the presentation and q deformation of special linear lie superalgebras it is shown that the naive serre presentation corresponding to the simplest cartan matrix of the special linear lie superalgebra sl m n yields for m n 2 a larger lie superalgebra s m n of which sl m n is a nontrivial quotient the missing relations are found and the q deformation of the universal enveloping algebra of sl m n is constructed some auxiliary results related to associative algebras and e lie algebras defined in terms of generators and relations are also included

brief paper estimation of the disturbance structure from data using semidefinite programming and optimal weighting designing a state estimator for a linear state space model requires knowledge of the characteristics of the disturbances entering the states and the measurements in odelson b j rajamani m r rawlings j b 2006 a new autocovariance least squares method for estimating noise covariances automatica 42 2 303 308 the correlations between the innovations data were used to form a least squares problem to determine the covariances for the disturbances in this paper we present new and simpler necessary and sufficient conditions for the uniqueness of the covariance estimates we also formulate the optimal weighting to be used in the least squares objective in the covariance estimation problem to ensure minimum variance in the estimates a modification to the above technique is then presented to estimate the number of independent stochastic disturbances affecting the states this minimum number of disturbances is usually unknown and must be determined from data a semidefinite optimization problem is solved to estimate the number of independent disturbances entering the system and their covariances

an online parameter estimator for quick convergence and time varying linear systems a recursive algorithm called 3 om is presented to estimate parameters and noise variances for discrete time linear stochastic systems the unprojected version of 3 om is globally convergent with probability 1 to minima of the asymptotic negative log likelihood function 3 om approximates the quick convergence attained by the optimal nonlinear filter used as a parameter estimator the state space form of 3 om permits application to time varying linear systems and to online tuning of a kalman filter

a convergent approximation of the continuous time optimal parameter estimator continuous time linear stochastic systems that are bilinear in the state and parameters are considered a specific approximation to the optimal nonlinear filter used as a recursive parameter estimator is derived by retaining third order moments and using a gaussian approximation for higher order moments with probability one the specific approximation is proved to converge to a minimum of the likelihood function the proof uses the ordinary differential equation technique and requires that the trajectories of the slow system be bounded on finite time intervals and that the fixed parameter fast system by asymptotically stable the fixed parameter fast system is proved to be asymptotically stable if the parameter update gain is small enough essentially the specific approximation is asympotically equivalent to the recursive prediction error method thus inheriting its asymptotic rate of convergence a numerical simulation for a simple example indicates that the specific approximation has better transient response than other commonly used convergent parameter estimators

some results on the controllability of planar variational inequalities abstract this note deals with the controllability of a class of planar complementarity dynamical systems which can also be viewed as planar evolution variational inequalities it is shown that the complementarity conditions influence the controllability of the system a lot

adaptive error covariances estimation methods for ensemble kalman filters this paper presents a computationally fast algorithm for estimating both the system and observation noise covariances of nonlinear dynamics that can be used in an ensemble kalman filtering framework the new method is a modification of belanger s recursive method to avoid an expensive computational cost in inverting error covariance matrices of product of innovation processes of different lags when the number of observations becomes large when we use only product of innovation processes up to one lag the computational cost is indeed comparable to a recently proposed method by berry sauer s however our method is more flexible since it allows for using information from product of innovation processes of more than one lag extensive numerical comparisons between the proposed method and both the original belanger s and berry sauer s schemes are shown in various examples ranging from low dimensional linear and nonlinear systems of sdes and 40 dimensional stochastically forced lorenz 96 model our numerical results suggest that the proposed scheme is as accurate as the original belanger s scheme on low dimensional problems and has a wider range of more accurate estimates compared to berry sauer s method on l 96 example

partially asymmetric exclusion process with open boundaries exclusive diffusion on a one dimensional lattice is studied in the model particles hop stochastically in both directions but with different rates at the ends of the lattice particles are injected and removed the exact stationary probability measure is represented in the form of a matrix product as a generalization of the solution given by derrida et al j phys a 26 1493 1993 for the fully asymmetric process the phase diagram of the current on the infinite lattice is obtained analytic expressions for the current in the different phases are derived the model is equivalent to an xxz heisenberg chain with a certain type of boundary terms the ground state of which corresponds to the stationary solution of the master equation

stability robustness of the continuous time lqg system under plant perturbation and noise uncertainty abstract in this paper the robustness of the continuous time lqg problem is studied the system to be controlled is described by the usual state space formulation that includes the structure of plant parameter perturbations and noise uncertainty a simple method is given to prove the saddle point inequality of the closed loop system performance to cope with noise uncertainty one sufficient condition which is applicable to general linear systems for system stability robustness under plant perturbation is presented

casimir elements of e lie algebras the classical framework for investigating the casimir elements of a lie algebra is generalized to the case of an e lie algebra l we construct the standard l module isomorphism of the e symmetric algebra of l onto its enveloping algebra and we introduce the harish chandra homomorphism in case the generators of l can be written in a canonical two index form we construct the associated standard sequence of casimir elements and derive a formula for their eigenvalues in an arbitrary highest weight module

exact solution of the totally asymmetric simple exclusion process shock profiles the microscopic structure of macroscopic shocks in the one dimensional totally asymmetric simple exclusion process is obtained exactly from the complete solution of the stationary state of a model system containing two types of particles first and second class this nonequilibrium steady state factorizes about any second class particle which implies factorization in the one component system about the random shock position it also exhibits several other interesting features including long range correlations in the limit of zero density of the second class particles the solution also shows that a finite number of second class particles in a uniform background of first class particles form a weakly bound state

