a new kernel based approach for linear system identification this paper describes a new kernel based approach for linear system identification of stable systems we model the impulse response as the realization of a gaussian process whose statistics differently from previously adopted priors include information not only on smoothness but also on bibo stability the associated autocovariance defines what we call a stable spline kernel the corresponding minimum variance estimate belongs to a reproducing kernel hilbert space which is spectrally characterized compared to parametric identification techniques the impulse response of the system is searched for within an infinite dimensional space dense in the space of continuous functions overparametrization is avoided by tuning few hyperparameters via marginal likelihood maximization the proposed approach may prove particularly useful in the context of robust identification in order to obtain reduced order models by exploiting a two step procedure that projects the nonparametric estimate onto the space of nominal models the continuous time derivation immediately extends to the discrete time case on several continuous and discrete time benchmarks taken from the literature the proposed approach compares very favorably with the existing parametric and nonparametric techniques

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

subspace identification of bilinear and lpv systems for open and closed loop data in this paper we present a novel algorithm to identify lpv systems with affine parameter dependence operating under open and closed loop conditions a factorization is introduced which makes it possible to form a predictor that predicts the output which is based on past inputs outputs and scheduling data the predictor contains the lpv equivalent of the markov parameters using this predictor ideas from closed loop lti identification are developed to estimate the state sequence from which the lpv system matrices can be constructed a numerically efficient implementation is presented using the kernel method it turns out that if structure is present in the scheduling sequence the computational complexity reduces even more

non stationary stochastic embedding for transfer function estimation this paper presents a consistent framework for the quantification of noise and undermodelling errors in transfer function model estimation we use the so called stochastic embedding approach in which both noise and undermodelling errors are treated as stochastic processes in contrast to previous applications of stochastic embedding in this paper we represent the undermodelling as a multiplicative error characterised by random walk processes in the frequency domain the benefit of the present formulation is that it significantly simplifies the estimation of the parameters of the embedded process yielding a closed form expression for the model error quantification simulation and experimental examples illustrate how the random walks effectively capture typical cases of undermodelling found in practice including underdamped modes the examples also show how to use the method as a tool in the determination of model order and pole location in fixed denominator model structures

asymptotically optimal orthonormal basis functions for lpv system identification a global model structure is developed for parametrization and identification of a general class of linear parameter varying lpv systems by using a fixed orthonormal basis function obf structure a linearly parametrized model structure follows for which the coefficients are dependent on a scheduling signal an optimal set of obfs for this model structure is selected on the basis of local linear dynamic properties of the lpv system system poles that occur for different constant scheduling signals the selected obf set guarantees in an asymptotic sense the least worst case modeling error for any local model of the lpv system through the fusion of the kolmogorov n width theory and fuzzy c means clustering an approach is developed to solve the obf selection problem for discrete time lpv systems based on the clustering of observed sample system poles

analytic phase derivatives all pass filters and signals of minimum phase it is accepted knowledge that inner functions and outer functions in complex analysis correspond respectively to all pass filters and signals of minimum phase the knowledge however has not been justified for general inner and outer functions in digital signal processing the correspondence and related results are based on studies of rational functions in this paper based on the recent result on positivity of phase derivatives of inner functions we establish the theoretical foundation for all pass filters and signals of minimum phase we in particular deal with infinite blaschke products and general singular inner functions induced by singular measures a number of results known for rational functions are generalized to general inner functions both the discrete and continuous signals cases are rigorously treated

robust em kernel based methods for linear system identification recent developments in system identification have brought attention to regularized kernel based methods this type of approach has been proven to compare favorably with classic parametric methods however current formulations are not robust with respect to outliers in this paper we introduce a novel method to robustify kernel based system identification methods to this end we model the output measurement noise using random variables with heavy tailed probability density functions pdfs focusing on the laplacian and the student s t distributions exploiting the representation of these pdfs as scale mixtures of gaussians we cast our system identification problem into a gaussian process regression framework which requires estimating a number of hyperparameters of the data size order to overcome this difficulty we design a new maximum a posteriori map estimator of the hyperparameters and solve the related optimization problem with a novel iterative scheme based on the expectation maximization em method in the presence of outliers tests on simulated data and on a real system show a substantial performance improvement compared to currently used kernel based methods for linear system identification

differentiation in star invariant subspaces i boundedness and compactness abstract given a discrete set c r let r p denote the subspace of lp r generated by rational functions with poles in we determine for which s the differentiation operator d dx r p lp r is bounded or compact

