radial symmetry of positive solutions in nonlinear polyharmonic dirichlet problems we extend the symmetry result of gidas ni nirenberg to semilinear polyharmonic dirichlet problems in the unit ball in the proof we develop a new variant of the method of moving planes relying on fine estimates for the green function of the polyharmonic operator we also consider minimizers for subcritical higher order sobolev embeddings for embeddings into weighted spaces with a radially symmetric weight function we show that the minimizers are at least axially symmetric this result is sharp since we exhibit examples of minimizers which do not have full radial symmetry

realization of stable models with subspace methods abstract subspace methods for system identification estimate the dynamics of state space models either by using the shiftinvariance property of an estimated observability or controllability matrix or by estimating a state sequence and then solving a least squares problem to obtain the system matrices in either case it is possible for the estimated system to be unstable we present algorithms to find stable approximants to a least squares problem which can then be applied to subspace methods to ensure stability either asymptotic or marginal stability can be ensured in the latter case a pole or a pair of poles being forced to lie on the unit circle in addition some results on a sufficient condition for stability for least squares solutions obtained by the shift invariance approach are derived

minimum phase properties of finite interval stochastic realization a finite interval stochastically balanced realization is analyzed based on the idealized assumption that an exact finite covariance sequence is available it is proved that a finite interval balanced realization algorithm maciejowski j m 1996 parameter estimation of multivariable systems using balanced realizations in s bittanti g picci eds identification adaptation learning pp 70 119 berlin springer provides stable minimum phase models if the size of the interval is at least two times larger than the order of a minimal realization new algorithms for finite interval stochastic realization and stochastic subspace identification are moreover derived by means of block lq decomposition and the stability and minimum phase properties of models obtained by these algorithms are considered numerical simulation results are also included

contraction of information in systems far from equilibrium the relationship between a physical model and a time series model or an innovation model is discussed from the viewpoint of contraction of information due to the way of observation in this framework measurable correlation functions are expressed in terms of both models by using the riccati type equation and the singular value decomposition of the hankel matrix a data oriented model is derived from measurable correlation functions there occurs the contraction in a noise source space or random forces from the mechanism of contraction random forces of systems can be identified by using two innovation models in different states

efficient recursive algorithms for detection of abrupt changes in signals and control systems this paper addresses a number of open problems concerning the generalized likelihood ratio glr rules for online detection of faults and parameter changes in control systems it is shown that with an appropriate choice of the threshold and window size these glr rules are asymptotically optimal the rules are also extended to non likelihood statistics that are widely used in monitoring adaptive algorithms for system identification and control by establishing gaussian approximations to these statistics when the window size is chosen suitably recursive algorithms are developed for practical implementation of the procedure and importance sampling techniques are introduced for determining the threshold of the rule to satisfy prescribed bounds on the false alarm rate

identification of continuous time models the paper considers the problem of estimation of the transfer function of a continuous time dynamic system in the presence of colored noise the author introduces an operator transformation that allows for keeping a continuous time parametrization whereas the parameter estimation can be made by means of a discrete time maximum likelihood algorithm a comparison is made between the performance of the new method in comparison with a standard identification of an armax model the method is useful in cases where it is important to estimate the coefficients of a continuous time transfer function and where it is important to maintain a physical interpretation of the transfer function results

some theoretical results on neural spike train probability models this article contains two main theoretical results on neural spike train models using the counting or point process on the real line as a model for the spike train the first part of this article considers template matching of multiple spike trains p values for the occurrences of a given template or pattern in a set of spike trains are computed using a general scoring system by identifying the pattern with an experimental stimulus multiple spike trains can be deciphered to provide useful information the second part of the article assumes that the counting process has a conditional intensity function that is a product of a free firing rate function s which depends only on the stimulus and a recovery function r which depends only on the time since the last spike if s and r belong to a q smooth class of functions it is proved that sieve maximum likelihood estimators for s and r achieve the optimal convergence rate except for a logarithmic factor under l 1 loss

