different types unknown and stochastic with partially known characteristics

accurate response of wing structures to free vibration load factors and nonstructural masses based on the carrera unified formulation this work extends variable kinematic finite beam elements to include load factors and nonstructural masses for the static and vibration analyses of complex metallic wing structures according to the carrera unified formulation variable kinematic beam theories are formulated in an automatic and hierarchical manner by expressing the displacement field as an arbitrary expansion through generic cross sectional functions both taylor like and lagrange polynomials are used in this paper to develop refined beam kinematics and the related theories are referred to as taylor expansion and lagrange expansion respectively the generalized unknowns of taylor expansion models are the beam axis displacements and the n order displacement derivatives with n being a free parameter of the analysis classical beam theories are clearly particular cases of the linear n 1 taylor expansion model on the other hand lagrange expansion models have only pure translational displacemen

free vibration analysis of civil engineering structures by component wise models abstract higher order beam models are used in this paper to carry out free vibration analysis of civil engineering structures refined kinematic fields are developed using the carrera unified formulation cuf which allows for the implementation of any order theory without the need for ad hoc formulations the principle of virtual displacements in conjunction with the finite element method fem is used to formulate stiffness and mass matrices in terms of fundamental nuclei the nuclei depend neither on the adopted class of beam theory nor on the fem approximation along the beam axis this paper focuses on a particular class of cuf models that makes use of lagrange polynomials to discretize cross sectional displacement variables this class of models are referred to as component wise cw in recent works according to the cw approach each structural component e g columns walls frame members and floors can be modeled by means of the same 1d formulation a number of typical civil engineering structures e g simple beams arches truss structures and complete industrial and civil buildings are analyzed and cw results are compared to classical beam theories euler bernoulli and timoshenko refined beam models based on taylor like expansions of the displacements on the cross section and classical solid shell fem solutions from the commercial code msc nastran the results highlight the enhanced capabilities of the proposed formulation it is in fact demonstrated that cw models are able to replicate 3d solid results with very low computational efforts

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

optimal solution of the two stage kalman estimator the two stage kalman estimator was originally proposed to reduce the computational complexity of the augmented state kalman filter it was also applied to the tracking of maneuvering targets by treating the target acceleration as a bias term except in certain restrictive conditions the conventional two stage estimators are suboptimal in the sense that they are not equivalent to the augmented state filter in this paper the authors propose a new two stage kalman estimator i e new structure which is an extension of friedland s estimator and is optimal in general conditions in addition we provide some analytic results to demonstrate the computational advantages of two stage estimators over augmented ones

optimal filtering for systems with unknown inputs an optimal filtering formula is derived for linear time varying discrete systems with unknown inputs by making use of the well known innovations filtering technique the derivation is an extension of a new observer design method for time invariant deterministic systems with unknown inputs the systems under consideration have the most general form the derived optimal filter has a similar form to the standard kalman filter with some modified covariance and gain matrices

extension of mitc to higher order beam models and shear locking analysis for compact thin walled and composite structures summary a class of mixed interpolated beam elements is introduced in this paper under the framework of the carrera unified formulation cuf to eliminate the detrimental effects due to shear locking the mixed interpolation of tensorial components mitc method is adopted to generate locking free displacement based beam models using general 1d finite elements an assumed distribution of the transverse shear strains is employed for the derivation of the virtual work and the full gauss legendre quadrature is used for the numerical computation of all the components of the stiffness matrix linear quadratic and cubic beam elements are developed using the unified formulation and applied to linear static problems including compact laminated and thin walled structures a comprehensive study of how shear locking affects general beam elements when different classical integration schemes are employed is presented evidencing the outstanding capabilities of the mitc method to overcome this numerical issue refined beam theories based on the expansion of pure and generalized displacement variables are implemented making use of lagrange and legendre polynomials over the cross sectional domain allowing one to capture complex states of stress with a 3d like accuracy the numerical examples are compared to analytic numerical solutions from the literature and commercial software solutions whenever it is possible the efficiency and robustness of the proposed method is demonstrated throughout all the assessments illustrating that mitc elements are the natural choice to avoid shear locking and showing an unprecedent accuracy in the computation of transverse shear stresses for beam formulations this article is protected by copyright all rights reserved

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

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

superspecies and their representations abstract superspecies are introduced to provide a construction of all finite dimensional superalgebras all acyclic superspecies are classified according to their graded representation types

modular quantizations of lie algebras of cartan type k via drinfeld twists of jordanian type we construct explicit drinfel d twists of jordanian type for the generalized cartan type k lie algebras in characteristic 0 and obtain the corresponding quantizations especially their integral forms by making modular reductions including modulo p and modulo p restrictedness reduction and base changes we derive certain modular quantizations of the restricted universal enveloping algebra u k 2n 1 1 for the restricted simple lie algebra of cartan type k in characteristic p they are new families of noncommutative and noncocommutative hopf algebras of dimension pp2n 1 1 if 2n 4 0 modp or pp2n 1 if 2n 4 0 modp over a truncated p polynomials ring which also contain the well known radford algebras see 20 as hopf subalgebras some open questions are proposed