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

the role of vector autoregressive modeling in predictor based subspace identification subspace identification for closed loop systems has been recently studied by several authors a class of new and consistent closed loop subspace algorithms is based on identification of a predictor model in a way similar as prediction error methods pem do experimental evidence suggests that these methods have a behavior which is very close to pem in certain examples the asymptotical statistical properties of one of these methods have been studied recently allowing to show i its relation with cca and ii that cramer rao lower bound is not reached in general very little however is known concerning their relative performance in this paper we shall discuss the link between these predictor based methods to this purpose we exploit the role which vector auto regressive with exogenous input models play in all these algorithms the results of this paper provide a unifying framework under which all these algorithms can be viewed also the link with varx modeling have important implications as to computational complexity is concerned leading to very computationally attractive implementations we also hope that this framework and in particular the relation with varx modeling followed by model reduction will turn out to be useful in future developments of subspace identification such as the quest for efficient procedures and the statistical analysis with finite data

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

maximum entropy vector kernels for mimo system identification abstract recent contributions have framed linear system identification as a nonparametric regularized inverse problem relying on l 2 type regularization which accounts for the stability and smoothness of the impulse response to be estimated these approaches have been shown to be competitive w r t classical parametric methods in this paper adopting maximum entropy arguments we derive a new l 2 penalty to do so we exploit the structure of the hankel matrix thus controlling at the same time complexity measured by the mcmillan degree stability and smoothness of the identified models as a special case we recover the nuclear norm penalty on the squared block hankel matrix in contrast with the previous literature on reweighted nuclear norm penalties our kernel is described by a small number of hyper parameters which are iteratively updated through marginal likelihood maximization constraining the structure of the kernel acts as a hyper regularizer which helps controlling the effective degrees of freedom of our estimator to optimize the marginal likelihood we adapt a scaled gradient projection sgp algorithm which is proved to be significantly computationally cheaper than other first and second order off the shelf optimization methods the paper also contains an extensive comparison with many state of the art methods on several monte carlo studies which confirms the effectiveness of our procedure

use of press residuals in dynamic system identification cross validation whereby the data is split into an estimation set and a prediction set is often used for model structure selection in dynamic system identification a related approach that simulates cross validation without requiring two sets of data is to compute the weighted residuals of the least squares estimated model that represent the true prediction errors the sum of the squared true prediction errors is defined as the press this paper will show that the computation of the press is straightforward when using an orthogonal decomposition algorithm to obtain the least squares model parameter estimates a benchmark example of ljung is used to illustrate how the press is applied for model structure selection

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

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

a smoothness priors long ar model method for spectral estimation a new smoothness priors long ar model method approach is taken to the short data span spectral estimation problem an autoregressive ar model that is relatively long compared to the data length is considered the smoothness priors are in the form of the integrated squared derivatives of the ar model whitening filter a smoothness tradeoff parameter or bayesian hyperparameter balances the tradeoff between the infidelity of the ar model to the data and the infidelity of the model to the smoothness constraint the critical computation of the likelihood of the hyperparameters of the bayesian model is realized by a constrained least squares computation numerical examples are shown the results of simulation studies using entropy comparison evaluations of the bayesian and minimum aic ar methods of spectral estimation are also shown

identification of non linear stochastic systems by state dependent parameter estimation the paper outlines how improved estimates of time variable parameters in models of stochastic dynamic systems can be obtained using recursive filtering and fixed interval smoothing techniques with the associated hyper parameters optimized by maximum likelihood based on prediction error decomposition it then shows how by exploiting special data re ordering and back fitting procedures similar recursive parameter estimation techniques can be utilized to estimate much more rapid state dependent parameter sdp variations in this manner it is possible to identify and estimate a widely applicable class of nonlinear stochastic systems as illustrated by several examples that include simulated and real data from chaotic processes finally the paper points out that such sdp models can form the basis for new methods of signal processing automatic control and state estimation for nonlinear stochastic systems