differential systems with strongly indefinite variational structure abstract the euler lagrange equations of lagrangians with a strongly indefinite quadratic part are studied by means of the direct min max method of benci and rabinowitz the simplest case is a system of two coupled semilinear poisson equations using an analytic framework of a suitable family of products of fractional sobolev spaces existence results are obtained for all nonlinearities with subcritical growth rates

consistency and asymptotic normality of some subspace algorithms for systems without observed inputs asymptotic normality for a class of subspace algorithms which estimate the state in a first step is derived expressions for the asymptotic variance are given linear systems with unobserved white noise inputs are considered a class of subspace estimates for the system matrices obtained by estimating the state in the first step is analyzed the main result presented here states asymptotic normality of subspace estimates in addition a consistency result for the system matrix estimates is given an algorithm to compute the asymptotic variances of the estimates is presented in a final section the implications of the result are discussed

state space approximation of multi input multi output systems with stochastic exogenous inputs instead of the usual ar ma x or var vector autoregressive modelling procedures will be described to obtain approximate balanced state space models and steady state kalman filters with prewhitened inputs these state space models and kalman filters can be used for prediction and also for control whenever the output and input variables are target and control variables respectively

realization and reduction of markovian models from nonstationary data the realization of markovian models for nonstationary processes generated by time invariant linear systems is considered a model is obtained by constructing an orthogonal finite step predictor for the process optimal model approximation by order reduction is naturally defined in this framework the construction and reduction of markovian models from multiple data records and the numerical considerations involved are illustrated by examples

balanced forms canonicity and parameterization we show that balanced forms are canonical and continuously parameterize the set of systems of a given order which are asymptotically stable minimal and have distinct singular values the advantage of the balanced canonical form over other classical canonical forms lies precisely in the guaranteed stability and minimality of the parameterization we also derive formulas allowing the synthesis of systems using gradient methods in balanced form

frequency weighted model reduction via quasi kalman decomposition a frequency weighted model reduction method based on quasi kalman decomposition is proposed for discrete systems the method is essentially an extension of the technique presented by lu and lee 1985 to the frequency weighted case and can handle both single sided as well as double sided weights two illustrative examples show the effectiveness of the method and results are compared with the method developed by enns 1984

embedded trees estimation of gaussian processes on graphs with cycles graphical models provide a powerful general framework for encoding the structure of large scale estimation problems however the graphs describing typical real world phenomena contain many cycles making direct estimation procedures prohibitively costly in this paper we develop an iterative inference algorithm for general gaussian graphical models it operates by exactly solving a series of modified estimation problems on spanning trees embedded within the original cyclic graph when these subproblems are suitably chosen the algorithm converges to the correct conditional means moreover and in contrast to many other iterative methods the tree based procedures we propose can also be used to calculate exact error variances although the conditional mean iteration is effective for quite densely connected graphical models the error variance computation is most efficient for sparser graphs in this context we present a modeling example suggesting that very sparsely connected graphs with cycles may provide significant advantages relative to their tree structured counterparts thanks both to the expressive power of these models and to the efficient inference algorithms developed herein the convergence properties of the proposed tree based iterations are characterized both analytically and experimentally in addition by using the basic tree based iteration to precondition the conjugate gradient method we develop an alternative accelerated iteration that is finitely convergent simulation results are presented that demonstrate this algorithm s effectiveness on several inference problems including a prototype distributed sensing application

l sub 2 optimal filter reduction a closed loop approach this paper is concerned with the problem of order reduction of a full order kalman filter for a stable linear signal model so that the steady state filtering error variance associated with the reduced order filter is minimized by an orthogonal parameterization the above problem is formulated to minimize the filtering error variance over a set of orthogonal matrices both continuous and iterative algorithms are derived to compute an optimal reduced order filter the algorithms are shown to possess good properties including the desirable convergence property the proposed algorithms are simple and effective numerical examples are presented to demonstrate the effectiveness and the significant advantages of the proposed algorithms over the existing open loop methods such as the well known balanced truncation method