optimal quadratic solution for the non gaussian finite horizon regulator problem in this paper the problem of the optimal quadratic regulator for non gaussian discrete time stochastic systems with a quadratic cost function is considered the main result here obtained is that such optimal control can be derived from the classical lqg solution by substituting the linear filtering part with a quadratic optimal filter numerical results show high performance of this method

lqg optimal control system design under plant perturbation and noise uncertainty a state space approach abstract in this paper the stochastic linear dynamic system with uncertain parametric perturbations and uncertain noise covariances is studied based on minimax theory and the bellman gronwall inequality a sufficient condition for robust stability is derived finally a robust lqg optimal control design technique is employed to treat this problem

continued fractions and the partially asymmetric exclusion process we note that a tridiagonal matrix representation of the algebra of the partially asymmetric exclusion process pasep lends itself to interpretation as the transfer matrix for weighted motzkin lattice paths a continued fraction j fraction representation of the lattice path generating function is particularly well suited to discussing the pasep for which the paths have height dependent weights we show that this not only allows a succinct derivation of the normalization and correlation lengths of the pasep but also reveals how finite dimensional representations of the pasep algebra valid only along special lines in the phase diagram relate to the general solution that requires an infinite dimensional representation

design of measurement difference autocovariance method for estimation of process and measurement noise covariances abstract the paper deals with the estimation of the process and measurement noise covariance matrices of a system described by the linear time varying state space model in particular the stress is laid on the correlation methods and a novel method the measurement difference autocovariance method is designed the proposed method is based on the statistical analysis of an augmented measurement prediction error leading to a system of linear matrix equations for the elements of the noise covariance matrices compared to other correlation methods the proposed method provides unbiased estimates even for a finite number of measurements the theoretical results are discussed and illustrated in a numerical example

invariant supersymmetric multilinear forms and the casimir elements of p type lie superalgebras the casimir elements of the p type lie superalgebras are investigated depending on the class of algebras under consideration either there do not exist any nontrivial casimir elements at all or else the casimir elements are highly degenerate basic to the investigation is a lemma about invariant supersymmetric multilinear forms on a finite dimensional module over a lie superalgebra some comments on the cartan subalgebras of a lie superalgebra are also included an appendix provides some information on multilinear algebra with e commuting scalars

noncausal minimax linear state estimation for systems with uncertain second order statistics this note considers the problem of minimax state estimation of the states of a linear time invariant system which is driven by and observed in the presence of noise processes with uncertain second order statistics when the process noise and observations are scalars the problem is shown to be equivalent to a scalar minimax estimation problem the existence of a minimax solution is thereby established and the minimax filter is shown to be a linear transformation of the minimax filter for the scalar problem

an estimator for uncertain output matrix systems a linear time invariant optimal estimator for uncertain output matrix systems is considered uncertainty of the output matrix is represented by a set of multiple parameters and the optimal estimator is introduced by minimizing the expected cost function of the estimation error when the number of measured variables is small the order of the optimal estimator does not depend on the number of models and meeting the computational demand becomes quite feasible

minimax robust deconvolution filters under stochastic parametric and noise uncertainties the author consider the design of robust deconvolution filters for linear discrete time systems with stochastic parameter and noise uncertainties it is assumed that some large but bounded uncertainties exist in the driving and measurement noise covariances as well as the second order statistics of stochastic parameters and initial conditions three kinds of minimax sensitivity criteria are used to develop the techniques to the synthesis of minimax deconvolution filters under uncertain linear stochastic systems their approach is based on saddle point theory and the sensitivity analysis of kalman filters the design algorithms give the recursive realization of the minimax deconvolution filters for the time varying uncertain systems under fairly general conditions for the time invariant uncertain case the existence and solutions of steady state deconvolution filters are further developed finally the utility of the minimax design approaches and the properties of the resulting minimax deconvolution filters are illustrated by a numerical example

a novel subspace identification approach with enforced causal models subspace identification methods sims for estimating state space models have been proven to be very useful and numerically efficient they exist in several variants but all have one feature in common as a first step a collection of high order arx models are estimated from vectorized input output data in order not to obtain biased estimates this step must include future outputs however all but one of the submodels include non causal input terms the coefficients of them will be correctly estimated to zero as more data become available they still include extra model parameters which give unnecessarily high variance and also cause bias for closed loop data in this paper a new model formulation is suggested that circumvents the problem within the framework the system matrices a b c d and markov parameters can be estimated separately it is demonstrated through analysis that the new methods generally give smaller variance in the estimate of the observability matrix and it is supported by simulation studies that this gives lower variance also of the system invariants such as the poles

on matrix product ground states for reaction diffusion models we discuss a new mechanism leading to a matrix product form for the stationary state of one dimensional stochastic models the corresponding algebra is quadratic and involves four different matrices for the example of a coagulation decoagulation model explicit four dimensional representations are given and exact expressions for various physical quantities are recovered we also find the general structure of n point correlation functions at the phase transition

state estimation with initial state uncertainty the problem of state estimation with initial state uncertainty is approached from a statistical decision theory point of view the initial state is regarded as deterministic and unknown it is only known that the initial state vector belongs to a specified parameter set the frequentist risk is considered as the performance measure and the minimax approach is adopted minimax estimators are derived for some important cases of unbounded parameter sets if the parameter set is bounded a method of finding estimators whose maximum risk is arbitrarily close to that of a minimax estimator is provided this method is illustrated with an example in which an estimator whose maximum risk is at most 3 larger than that of a minimax estimator is derived

exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

autocovariance based plant model mismatch estimation for linear model predictive control abstract in this paper we present autocovariance based estimation as a novel methodology for determining plant model mismatch for multiple input multiple output systems operating under model predictive control considering discrete time linear time invariant systems under reasonable assumptions we derive explicit expressions of the autocovariances of the system inputs and outputs as functions of the plant model mismatch we then formulate the mismatch estimation problem as a global optimization aimed at minimizing the discrepancy between the theoretical autocovariance estimates and the corresponding values computed from historical closed loop operating data practical considerations related to implementing these ideas are discussed and the results are illustrated with a chemical process case study

brief constrained linear state estimation a moving horizon approach this article considers moving horizon strategies for constrained linear state estimation additional information for estimating state variables from output measurements is often available in the form of inequality constraints on states noise and other variables formulating a linear state estimation problem with inequality constraints however prevents recursive solutions such as kalman filtering and consequently the estimation problem grows with time as more measurements become available to bound the problem size we explore moving horizon strategies for constrained linear state estimation in this work we discuss some practical and theoretical properties of moving horizon estimation we derive sufficient conditions for the stability of moving horizon state estimation with linear models subject to constraints on the estimate we also discuss smoothing strategies for moving horizon estimation our framework is solely deterministic

on minimax robustness a general approach and applications the minimax approach to the design of systems that are robust with respect to modeling uncertainties is studied using a game theoretic formulation in which the performance functional and the sets of modeling uncertainties and admissible design policies are arbitrary the existence and characterization of minimax robust solutions that form saddle points are discussed through various methods that take into account several common features of the games encountered in applications in particular it is shown that if the performance functional and the uncertainty set are convex then a certain type of regularity condition on the functional is sufficient to ensure that the optimal strategy for a least favorable element of the uncertainty set is minimax robust the efficacy of the methods proposed for a general game is tested in the problems of matched filtering wiener filtering quadratic detection and output energy filtering in which uncertainties in their respective signal and noise models are assumed to exist these problems are analyzed in a common hilbert space framework and they serve to point out the advantages and limitations of the proposed techniques

minimax quadratic filtering of uncertain linear stochastic systems with partial fourth order information a minimax filtering problem for a class of uncertain linear stochastic systems is studied uncertainties involving fourth order moments of the noise distribution and of the initial state are considered under the hypothesis that the second order statistics are known hence the linear filter is available the quadratic minimax filter is found moreover it is shown that the minimax filter gives a worst case error variance even less than the exact error variance of the linear filter numerical simulations show that this improvement is meaningful also in cases of great uncertainty regarding the higher order statistics

stochastic models on a ring and quadratic algebras the three species diffusion problem the stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations we consider only exclusion processes and restrict the type of algebras such that one has recurrence relations for traces of words of different lengths this is possible only if the rates satisfy certain compatibility conditions these conditions are derived and explicit representations of the generators of the quadratic algebras are given

cohomology theory and deformations of z2 graded lie algebras the algebraic cohomology and the spectral sequences for a z2 graded lie algebra are briefly reviewed the reducibility property of a strongly semisimple lie superalgebra is established the role of second and third cohomologies in the deformation of a lie superalgebra is discussed using spectral sequences the second cohomology of the full brs algebra is shown to be the ground field and the third cohomology being trivial implies that osp 1 2 is the only graded lie algebra obtained by deformation of the full brs algebra a similar analysis yields the superconformal algebra as a deformation of the super poincare algebra the superconformal algebra so derived contains so 4 1 as the even part ruling out the existence of negative curvature of a de sitter universe

a unifying theorem for three subspace system identification algorithms the aim of this paper is to indicate and explore the similarities between three different subspace algorithms for the identification of combined deterministic stochastic systems the similarities between these algorithms have been obscured due to different notations and backgrounds it is shown that all three algorithms are special cases of one unifying theorem the comparison also reveals that the three algorithms use exactly the same subspace to determine the order and the extended observability matrix but that the weighting matrix used to calculate a basis for the column space of the observability matrix is different in the three cases

graded tensor calculus we develop a graded tensor calculus corresponding to arbitrary abelian groups of degrees and arbitrary commutation factors the standard basic constructions and definitions like tensor products spaces of multilinear mappings contractions symmetrization symmetric algebra as well as the transpose adjoint and trace of a linear mapping are generalized to the graded case and a multitude of canonical isomorphisms is presented moreover the graded versions of the classical lie algebras are introduced and some of their basic properties are described

on autocovariance least squares method for noise covariance matrices estimation the technical note focuses on the estimation of the noise covariance matrices of the state space models stress is laid on the autocovariance least squares method providing unbiased estimates of the noise covariance matrices of linear systems in particular two topics are discussed first selection of the predictor gain as a key parameter of the method second generalization of the method for linear systems with a time varying measurement equation the theoretical results are illustrated in numerical examples

robust filtering and prediction for linear systems with uncertain dynamics a game theoretic approach we examine the existence and behavior of game theoretic solutions for robust linear filters and predictors our basic uncertainty class includes m th order time varying discrete time systems with uncertain dynamics uncertain initial state covariance and uncertain nonstationary input and observation noise covariance our results include recursive kalman filter predictor realizations for the resulting robust procedures our approach is based on saddle point theory we emphasize the notion of a least favorable prior distribution for the uncertain parameter values to obtain a worst case design technique in this paper we highlight the role such distributions with finite support play in these decision models in particular we demonstrate that in these decision models the least favorable prior distribution is always discrete