optimal time weighted h 2 model reduction for markovian jump systems this article addresses the optimal time weighted h 2 model reduction problem for markovian jump linear systems that is for a given mean square stable markovian jump system our aim is to find a mean square stable jump system of lower order such that the time weighted h 2 norm of the corresponding error system is minimised the time weighted h 2 norm of the system is first defined and then a computational method is constructed the computation requires the solution of two sets of recursive lyapunov type linear matrix equations associated with the markovian jump system to solve the optimal time weighted h 2 model reduction problem we propose a gradient flow method for its solution a necessary condition for minimality is derived and a computational procedure is provided to obtain the minimising reduced order model the necessary condition generalises the standard result for systems when markov jumps and the time weighting term do not appear finally two numerical examples are given to demonstrate the

a new kernel based approach for nonlinearsystem identification we present a novel nonparametric approach for identification of nonlinear systems exploiting the framework of gaussian regression the unknown nonlinear system is seen as a realization from a gaussian random field its covariance encodes the idea of fading memory in the predictor and consists of a mixture of gaussian kernels parametrized by few hyperparameters describing the interactions among past inputs and outputs the kernel structure and the unknown hyperparameters are estimated maximizing their marginal likelihood so that the user is not required to define any part of the algorithmic architecture e g the regressors and the model order once the kernel is estimated the nonlinear model is obtained solving a tikhonov type variational problem the hilbert space the estimator belongs to is characterized benchmarks problems taken from the literature show the effectiveness of the new approach also comparing its performance with a recently proposed algorithm based on direct weight optimization and with parametric approaches with model order estimated by aic or bic

nonparametric identification of population models via gaussian processes population models are used to describe the dynamics of different subjects belonging to a population and play an important role in drug pharmacokinetics a nonparametric identification scheme is proposed in which both the average impulse response of the population and the individual ones are modelled as gaussian stochastic processes assuming that the average curve is an integrated wiener process it is shown that its estimate is a cubic spline an empirical bayes algorithm for estimating both the average and the individual curves is worked out the model is tested on simulated data sets as well as on xenobiotics pharmacokinetic data

comparison of approximate methods for handling hyperparameters i examine two approximate methods for computational implementation of bayesian hierarchical models that is models that include unknown hyperparameters such as regularization constants and noise levels in the evidence framework the model parameters are integrated over and the resulting evidence is maximized over the hyperparameters the optimized hyperparameters are used to define a gaussian approximation to the posterior distribution in the alternative map method the true posterior probability is found by integrating over the hyperparameters the true posterior is then maximized over the model parameters and a gaussian approximation is made the similarities of the two approaches and their relative merits are discussed and comparisons are made with the ideal hierarchical bayesian solution in moderately ill posed problems integration over hyperparameters yields a probability distribution with a skew peak which causes signifi cant biases to arise in the map method in contrast the evidence fram

bayes and empirical bayes semi blind deconvolution using eigenfunctions of a prior covariance we consider the semi blind deconvolution problem i e estimating an unknown input function to a linear dynamical system using a finite set of linearly related measurements where the dynamical system is known up to some system parameters without further assumptions this problem is often ill posed and ill conditioned we overcome this difficulty by modeling the unknown input as a realization of a stochastic process with a covariance that is known up to some finite set of covariance parameters we first present an empirical bayes method where the unknown parameters are estimated by maximizing the marginal likelihood posterior and subsequently the input is reconstructed via a tikhonov estimator with the parameters set to their point estimates next we introduce a bayesian method that recovers the posterior probability distribution and hence the minimum variance estimates for both the unknown parameters and the unknown input function both of these methods use the eigenfunctions of the random process covariance to obtain an efficient representation of the unknown input function and its probability distributions simulated case studies are used to test the two methods and compare their relative performance

order estimation for subspace methods three different order estimation criteria in the context of subspace algorithms are introduced and sufficient conditions for strong consistency are derived a simulation study points to open questions