a realization approach to stochastic model reduction the problem of discrete time stochastic model reduction approximation is considered using the canonical correlation analysis approach of akaike 1975 a new order reduction algorithm is developed furthermore it is shown that the inverse of the reduced order realization is asymptotically stable next an explicit relationship between canonical variables and the linear least squares estimate of the state vector is established using this a more direct approach for order reduction is presented and also a new design for reduced order kalman filters is developed finally the uniqueness and symmetry properties for the new realization the balanced stochastic realization along with a simulation result are presented

state space model identification with data correlation abstract it is proved that a certain sample auto and cross correlation hankel matrix can be used to develop an effective state space model identification procedure by incorporating data correlation with a state space model identification method identification bias which is inherent in using the singular value decomposition of a noise corrupted hankel data matrix can be significantly reduced the proposed new identification procedure is different from other state space identification methods which use correlation or covariance matrices since the input excitation signals are not limited to a white gaussian noise or to an impulse these inputs can be any time functions provided the persistent excitation condition is satisfied communicated by dr d a wilson

information bounds and quick detection of parameter changes in stochastic systems by using information theoretic bounds and sequential hypothesis testing theory this paper provides a new approach to optimal detection of abrupt changes in stochastic systems this approach not only generalizes previous work in the literature on optimal detection far beyond the relatively simple models treated but also suggests alternative performance criteria which are more tractable and more appropriate for general stochastic systems in addition it leads to detection rules which have manageable computational complexity for on line implementation and yet are nearly optimal under the different performance criteria considered

maxima of asymptotically gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices several classical results on boundary crossing probabilities of brownian motion and random walks are extended to asymptotically gaussian random fields which include sums of i i d random variables with multidimensional indices multivariate empirical processes and scan statistics in change point and signal detection as special cases some key ingredients in these extensions are moderate deviation approximations to marginal tail probabilities and weak convergence of the conditional distributions of certain clumps around high level crossings we also discuss how these results are related to the poisson clumping heuristic and tube formulas of gaussian random fields and describe their applications to laws of the iterated logarithm in the form of the kolmogorov erdos feller integral tests

asymptotic minimax robust quickest change detection for dependent stochastic processes with parametric uncertainty in this paper we consider the problem of quickly detecting an unknown change in the conditional densities of a dependent stochastic process in contrast to the existing quickest change detection approaches for dependent stochastic processes we propose minimax robust versions of the popular lorden pollak and bayesian criteria for when there is uncertainty about the parameter of the post change conditional densities under an information theoretic pythagorean inequality condition on the uncertainty set of possible post change parameters we identify asymptotic minimax robust solutions to our lorden pollak and bayesian problems finally through simulation examples we illustrate that asymptotically minimax robust rules can provide detection performance comparable to the popular but more computationally expensive generalized likelihood ratio rule

a subspace algorithm for balanced state space system identification in an earlier paper by moonen et at 1989 an algorithm has been introduced for identifying multivariable linear systems directly from input output data this new algorithm falls in the class of so called subspace methods and resembles impulse response based realization algorithms in this paper we extend this algorithm by incorporating a balancing step such that the identified model is always in balanced coordinates with this modification one obtains a data driven counterpart for kung s realization algorithm

brief paper an integrated trade off design of observer based fault detection systems in this paper problems related to the integrated design of observer based fault detection systems are addressed in the context of norm based residual evaluation a trade off between false alarm rate far and fault detection rate fdr is first formulated aiming at minimizing far under given fdr an approach is then presented for the design of observer based fault detection systems for this purpose the well established factorization technique is applied finally study is devoted to the comparison between the existing methods and the proposed one