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

cohomology of lie superalgebras and their generalizations the cohomology groups of lie superalgebras and more generally of e lie algebras are introduced and investigated the main emphasis is on the case where the module of coefficients is nontrivial two general propositions are proved which help to calculate the cohomology groups several examples are included to show the peculiarities of the super case for l sl 1 2 the cohomology groups h1 l v and h2 l v with v a finite dimensional simple graded l module are determined and the result is used to show that h2 l u l with u l the enveloping algebra of l is trivial this implies that the superalgebra u l does not admit any nontrivial formal deformations in the sense of gerstenhaber garland s theory of universal central extensions of lie algebras is generalized to the case of e lie algebras

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

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

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

state observers for discrete time linear systems with unknown inputs in the paper the problem of designing a full order state observer for a general discrete time linear system with unknown inputs is analyzed necessary and sufficient conditions for the existence either of an asymptotic or of a deadbeat observer are provided and a constructive design procedure together with some examples are discussed finally the equivalence of these conditions for problem solvability with those derived in previous contributions by means of different approaches is explicitly proved

kalman filtering for general discrete time linear systems recursive state estimation problems for explicit and implicit time invariant linear systems both for systems with and without unknown inputs can be formulated as a single problem usually referred to as descriptor kalman filtering solutions to this problem have been proposed in the literature however these solutions either neglect possible contributions of future dynamics to the current estimate or make unnecessary assumptions on the structure of the system in this paper the authors propose a solution to this problem which leads to a constructive method lifting these unnecessary assumptions this method uses a generalization of the shuffle algorithm

refined one dimensional formulations for laminated structure analysis this paper proposes one dimensional formulations based on hierarchical expansions of the unknown displacement variables for the analysis of multilayered structures made of anisotropic composite layers the hierarchical technique shows variable kinematic properties and it is based on the carrera unified formulation two different classes of refined theories are proposed the first expands the unknown variables in terms of power polynomials of the cross sectional coordinates it consists of a taylor like expansion the second class of onedimensional theories uses lagrange polynomials lagrange expansion and subdomain discretizations of the cross section and it leads to only pure displacements as the unknown variables taylor like expansion is used to develop equivalent single layer formulations and lagrange expansion is used to construct both equivalent single layer and layerwise descriptions the finite element method is employed to develop numerical applications using the carrera unified formulation finite element matrices are obtained in terms of a few fundamental nuclei that are formally independent of all the considered one dimensional formulations a number of numerical examples are given concerning on beams plates and more complex structures comparisons with results from plate and solid models are provided the following has been concluded 1 the proposed formulation represents a reliable compact and accurate method to develop refined one dimensional models 2 the present one dimensional models are very effective at detecting both global and local responses of composite structures 3 shell and solidlike results are obtained with a significant reduction in the computational costs

some remarks on quantized lie superalgebras of classical type abstract in this paper we use the etingof kazhdan quantization of lie bi superalgebras to investigate some interesting questions related to drinfeld jimbo type superalgebra associated to a lie superalgebra of classical type it has been shown that the d j type superalgebra associated to a lie superalgebra of type a g with the distinguished cartan matrix is isomorphic to the e k quantization of the lie superalgebra the first main result in the present paper is to extend this to arbitrary cartan matrices this paper also contains two other main results 1 a theorem stating that all highest weight modules of a lie superalgebra of type a g can be deformed to modules over the corresponding d j type superalgebra and 2 a super version of the drinfeld kohno theorem

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

h infinity kalman estimation for rectangular descriptor systems with unknown inputs this note considers h filtering and prediction for rectangular descriptor systems with unknown inputs that affect both the system and the output an optimal h descriptor kalman estimator hdke which can simultaneously solve the h filtering and prediction problems for rectangular descriptor systems with unknown inputs is developed based on the maximum likelihood descriptor kalman filtering method the hdke serves as a unified solution to solve h and kalman filtering for descriptor systems and standard systems with or without unknown inputs to reduce the computational complexity problem some efficient alternatives to the developed hdke are further proposed the relationship between the hdke and the existing literature results is also addressed an illustrative example is given to show the usefulness of the proposed results

technical communique unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough this paper extends previous work on joint input and state estimation to systems with direct feedthrough of the unknown input to the output using linear minimum variance unbiased estimation a recursive filter is derived where the estimation of the state and the input are interconnected the derivation is based on the assumption that no prior knowledge about the dynamical evolution of the unknown input is available the resulting filter has the structure of the kalman filter except that the true value of the input is replaced by an optimal estimate

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

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

etingof kazhdan quantization of lie superbialgebras abstract for every semi simple lie algebra g one can construct the drinfeld jimbo algebra u h dj g this algebra is a deformation hopf algebra defined by generators and relations to study the representation theory of u h dj g drinfeld used the kz equations to construct a quasi hopf algebra a g he proved that particular categories of modules over the algebras u h dj g and a g are tensor equivalent analogous constructions of the algebras u h dj g and a g exist in the case when g is a lie superalgebra of type a g however drinfeld s proof of the above equivalence of categories does not generalize to lie superalgebras in this paper we will discuss an alternate proof for lie superalgebras of type a g our proof utilizes the etingof kazhdan quantization of lie super bialgebras it should be mentioned that the above equivalence is very useful for example it has been used in knot theory to relate quantum group invariants and the kontsevich integral

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