lqg controller synthesis with plant and noise spectral uncertainties in this paper we consider the problem of robust controller synthesis with plant and noise spectral uncertainties in lqg optimal systems we frame an algorithm for synthesizing the robust controller to minimize the least favourable cost functional j via specifying the weighting matrices q and r the wiener hopf technique in the lqg optimal system the saddle point theory and a property of the contractive operator are employed to solve this problem

laplace operators of infinite dimensional lie algebras and theta functions abstract until recently the generalized casimir operator constructed by kac kac v g 1974 funct anal appl 8 68 70 has been the only known element of the center of a completion of the enveloping algebra of a kac moody algebra it has been conjectured deodhar v v gabber o kac v g 1982 adv math 45 92 116 however that the image of the harish chandra homomorphism contains all theta functions defined on the interior of the complexified tits cone and hence separates the orbits of the weyl group developing the ideas of feigin and fuchs feigin b l fuchs d b 1983 dokl akad nauk sssr 269 1057 1060 i prove this conjecture another application of this method is the chevalley type restriction theorem for simple finite dimensional lie superalgebras

twisted hopf algebras ringel hall algebras and green s categories with an appendix by the referee abstract the concept and some basic properties of a twisted hopf algebra are introduced and investigated its unique difference from a hopf algebra is that the comultiplication a a a is an algebra homomorphism not for the componentwise multiplication on a a but for the twisted multiplication on a a given by lusztig s rule also it is proved that any object a in green s category has a twisted hopf algebra structure any morphism between objects is a twisted hopf algebra homomorphism the antipode s of a is self adjoint under the lusztig form on a and the green polynomials m a b t share a so called cyclic symmetry as examples the twisted ringel hall algebras ringel s twisted composition algebras lusztig s free algebras f and non degenerate algebras f the positive part u of the drinfeld jimbo quantized enveloping algebras u and rosso s quantum shuffle algebra t v all are twisted hopf algebras the antipode and its inverse for a twisted ringel hall are explicitly given and all primitive elements are determined

an efficient algorithm for estimating noise covariances in distributed systems we present an efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochasticdynamic systems such systems arise typically by discretizing distributed parameter systems and their size renders computational efficiency a major consideration our adaptive filtering algorithm is based on the ideas of belanger and is algebraically equivalent to his algorithm the earlier algorithm however has computational complexity proportional to p6 where p is the number of observations of the system state while the new algorithm has complexity proportional to only p3 furthermore our formulation of noise covariance estimation as a secondary filter analogous to state estimation as a primary filter suggests several generalizations of the earlier algorithm the performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction

a new autocovariance least squares method for estimating noise covariances industrial implementation of model based control methods such as model predictive control is often complicated by the lack of knowledge about the disturbances entering the system in this paper we present a new method constrained als to estimate the variances of the disturbances entering the process using routine operating data a variety of methods have been proposed to solve this problem of note we compare als to the classic approach presented in mehra 1970 on the identification of variances and adaptive kalman filtering ieee transactions on automatic control 15 12 175 184 this classic method and those based on it use a three step procedure to compute the covariances the method presented in this paper is a one step procedure which yields covariance estimates with lower variance on all examples tested the formulation used in this paper provides necessary and sufficient conditions for uniqueness of the estimated covariances previously not available in the literature we show that the estimated covariances are unbiased and converge to the true values with increasing sample size the proposed method also guarantees positive semidefinite covariance estimates by adding constraints to the als problem the resulting convex program can be solved efficiently

intrinsically optimal bayesian robust filtering when designing optimal filters it is often unrealistic to assume that the statistical model is known perfectly the issue is then to design a robust filter that is optimal relative to an uncertainty class of processes robust filter design has been treated from minimax best worst case performance and bayesian best average performance perspectives heretofore the bayesian approach has involved finding a model specific optimal filter one that is optimal for some model in the uncertainty class lifting this constraint we optimize over the full class from which the original optimal filters were obtained for instance over all linear filters by extending the original characteristics determining the filter such as the power spectral density to effective characteristics that apply across the uncertainty class we demonstrate for both linear and morphological filtering that an intrinsically optimal bayesian robust filter can be represented in the same form as the standard solution to the optimal filter except via the effective characteristics solutions for intrinsic bayesian robust filters are more transparent and intuitive than solutions for model specific filters and also less tedious because effective characteristics push through the spectral theory into the bayesian setting whereas solutions in the model specific case depend on grinding out the optimization

l_2 e fir filters for deterministic continuous time state space signal models in this paper a new l2 e performance criterion is introduced which is represented as a gain between the disturbance during the recent time interval and the current estimation error based on the l2 e performance criterion the l2 e finite impulse response fir filter leff is proposed for deterministic continuous time state space signal models without requiring the stochastic information such as variances and means the leff is designed to minimize the maximum value of the l2 e performance criterion together with prior constraints such as linearity unbiased property in the deterministic sense and fir structure simultaneously via simulation the leff is compared with other deterministic infinite impulse response iir filters such as the hinfin and l2 linfin filters

quantifying the objective cost of uncertainty in complex dynamical systems real world problems often involve complex systems that cannot be perfectly modeled or identified and many engineering applications aim to design operators that can perform reliably in the presence of such uncertainty in this paper we propose a novel bayesian framework for objective based uncertainty quantification uq which quantifies the uncertainty in a given system based on the expected increase of the operational cost that it induces this measure of uncertainty called mocu mean objective cost of uncertainty provides a practical way of quantifying the effect of various types of system uncertainties on the operation of interest furthermore the proposed uq framework provides a general mathematical basis for designing robust operators and it can be applied to diverse applications including robust filtering classification and control we demonstrate the utility and effectiveness of the proposed framework by applying it to the problem of robust structural intervention of gene regulatory networks an important application in translational genomics