prediction error identification of linear systems a nonparametric gaussian regression approach a novel bayesian paradigm for the identification of output error models has recently been proposed in which in place of postulating finite dimensional models of the system transfer function the system impulse response is searched for within an infinite dimensional space in this paper such a nonparametric approach is applied to the design of optimal predictors and discrete time models based on prediction error minimization by interpreting the predictor impulse responses as realizations of gaussian processes the proposed scheme describes the predictor impulse responses as the convolution of an infinite dimensional response with a low dimensional parametric response that captures possible high frequency dynamics overparameterization is avoided because the model involves only a few hyperparameters that are tuned via marginal likelihood maximization numerical experiments with data generated by armax and infinite dimensional models show the definite advantages of the new approach over standard parametric prediction error techniques and subspace methods both in terms of predictive capability on new data and accuracy in reconstruction of system impulse responses

on the relation between cca and predictor based subspace identification in this paper we investigate the relation between a recently proposed subspace method based on predictor identification pbsid known also as ldquowhitening filter algorithm rdquo and the classical cca algorithm the comparison is motivated by i the fact that cca is known to be asymptotically efficient for time series identification and optimal for white measured inputs and ii some recent results showing that a number of recently developed algorithms are very closely related to pbsid we show that pbsid is asymptotically equivalent to cca precisely in the situations in which cca is optimal while an ldquooptimizedrdquo version of pbsid behaves no worse than cca also for nonwhite inputs even though pbsid and its optimized version are consistent regardless of the presence of feedback in this paper we work under the assumption that there is no feedback to make the comparison with cca meaningful the results of this paper imply that the ldquooptimizedrdquo pbsid besides being able to handle feedback is to be preferred to cca also when there is no feedback only in very specific cases white or no inputs are the two algorithms asymptotically equivalent

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

principal components algorithms for arma spectrum estimation principal components algorithms are presented for the problem of fitting an arma model to a given segment of a sample sequence of a discrete time stochastic process and the model is used to estimate the process power spectrum to reduce the effects of finite wordlength errors balanced state pace parameterization of the arma model is used instead of the more popular difference equation parameterization model identification is formulated as a problem of selecting a partial state to span approximately an apparently large dimensional information interface between the past and the future of the process different criteria are used to measure the quality of the approximation which leads to principal components algorithms for the problem that are based on singular value decomposition

parameter and state model reduction for large scale statistical inverse problems a greedy algorithm for the construction of a reduced model with reduction in both parameter and state is developed for an efficient solution of statistical inverse problems governed by partial differential equations with distributed parameters large scale models are too costly to evaluate repeatedly as is required in the statistical setting furthermore these models often have high dimensional parametric input spaces which compounds the difficulty of effectively exploring the uncertainty space we simultaneously address both challenges by constructing a projection based reduced model that accepts low dimensional parameter inputs and whose model evaluations are inexpensive the associated parameter and state bases are obtained through a greedy procedure that targets the governing equations model outputs and prior information the methodology and results are presented for groundwater inverse problems in one and two dimensions

subspace identification by data orthogonalization and model decoupling it has been observed that identification of state space models with inputs may lead to unreliable results in certain experimental conditions even when the input signal excites well within the bandwidth of the system this may be due to ill conditioning of the identification problem which occurs when the state space and the future input space are nearly parallel we have in particular shown in the companion papers automatica 40 4 2004 575 automatica 40 4 2004 677 that under these circumstances subspace methods operating on input output data may be ill conditioned quite independently of the particular algorithm which is used in this paper we indicate that the cause of ill conditioning can sometimes be cured by using orthogonalized data and by recasting the model into a certain natural block decoupled form consisting of a deterministic and a stochastic subsystem the natural subspace algorithm for the identification of the deterministic subsystem is then a weighted version of the pi moesp method of verhaegen and dewilde int j control 56 1993 1187 1211 the analysis shows that under certain conditions methods based on the block decoupled parametrization and orthogonal decomposition of the input output data perform better than traditional joint model based methods in the circumstance of nearly parallel regressors