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

system identification via sparse multiple kernel based regularization using sequential convex optimization techniques model estimation and structure detection with short data records are two issues that receive increasing interests in system identification in this paper a multiple kernel based regularization method is proposed to handle those issues multiple kernels are conic combinations of fixed kernels suitable for impulse response estimation and equip the kernel based regularization method with three features first multiple kernels can better capture complicated dynamics than single kernels second the estimation of their weights by maximizing the marginal likelihood favors sparse optimal weights which enables this method to tackle various structure detection problems e g the sparse dynamic network identification and the segmentation of linear systems third the marginal likelihood maximization problem is a difference of convex programming problem it is thus possible to find a locally optimal solution efficiently by using a majorization minimization algorithm and an interior point method where the cost of a single interior point iteration grows linearly in the number of fixed kernels monte carlo simulations show that the locally optimal solutions lead to good performance for randomly generated starting points

pole assignment via the schur form abstract we propose an algorithm for the state feedback pole assignment problem the algorithm is the first of its kind making direct use of the schur form and minimizing the departure from normality of the closed loop poles for a given first schur vector x 1 the robust pole assignment problem can then be solved via choosing x 1 optimally several numerical examples were presented to illustrate the feasibility of the algorithm

on kernel design for regularized lti system identification abstract there are two key issues for the kernel based regularization method one is how to design a suitable kernel to embed in the kernel the prior knowledge of the lti system to be identified and the other one is how to tune the kernel such that the resulting regularized impulse response estimator can achieve a good bias variance tradeoff in this paper we focus on the issue of kernel design depending on the type of the prior knowledge we propose two methods to design kernels one is from a machine learning perspective and the other one is from a system theory perspective we also provide analysis results for both methods which not only enhances our understanding for the existing kernels but also directs the design of new kernels

on the estimation of transfer functions regularizations and gaussian processes revisited intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques we revisit the old problem of transfer function estimation from input output measurements we formulate a classical regularization approach focused on finite impulse response fir models and find that regularization is necessary to cope with the high variance problem this basic regularized least squares approach is then a focal point for interpreting other techniques like bayesian inference and gaussian process regression the main issue is how to determine a suitable regularization matrix bayesian prior or kernel several regularization matrices are provided and numerically evaluated on a data bank of test systems and data sets our findings based on the data bank are as follows the classical regularization approach with carefully chosen regularization matrices shows slightly better accuracy and clearly better robustness in estimating the impulse response than the standard approach the prediction error method maximum likelihood pem ml approach if the goal is to estimate a model of given order as well as possible a low order model is often better estimated by the pem ml approach and a higher order model is often better estimated by model reduction on a high order regularized fir model estimated with careful regularization moreover an optimal regularization matrix that minimizes the mean square error matrix is derived and studied the importance of this result lies in that it gives the theoretical upper bound on the accuracy that can be achieved for this classical regularization approach

subspace identification of hammerstein systems using least squares support vector machines this paper presents a method for the identification of multiple input multiple output mimo hammerstein systems for the goal of prediction the method extends the numerical algorithms for subspace state space system identification n4sid mainly by rewriting the oblique projection in the n4sid algorithm as a set of componentwise least squares support vector machines ls svms regression problems the linear model and static nonlinearities follow from a low rank approximation of a matrix obtained from this regression problem

regularization networks fast weight calculation via kalman filtering regularization networks are nonparametric estimators obtained from the application of tychonov regularization or bayes estimation to the hypersurface reconstruction problem their main drawback back is that the computation of the weights scales as o n sup 3 where n is the number of data in this paper we show that for a class of monodimensional problems the complexity can be reduced to o n by a suitable algorithm based on spectral factorization and kalman filtering moreover the procedure applies also to smoothing splines

brief augmented gradient flows for on line robust pole assignment via state and output feedback this paper is concerned with robust pole assignment in synthesis of linear control systems via state and output feedbacks first both the pole assignment and robustness requirements are appropriately formulated as two optimization problems then gradient flow models are developed for the on line computation of feedback gain matrices that result in robust pole assignment by solving these two optimization problems a technique is introduced to facilitate the real time matrix inverse involved for realizing the gradient flow models the resulting augmented gradient flows have desired convergence properties simulation results are included to show the effectiveness of the proposed approach