minimax linear observers and regulators for stochastic systems with uncertain second order statistics the problem of minimax design of linear observers and regulators for linear time varying multivariable stochastic systems with uncertain models of their second order statistics is treated in this paper general classes of allowable covariance matrices and means of the process and observation noises and of the random initial condition are considered a game formulation of the problem is adopted and it is shown that the optimal filter for the least favorable set of covariances is minimax robust for each of the filtering situations analyzed conditions satisfied by the saddle point solutions are given and their utility for finding the worst case covariances is illustrated by way of several examples of uncertainty classes of practical interest

general results on the convergence of stochastic algorithms a deterministic approach is proposed for proving the convergence of stochastic algorithms of the most general form under necessary conditions on the input noise and reasonable conditions on the nonnecessarily continuous mean field emphasis is placed on the case where more than one stationary point exists we also use this approach to prove the convergence of a stochastic algorithm with markovian dynamics

the kalman bucy filter accuracy in the guaranteed parameter estimation problem with uncertain statistics the guaranteed parameter estimation problem for a linear dynamical system with uncertain disturbance statistics is considered the estimate of the kalman bucy filter nonoptimality degree is constructed it is based on the duality theory this estimate is determined by the kalman bucy filter characteristics only and can be calculated without knowledge of the accurate solution of the optimal guaranteed estimation problem

the polynomial approach to the lq non gaussian regulator problem a new approach for the solution of the regulator problem for linear discrete time dynamical systems with non gaussian disturbances is proposed this approach generalizes a previous result concerning the definition of the quadratic optimal regulator it consists of the definition of the polynomial optimal algorithm of an order spl nu for the solution of the linear quadratic non gaussian stochastic regulator problem for systems with partial state information the validity of the separation principle has also been proved in this case numerical simulations show the high performance of the proposed method with respect to the classical linear regulation techniques

on the symmetric solutions of linear matrix equations abstract the symmetric solutions of linear matrix equations ax c and axb c are considered the necessary and sufficient conditions for the consistency of the equations with a symmetric condition on solutions are derived using the singular value decomposition and the generalized singular value decomposition numerical algorithms for solving the equations are suggested

noise covariance identification for time varying and nonlinear systems abstractkalman based state estimators assume a priori knowledge of the covariance matrices of the process and observation noise however in most practical situations noise statistics and initial conditions are often unknown and need to be estimated from measurement data this paper presents an auto covariance least squares based algorithm for noise and initial state error covariance estimation of large scale linear time varying ltv and nonlinear systems compared to existing auto covariance least squares based algorithms our method does not involve any approximations for ltv systems has fewer parameters to determine and is more memory computationally efficient for large scale systems for nonlinear systems our algorithm uses full information estimation moving horizon estimation instead of the extended kalman filter so that the stability and accuracy of noise covariance estimation for nonlinear systems can be guaranteed or improved respectively

state estimation with probability constraints this paper considers a state estimation problem for a discrete time linear system driven by a gaussian random process the second order statistics of the input process and state initial condition are uncertain however the probability that the state and input satisfy linear constraints during the estimation interval is known a minimax estimation problem is formulated to determine an estimator that minimises the worst case mean square error criterion over the uncertain second order statistics subject to the probability constraints it is shown that a solution to this constrained state estimation problem is given by a kalman filter for appropriately chosen input and initial condition models these models are obtained from a finite dimensional convex optimisation problem the application of this estimator to an aircraft tracking problem quantifies the improvement in estimation accuracy obtained from the inclusion of probability constraints in the minimax formulation

brief state estimation of continuous time radial basis function networks this paper presents state estimators for previously trained rbf networks based on a minimax approach the uncertainty class is characterized in terms of an approximation error vector minimizing the objective function over this uncertainty class is used to obtain state estimates the initial portion of the paper presents the derivation and properties of such a minimax state estimator for rbf networks in the later portion this is extended to the problem of minimax adaptive state estimation this approach is useful in the cases where the pretrained rbf network is to be used in state estimation since the latest information is used in improving estimates of the rbf weights a special class of estimators for the appended state estimation problem is also considered where a constant gain estimator matrix can be obtained this section gives sufficient conditions for the existence of such an observer and follows directly from the structure of the rbf networks finally example applications of the minimax and adaptive minimax estimation for nonlinear problems are presented the results show the accuracy of state estimation using the proposed minimax estimator

minimax control of linear stochastic systems with noise uncertainty the problem of linear quadratic gaussian control of multivariable linear stochastic systems with uncertain second order statistical properties is considered uncertainty is modeled by allowing process and observation noise spectral density matrices to vary arbitrarily within given classes and a minimax control formulation is applied to the quadratic objective functional general theorems proving the existence and characterization of saddle point solutions to this problem are presented and the relationship of these results to earlier results on minimax state estimation are discussed to illustrate the analytical results the specific example of regulating a double integrator plant is treated in detail

intrinsically bayesian robust kalman filter an innovation process approach in many contemporary engineering problems model uncertainty is inherent because accurate system identification is virtually impossible owing to system complexity or lack of data on account of availability time or cost the situation can be treated by assuming that the true model belongs to an uncertainty class of models in this context an intrinsically bayesian robust ibr filter is one that is optimal relative to the cost function in the classical sense and the prior distribution over the uncertainty class in the bayesian sense ibr filters have previously been found for both wiener and granulometric morphological filtering in this paper we derive the ibr kalman filter that performs optimally relative to an uncertainty class of state space models introducing the notion of bayesian innovation process and the bayesian orthogonality principle we show how the problem of designing an ibr kalman filter can be reduced to a recursive system similar to the classical kalman recursive equations except with effective counterparts such as the effective kalman gain matrix after deriving the recursive ibr kalman equations for discrete time we use the limiting method to obtain the ibr kalman bucy equations for continuous time finally we demonstrate the utility of the proposed framework for two real world problems sensor networks and gene regulatory network inference