uniqueness of the positive solution for a class of semilinear elliptic systems abstract we prove the uniqueness of the positive radially symmetric solution to the following problem u v p 1 0 x b 1 v w p 2 0 x b 1 w u p 3 0 x b 1 u v w 0 x b 1 where p i 0 i 1 2 3 and b 1 is the unit ball in r n

subspace algorithms for the identification of multivarible dynamic errors in variables models abstract we consider the problem of identifying multivariable finite dimensional linear time invariant systems from noisy input output measurements apart from the fact that both the measured input and output are corrupted by additive white noise the output may also be contaminated by a term which is caused by a white input process noise furthermore all these noise processes are allowed to be correlated with each other we shall develop a solution to this problem in the framework of subspace identification and we shall show that our algorithms give consistent estimates when the system is operating in open or closed loop two realistic simulation studies are presented to demonstrate the practical applicability of the proposed algorithms 1997 elsevier science ltd

reduced complexity lqr design using canonical correlation analysis abstract canonical correlation analysis is developed for the discrete infinite time lqr problem having an asymptotically stable plant it is shown that the optimal control sequence belongs to the range space of the canonical vectors weighted by the canonical correlation coefficients using this analysis a reduced complexity controller for the lqr problem is obtained furthermore it is established that when this reduced complexity controller is applied to the original plant the corresponding closed loop system is asymptotically stable

existence of solutions to higher order lane emden type systems abstract we prove existence results for the lane emdentype system u v q v u p in b 1 r n r u r 0 r 0 1 on b 1 r v r 0 r 0 1 on b 1 where b 1 is the unitary ball in r n n max 2 2 is the outward pointing normal n 1 and 1 is the polyharmonic operator a continuation method together with a priori estimates will be exploited moreover we prove uniqueness for the particular case 2 1 and p q 1

system identification using balanced parametrizations some general issues in the black box identification of multivariable systems are first discussed it is then suggested that balanced parametrizations can be used to give identifiable forms a particular advantage is that balanced parametrizations are known for several useful classes of linear dynamic models including stable minimal models minimum phase models positive real models and normalized coprime factor models before optimizing the parameters of balanced parametrizations an initial model must be found we use realization based methods and so called subspace methods for this purpose these methods are very effective at finding accurate initial models without preliminary estimation of various structural indexes the paper ends with two simulation examples which compare the use of balanced parametrizations with more traditional ones and three real examples based on practical problems a distillation column an industrial dryer and the irrational spectrum or sea waves

a unified derivation and critical review of modal approaches to model reduction six of the most commonly used modal reduction techniques are represented by means of signal flow diagrams connecting inputs and state variables in this representation the derivation and the cross comparison of the various methods are greatly facilitated each method is then analysed to determine key characteristics i e i steady state agreement ii initial value agreement iii independence of the reduced model on the choice of retained state variables and inputs and iv eigen vector orientation realistic large scale systems are used to evaluate the static and dynamic characteristics of each model reduction method numerically these studies reveal some important and often unrecognized weaknesses of several traditional techniques and confirm the strength of the newly developed technique of litz

on the ill conditioning of subspace identification with inputs there is experimental evidence that the performance of standard subspace algorithms from the literature e g the n4sid method may be surprisingly poor in certain experimental conditions this happens typically when the past signals past inputs and outputs and future input spaces are nearly parallel in this paper we argue that the poor behavior may be attributed to a form of ill conditioning of the underlying multiple regression problem which may occur for nearly parallel regressors an elementary error analysis of the subspace identification problem shows that there are two main possible causes of ill conditioning the first has to do with near collinearity of the state and future input subspaces the second has to do with the dynamical structure of the input signal and may roughly be attributed to lack of excitation stochastic realization theory constitutes a natural setting for analyzing subspace identification methods in this setting we undertake a comparative study of three widely used subspace methods n4sid robust n4sid and po moesp the last two methods are proven to be essentially equivalent and the relative accuracy regarding the estimation of the a c parameters is shown to be the same