noise covariance identification for nonlinear systems using expectation maximization and moving horizon estimation in order to estimate states from a noise driven state space system the state estimator requires a priori knowledge of both process and output noise covariances unfortunately noise statistics are usually unknown and have to be determined from output measurements current expectation maximization em based algorithms for estimating noise covariances for nonlinear systems assume the number of additive process and output noise signals are the same as the number of states and outputs respectively however in some applications the number of additive process noises could be less than the number of states in this paper a more general nonlinear system is considered by allowing the number of process and output noises to be smaller or equal to the number of states and outputs respectively in order to estimate noise covariances a semi definite programming solver is applied since an analytical solution is no longer easy to obtain the expectation step in current em algorithms rely on state estimates from the extended kalman filter ekf or smoother however the instability and divergence problems of the ekf could cause the em algorithm to converge to a local optimum that is far away from true values we use moving horizon estimation instead of the ekf smoother so that the accuracy of the covariance estimation in nonlinear systems can be significantly improved

nonequilibrium steady states of matrix product form a solver s guide we consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model among other things biological transport and traffic flow we begin with a broad overview of this class of driven diffusive systems which includes exclusion processes focusing on interesting physical properties such as shocks and phase transitions we then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form in addition to a gentle introduction to this matrix product approach how it works and how it relates to similar constructions that arise in other physical contexts we present a unified pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed we also review a number of more advanced topics including nonequilibrium free energy functionals the classification of exclusion processes involving multiple particle species existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled we conclude with a brief discussion of open problems for future research

optimization of linear filters under power spectral density stabilization geometric mean filters compose a family of filters indexed by a parameter k varying between 0 and 1 they have been used to provide frequency based filtering that mitigates the noise suppression of the optimal linear wiener filter in the blurred signal plus noise model for k 0 and k 1 the geometric mean filter gives the inverse filter and the wiener filter for the model respectively the geometric mean for k 1 2 has previously been derived as the optimal linear filter for the model under power spectral density psd equalization this constraint requires the psd of the filtered signal to be equal to the psd of the uncorrupted signal that it estimates this paper defines the notion of psd stabilization in which the psd of the restored signal is equal to a predetermined function times the psd of the uncorrupted signal a particular parameterized stabilization function yields the geometric mean family as the optimal linear filter for the model under psd stabilization relative to unconstrained optimization geometric means are suboptimal however we consider a parameterized model for which the noise is such that the geometric mean filters provide optimal linear filtering in the altered signal plus noise model for which the geometric mean is optimal the blur is the same as the original model in which the geometric mean is defined but the noise psd is a function of the fourier transform of the blur and the psd of the original noise since the altered model depends on k we consider a robustness question what kind of suboptimality results from applying the geometric mean for k sub 1 to the model fur which the geometric mean for k sub 2 is optimal

multiple models multiplicative noise and linear quadratic control algorithmic aspects numerical solution of certain linear quadratic lq control problems for robust design is addressed an iterative method is suggested and analysed for solving a minimax multiple model lq control problem a convergent iterative method is studied for finding the constant feedback gains of a given linear controller so as to solve a spectral radius functional minimization problem for multiple plants furthermore a convergent iterative method is proposed for solving the maximum entropy parametric lq control problem with multiplicative noise

estimation and control of systems with unknown covariance and multiplicative noise the problem of estimation and control for systems with multiplicative noise and unknown second order statistics is considered conditions are found for the existence of a solution based on game theoretic ideas the conditions for the existence of a saddle point for the time invariant filtering problem are necessary and sufficient whereas for all other cases only necessary the central idea of the solution is to convert the stochastic problem to a deterministic optimal control problem whose minimax point is sought with respect to the control filter and unknown statistics parameters the results that are derived show that the problem of estimation for systems with unknown covariances depends on the costate matrix which in turn is a function of the performance measure thus the filter loses one of its best known properties that of independence of the performance functional this property holds not only for the classical kalman filter but also for multiplicative systems

the ubiquitous kronecker product abstract the kronecker product has a rich and very pleasing algebra that supports a wide range of fast elegant and practical algorithms several trends in scientific computing suggest that this important matrix operation will have an increasingly greater role to play in the future first the application areas where kronecker products abound are all thriving these include signal processing image processing semidefinite programming and quantum computing second sparse factorizations and kronecker products are proving to be a very effective way to look at fast linear transforms researchers have taken the kronecker methodology as developed for the fast fourier transform and used it to build exciting alternatives third as computers get more powerful researchers are more willing to entertain problems of high dimension and this leads to kronecker products whenever low dimension techniques are tensored together

cohomology of 3 dimensional color lie algebras we develop the cohomology theory of color lie algebras due to scheunert zhang in a framework of non homogeneous quadratic koszul algebras in this approach the chevalley eilenberg complex of a color lie algebra becomes a standard koszul complex for its universal enveloping algebra providing a constructive method for computation of cohomology as an application we compute cohomologies with trivial coefficients of z 2 n graded 3 dimensional color lie algebras 2 c 2006 elsevier inc all rights reserved