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

uniqueness results for higher order lane emden systems abstract in this paper we develop a gidas ni nirenberg technique for polyharmonic equations and systems of lane emden type as far as we are concerned with dirichlet boundary conditions we prove uniqueness of solutions up to eighth order equations namely which involve the fourth iteration of the laplace operator then we can extend the result to arbitrary polyharmonic operators of any order provided some natural boundary conditions are satisfied but not for dirichlet s the obstruction is apparently a new phenomenon and seems due to some loss of information when the polyharmonic operator turns out to be a power of the laplacian and this is the case of navier s boundary conditions as byproduct uniqueness of solutions holds in a fairly general context new existence results for systems are also established

a suboptimal quadratic change detection scheme we address the problem of detecting changes in multivariate gaussian random signals with an unknown mean after the change the window limited generalized likelihood ratio glr scheme is a well known approach to solve this problem however this algorithm involves at least log spl gamma spl rho likelihood ratio computations at each stage where spl gamma spl gamma spl rarr spl infin is the mean time before a false alarm and spl rho is the kullback leibler information we establish a new suboptimal recursive approach which is based on a collection of l parallel recursive spl chi sup 2 tests instead of the window limited glr scheme this new approach involves only a fixed number l of likelihood ratio computations at each stage for any combinations of spl gamma and spl rho by choosing an acceptable value of nonoptimality the designer can easily find a tradeoff between the complexity of the quadratic change detection algorithm and its efficiency

scan statistics with weighted observations we examine scan statistics for one dimensional marked poisson processes such statistics tabulate the maximum weighted count of event occurrences within a window of predetermined width over all windows within an observed interval we derive analytical formulas and also give an importance sampling method for approximating the tail probabilities of scan statistics because high throughput genomic sequencing has led to the availability of massive amounts of biomolecular sequence data it is often of interest to search long dna or protein sequences for local regions that are enriched for a certain characteristic thus scan statistics have become a useful tool in modern computational biology we illustrate the application of our p value approximations with such examples

brief a stochastic realization algorithm via block lq decomposition in hilbert space a stochastic realization problem of a stationary stochastic process is re visited and a new stochastically balanced realization algorithm is derived in a hilbert space generated by second order stationary processes the present algorithm computes a stochastically balanced realization by means of the singular value decomposition of a weighted block hankel matrix derived by a block lq decomposition extension to a stochastic subspace identification method explains how the proposed abstract algorithm is implemented in system identification

an algorithm for detecting a change in a stochastic process the problem of detecting a change from one given stationary and ergodic stochastic process to another such process is considered it is assumed that both stochastic processes are processes with memory and that they are mutually independent a sequential test is proposed and analyzed it is proved that the proposed test is asymptotically optimal in a mathematically precise sense

a generalized approach to q markov covariance equivalent realizations for discrete systems abstract a new algorithm is developed which constructs q markov covariance equivalent realizations q markov covers of multivariable linear discrete time systems a q markov cover is a state realization which matches exactly a finite portion of the impulse response sequence markov parameters and output autocorrelation sequence covariance parameters of a linear system the algorithm generates the q markov covers starting with only the basic data namely the q markov parameters and the q covariance parameters the algorithm leads to a parameterization of all minimal stable q markov covers which can be constructed since the data are easily computed from a given state space model the algorithm presented will be useful for both realization and model reduction of multivariable linear discrete time systems an example is presented to demonstrate the algorithm