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

partially asymmetric simple exclusion model in the presence of an impurity on a ring we study a generalized two species model on a ring the original model mallick k 1996 j phys a math gen 29 5375 describes ordinary particles hopping exclusively in one direction in the presence of an impurity the impurity hops with a rate different from that of ordinary particles and can be overtaken by them here we let the ordinary particles also hop backward with rate q using the matrix product ansatz we obtain the relevant quadratic algebra a finite dimensional representation of this algebra enables us to compute the stationary bulk density of the ordinary particles as well as the speed of impurity on a set of special surfaces of the parameter space we will obtain the phase structure of this model in the accessible region and show how the phase structure of the original model is modified in the infinite volume limit this model presents a shock in one of its phases

flow estimation of boundary layers using dns based wall shear information this article investigates the problem of obtaining a state space model of the disturbance evolution that precedes turbulent flow across aerodynamic surfaces this problem is challenging since the flow is governed by nonlinear partial differential algebraic equations for which there currently exists no efficient controller estimator synthesis techniques a sequence of model approximations is employed to yield a linear low order state space model to which standard tools of control theory can be applied one of the novelties of this article is the application of an algorithm that converts a system of differential algebraic equations into one of ordinary differential equations this enables straightforward satisfaction of boundary conditions whilst dispensing with the need for parallel flow approximations and velocity vorticity transformations the efficacy of the model is demonstrated by the synthesis of a kalman filter that clearly reconstructs the characteristic features of the flow using only wall vel

two way traffic flow exactly solvable model of traffic jam we study completely asymmetric two channel exclusion processes in one dimension it describes a two way traffic flow with cars moving in opposite directions the interchannel interaction makes cars slow down in the vicinity of approaching cars in the other lane particularly we consider in detail the system with a finite density of cars on one lane and a single car on the other when the interchannel interaction reaches a critical value a traffic jam occurs which turns out to be of first order phase transition we derive exact expressions for the average velocities the current the density profile and the k point density correlation functions we also obtain the exact probability of two cars being in one lane of distance r apart provided there is a finite density of cars on the other lane and show that the two cars form a weakly bound state in the jammed phase

optimal robust linear quadratic regulator for systems subject to uncertainties in this technical note a robust recursive regulator for linear discrete time systems which are subject to parametric uncertainties is proposed the main feature of the optimal regulator developed is the absence of tuning parameters in online applications to achieve this purpose a quadratic cost function based on the combination of penalty function and robust weighted least squares methods is formulated the convergence and stability proofs for the stationary system and a numerical comparative study among the standard linear quadratic regulator guaranteed cost and h controllers are provided

restricted risk bayes linear state estimation the problem of state estimation with stochastic uncertainties in the initial state model noise and measurement noise is considered using the restricted risk bayes approach it is assumed that the a priori distributions of these quantities are not perfectly known but that some information about them may be available while offering robustness the restricted risk bayes approach incorporates the available a priori information to give less conservative state estimators than the gamma minimax approach popular in the literature when attention is restricted to linear estimators based on a quadratic loss function a systematic method to derive restricted risk bayes estimators is proposed applying to the filtering problem the restricted risk bayes approach provides us with a robust method to calibrate the kalman filter kf considering the presence of stochastic uncertainties this method is illustrated with a target tracking example and a wireless channel tracking example for which the bayes minimax and restricted risk bayes estimators are derived and their performance is compared

n4sid subspace algorithms for the identification of combined deterministic stochastic systems abstract recently a great deal of attention has been given to numerical algorithms for subspace state space system identification n4sid in this paper we derive two new n4sid algorithms to identify mixed deterministic stochastic systems both algorithms determine state sequences through the projection of input and output data these state sequences are shown to be outputs of non steady state kalman filter banks from these it is easy to determine the state space system matrices the n4sid algorithms are always convergent non iterative and numerically stable since they only make use of qr and singular value decompositions both n4sid algorithms are similar but the second one trades off accuracy for simplicity these new algorithms are compared with existing subspace algorithms in theory and in practice

quasi deadbeat minimax filters for deterministic state space models in this note a quasi deadbeat property is introduced and a quasi deadbeat minimax filter dmf is proposed as a new class of filters for deterministic discrete time state space models constraints such as linearity quasi deadbeat property and independence of the initial state information will be required in advance in addition to a new performance index of the worst case gain between the disturbance and the current estimation error the proposed dmf is obtained by directly minimizing the new performance index with above constraints finite impulse response fir and infinite impulse response iir structures are suggested with emphasis on the fir structure the proposed dmf is represented first in a standard batch form and then in an iterative form it is shown that the dmf with fir and iir structures for deterministic systems are similar in form to the existing receding horizon unbiased fir filter rhuff and the kalman filter respectively for stochastic systems

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

stability robustness of the discrete time lqg system under plant perturbation and noise uncertainty in this paper the robustness of discrete time lqg problems is studied the system to be controlled is described by the usual state space formulation but includes the structure of plant parameter perturbations and noise uncertainty a simple and direct way is given to derive a saddle point inequality of the closed loop system performance to cope with noise uncertainty and one sufficient condition for system stability robustness under plant perturbation is presented

note on the cohomology of color hopf and lie algebras abstract let a be a g hopf algebra with bijective antipode and let m be a g graded a bimodule we prove that there exists an isomorphism hh gr a m ext a gr k m ad where k is viewed as the trivial graded a module via the counit of a m ad is the adjoint a module associated to the graded a bimodule m and hh gr denotes the g graded hochschild cohomology as an application we deduce that the graded cohomology of color lie algebra l is isomorphic to the graded hochschild cohomology of its universal enveloping algebra u l solving a question of m scheunert