misspecified and asymptotically minimax robust quickest change detection we investigate the quickest detection of an unknown change in the distribution of a stochastic process generating independent and identically distributed observations we develop new bounds on the performance of misspecified cumulative sum cusum rules and pose minimax robust versions of the popular lorden and pollak criteria with polynomial or higher order moment detection delay penalties by exploiting our results for misspecified cusum rules we identify solutions to our robust quickest change detection problems in the asymptotic regime of few false alarms in contrast to previous robust quickest change detection treatments our asymptotic results hold under relaxed conditions on the uncertainty sets of possible prechange and postchange distributions we illustrate our results in simulations and apply them to the problem of detecting target manoeuvres in low signal to noise ratio settings i e dim target manoeuvre detection

brief paper on the stability of a reduced order filter based on dominant singular value decomposition of the system dynamics the stability of a reduced order filter rof the gain of which is constructed on the basis of a subspace of dominant singular vectors of the system dynamics is examined a definition of s detectability is introduced it is found that the observability of all unstable and neutral singular vectors s detectability is a sufficient condition for the existence of a stable filter

another balanced controller reduction algorithm the problem of controller reduction has been addressed by a number of authors 1 4 using the concept of balanced coordinates originally proposed by moore 5 this note establishes a more direct link between the riccati balancing methods in 2 4 and moore s work and proposes yet another candidate method as a logical extension of 2 4

a cyclic low rank smith method for large sparse lyapunov equations in this paper we present the cyclic low rank smith method which is an iterative method for the computation of low rank approximations to the solution of large sparse stable lyapunov equations it is based on a generalization of the classical smith method and profits by the usual low rank property of the right hand side matrix the requirements of the method are moderate with respect to both computational cost and memory furthermore we propose a heuristic for determining a set of suboptimal alternating direction implicit adi shift parameters this heuristic which is based on a pair of arnoldi processes does not require any a priori knowledge on the spectrum of the coefficient matrix of the lyapunov equation numerical experiments show the efficiency of the iterative scheme combined with the heuristic for the adi parameters

on board component fault detection and isolation using the statistical local approach we describe both the key principles and real application examples of a unified theory which allows us to perform the on board incipient fault detection and isolation tasks involved in monitoring for condition based maintenance this theory is known under the name of local approach and it is especially suited to component faults it aims at transforming complex detection problems concerning a parameterized stochastic process into the universal problem of monitoring the mean of a gaussian vector based on a small deviation assumption the key tools are the first order taylor expansion and the asymptotic gaussianity of a convenient parameter estimating function ml ls iv and subspace identification methods are addressed in this perspective in the case of dynamic processes given in state space form the approach may also call for observer based state estimation or state elimination experiments concerning both simulated and real data for linear and nonlinear dynamical processes are reported how the key principles and features of the local approach compare with those of other approaches is discussed

on balanced realizations of bounded real and positive real functions based on normalized coprime factorizations with respect to indefinite metrics and the construction of suitable characteristic functions the ober balanced canonical forms for the classes of bounded real and positive real functions are derived this uses a matrix representation of the shift realization with respect to a basis related to sets of orthogonal polynomials

optimality of cusum rule approximations in change point detection problems application to nonlinear state space systems the well known cumulative sum cusum sequential rule for abrupt model change detection in stochastic dynamic systems relies on the knowledge of the probability density functions of the system output variables conditional on their past values and on the system functioning mode at each time step this paper shows how to build an asymptotically optimal detection rule under the common average run length arl constraint when these densities are not available but can be consistently estimated this is the case for nonlinear state space systems observed through output variables for such systems a new class of particle filters based on convolution kernels allows to get consistent estimates of the conditional densities leading to an optimal cusum like filter detection rule fdr

acausal models and balanced realizations of stationary processes abstract we study acausal realizations of stationary or stationary increment processes in particular we characterize the family of models whose corresponding spectral factors have a fixed zero structure acausal models with a fixed zero structure are related to each other by a certain group of state feedback transformations which is naturally parametrized by the solution set of a homogeneous algebraic riccati equation each feedback transformation reflects some of the eigenvalues of the generator matrix a of the representation to a mirror image with respect to the imaginary axis dually acausal models with a fixed pole structure are parametrized by a dual riccati equation and by a corresponding family of output injection transformations from a general standpoint the results of this study clarify the role played by dual pairs of riccati equations in spectral factorization and may be relevant to other problem areas than stochastic modelling one natural application of the concepts discussed in the paper is to stochastic balancing balancing of models with an essentially arbitrary eigenvalue location can be accomodated very naturally in this framework a balancing algorithm involving the solution of a dual pair of riccati equations is discussed

brief paper balanced truncation model reduction for systems with inhomogeneous initial conditions we present a rigorous approach to extend balanced truncation model reduction btmr to systems with inhomogeneous initial conditions we provide an estimate for the error between the input output maps of the original and of the reduced initial value system and we illustrate numerically the superiority of our approach over the naive application of btmr when btmr is applied to linear time invariant systems with inhomogeneous initial conditions it is crucial that the initial data are well represented by the subspaces generated by btmr this requirement is often ignored or it is avoided by making the restrictive assumption that the initial data are zero to ensure that the initial data are well represented by the btmr subspaces we add auxiliary inputs determined by the initial data

existence and uniqueness of positive radial solutions for the lane emden system in this article we consider component wise positive radial solutions of a weakly coupled system of elliptic equations in a ball with homogeneous nonlinearities the existence is well known in general we give a result for the remaining cases the uniqueness is less studied we complement the known results

using the generalized likelihood ratio statistic for sequential detection of a change point we study sequential detection of a change point using the generalized likelihood ratio statistic for the special case of detecting a change in a normal mean with known variance we give approximations to the average run lengths and compare our procedure to standard cusum tests and combined cusum shewhart tests several examples indicating extensions to problems involving multiple parameters are discussed

forecasting international growth rates with leading indicators a system theoretic approach abstract an approach to estimating multivariate time invariant state space models for armax type processes is considered it is based on estimated markov parameters unit impulse responses and involves singular value decomposition techniques and leads to internally balanced state space representations the method is applied to forecast the growth rate of real output of nine countries using leading indicators the forecasting performance of this state space approach is compared to the performance of autoregressive models with leading indicators

canonical correlation analysis approximate covariance extension and identification of stationary time series abstract in this paper we analyze a class of state space identification algorithms for time series based on canonical correlation analysis in the light of recent results on stochastic systems theory in principle these so called subspace methods can be described as covariance estimation followed by stochastic realization the methods offer the major advantage of converting the nonlinear parameter estimation phase in traditional arma models identification into the solution of a riccati equation but introduce at the same time some nontrivial mathematical problems related to positivity the reason for this is that an essential part of the problem is equivalent to the well known rational covariance extension problem therefore the usual deterministic arguments based on factorization of a hankel matrix are not valid for generic data something that is habitually overlooked in the literature we demonstrate that there is no guarantee that several popular identification procedures based on the same principle will not fail to produce a positive extension unless some rather stringent assumptions are made which in general are not explicitly reported in this paper the statistical problem of stochastic modeling from estimated covariances is phrased in the geometric language of stochastic realization theory we review the basic ideas of stochastic realization theory in the context of identification discuss the concept of stochastic balancing and of stochastic model reduction by principal subsystem truncation the model reduction method of desai and pal 1982 a realization approach to stochastic model reduction proc 1st decision and control conf pp 1105 1112 based on truncated balanced stochastic realizations is partially justified showing that the reduced system structure has a positive covariance sequence but is in general not balanced as a byproduct of this analysis we obtain a theorem prescribing conditions under which the subspace identification methods produce bona fide stochastic systems

realization of stochastic systems with exogenous inputs and subspace identification methods a stochastic realization theory for a discrete time stationary process with an exogenous input is developed by extending the classical cca technique some stochastic subspace identification methods are derived by adapting the realization procedure to finite input output data