bayesian parameter estimation taking the bayesian approach in solving the discrete time parameter estimation problem has two major results the unknown parameters are legitimately included as additional system states and the computational objective becomes calculation of the entire posterior density instead of just its first few moments this viewpoint facilitates intuitive analysis allowing increased qualitative understanding of the system behavior with the actual posterior density in hand the true optimal estimate for any given loss function can be calculated although the computational burden of doing so might preclude online use it does not provide a clearly justified baseline for comparative studies these points are demonstrated by analyzing a scalar problem with a single unknown and by comparing an established point estimator s performance to the true optimal estimate

bootstrapping state space models gaussian maximum likelihood estimation and the kalman filter abstract the bootstrap is proposed as a method for assessing the precision of gaussian maximum likelihood estimates of the parameters of linear state space models our results also apply to autoregressive moving average models since they are a special case of state space models it is shown that for a time invariant stable system the bootstrap applied to the innovations yields asymptotically consistent standard errors to investigate the performance of the bootstrap for finite sample lengths simulation results are presented for a two state model with 50 and 100 observations two cases are investigated one with real characteristic roots and one with complex characteristic roots the bootstrap is then applied to two real data sets one used in a test for efficient capital markets and one used to develop an autoregressive integrated moving average model for quarterly earnings data we find the bootstrap to be of definite value over the conventional asymptotics

finite dimensional representations of the quadratic algebra applications to the exclusion process we study the one dimensional partially asymmetric simple exclusion process asep with open boundaries that describes a system of hard core particles hopping stochastically on a chain coupled to reservoirs at both ends derrida and coworkers showed in 1993 that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra closely related to the deformed oscillator algebra we construct all finite dimensional irreducible representations of this algebra this enables us to compute the stationary bulk density as well as all correlation lengths for the asep on a set of special curves of the phase diagram

numerical aspects of different kalman filter implementations a theoretical analysis is made of the error propagation due to numerical roundoff for four different kalman filter implementations the conventional kalman filter the square root covariance filter the square root information filter and the chandrasekhar square root filter an experimental analysis is performed to validate the new insights gained by the theoretical analysis

eigenvalues of casimir operators for the general linear the special linear and the orthosymplectic lie superalgebras the generators of the algebras under consideration can be written in a canonical two index form and hence the associated standard sequence of casimir elements can be constructed following the classical approach by perelomov and popov we obtain the eigenvalues of these casimir elements in an arbitrary highest weight module by calculating the corresponding generating functions

adaptive kalman filtering for histogram based appearance learning in infrared imagery targets of interest in video acquired from imaging infrared sensors often exhibit profound appearance variations due to a variety of factors including complex target maneuvers ego motion of the sensor platform background clutter etc making it difficult to maintain a reliable detection process and track lock over extended time periods two key issues in overcoming this problem are how to represent the target and how to learn its appearance online in this paper we adopt a recent appearance model that estimates the pixel intensity histograms as well as the distribution of local standard deviations in both the foreground and background regions for robust target representation appearance learning is then cast as an adaptive kalman filtering problem where the process and measurement noise variances are both unknown we formulate this problem using both covariance matching and for the first time in a visual tracking application the recent autocovariance least squares als method although convergence of the als algorithm is guaranteed only for the case of globally wide sense stationary process and measurement noises we demonstrate for the first time that the technique can often be applied with great effectiveness under the much weaker assumption of piecewise stationarity the performance advantages of the als method relative to the classical covariance matching are illustrated by means of simulated stationary and nonstationary systems against real data our results show that the als based algorithm outperforms the covariance matching as well as the traditional histogram similarity based methods achieving sub pixel tracking accuracy against the well known amcom closure sequences and the recent sensiac automatic target recognition dataset

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

minimax robust discrete time matched filters the problem of designing finite length discrete time matched filters is considered for situations in which exact knowledge of the input signal and or noise characteristics is not available such situations arise in many applications due to channel distortion incoherencies nonlinear effects and other modeling uncertainties in such cases it is often of interest to design a minimax robust matched filter i e a nonadaptive filter with an optimum level of worst case performance for the expected uncertainty class this problem is investigated here for three types of uncertainty models for the input signal namely the mean absolute mean square and maximum absolute distortion classes and for a wide generality of norm deviation models for the noise covariance matrix some numerical examples illustrate the robustness properties of the proposed designs

on second order and fourth order moments of jointly distributed random matrices a survey abstract the study is concerned with second order and fourth order moments of jointly distributed random matrices when distributional properties are required normality is adopted some of the results can also be applied to elliptical or wishart distributions the developments are entirely algebraic full use is made of the kronecker product repeated vectorization commutation matrices and related items there are a few references in the main text but many additional references to other work in which the same or kindred results obtained by other methods procedures or concepts can be found have been included in the references

on the efficient low cost procedure for estimation of high dimensional prediction error covariance matrices abstract a simple efficient algorithm is proposed for estimating the prediction error covariance matrix which plays the key role for successful state estimation in very high dimensional systems the main results are obtained by introducing the hypothesis on the separability of vertical and horizontal structure of the error covariance matrix and its parameterization a new parameter optimization problem is formulated which is closely related to the nearest kronecker problem nkp this allows to estimate optimally the unknown parameters of the structured parametrized ecm as well as to approach numerically the solution of the traditional nkp in a simple and efficient way the algorithm for the state estimation will be detailed the results from experiments on parameter and state estimation problems for both moderate and high dimensional numerical models demonstrate a high effectiveness of the proposed filtering approach