input estimation in nonlinear dynamical systems using differential algebra techniques the paper considers the problem of estimating the unknown input of a nonlinear dynamical system described by polynomial or rational differential equations from a finite set of noisy output samples without additional information this problem is ill posed since the unknown function may belong to an arbitrary infinite dimensional space we tackle this difficulty by designing a novel class of fast regularization algorithms that relies upon differential algebra techniques monte carlo studies are used to demonstrate the effectiveness of the new approach

neurodynamics based robust pole assignment for high order descriptor systems in this paper a neurodynamic optimization approach is proposed for synthesizing high order descriptor linear systems with state feedback control via robust pole assignment with a new robustness measure serving as the objective function the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem a neurodynamic optimization approach is applied and shown to be capable of maximizing the robust stability margin for high order singular systems with guaranteed optimality and exact pole assignment two numerical examples and vehicle vibration control application are discussed to substantiate the efficacy of the proposed approach

a scaled gradient projection method for bayesian learning in dynamical systems a crucial task in system identification problems is the selection of the most appropriate model class and is classically addressed resorting to cross validation or using order selection criteria based on asymptotic arguments as recently suggested in the literature this can be addressed in a bayesian framework where model complexity is regulated by a few hyperparameters which can be estimated via marginal likelihood maximization it is thus of primary importance to design effective optimization methods to solve the corresponding optimization problem if the unknown impulse response is modeled as a gaussian process with a suitable kernel the maximization of the marginal likelihood leads to a challenging nonconvex optimization problem which requires a stable and effective solution strategy in this paper we address this problem by means of a scaled gradient projection algorithm in which the scaling matrix and the steplength parameter play a crucial role to provide a meaningful solution in a computatio

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

can the strengths of aic and bic be shared a conflict between model indentification and regression estimation a traditional approach to statistical inference is to identify the true or best model first with little or no consideration of the specific goal of inference in the model identification stage can the pursuit of the true model also lead to optimal regression estimation in model selection it is well known that bic is consistent in selecting the true model and aic is minimax rate optimal for estimating the regression function a recent promising direction is adaptive model selection in which in contrast to aic and bic the penalty term is data dependent some theoretical and empirical results have been obtained in support of adaptive model selection but it is still not clear if it can really share the strengths of aic and bic model combining or averaging has attracted increasing attention as a means to overcome the model selection uncertainty can bayesian model averaging be optimal for estimating the regression function in a minimax sense we show that the answers to these questions are basically in the negative for any model selection criterion to be consistent it must behave suboptimally for estimating the regression function in terms of minimax rate of covergence and bayesian model averaging cannot be minimax rate optimal for regression estimation

transfer function and transient estimation by gaussian process regression in the frequency domain inspired by the recent promising developments of bayesian learning techniques in the context of system identification this paper proposes a transfer function estimator based on gaussian process regression contrary to existing kernel based impulse response estimators a frequency domain approach is adopted this leads to a formulation and implementation which is seamlessly valid for both continuous and discrete time systems and which conveniently enables the selection of the frequency band of interest a pragmatic approach is proposed in an output error framework from sampled input and output data the transient is dealt with by estimating it simultaneously with the transfer function modelling the transfer function and the transient as gaussian processes allows for the incorporation of relevant prior knowledge on the system in the form of suitably designed kernels the ss stable spline and dc diagonal correlated kernels from the literature are translated to the frequency domain and are proven to impose the stability of the estimated transfer function specifically the estimates are shown to be stable rational functions in the frequency variable the hyperparameters of the kernel are tuned via marginal likelihood maximisation the comparison between the proposed method and three existing methods from the literature the regularised finite impulse response rfir estimator the local polynomial method lpm and the local rational method for frequency response function estimation is illustrated on simulations on multiple case studies

an lmi approach to control oriented identification and model in validation of lpv systems this note proposes a control oriented identification framework for a class of linear parameter varying systems that takes into account both the dependence of part of the model on time varying parameters as well as the possible existence of a nonparametric component the main results of the note show that the problems of obtaining and validating a model for these systems can be recast as linear matrix inequality feasibility problems moreover as the information is completed the algorithm is shown to converge in the l sub 2 induced topology to the actual plant additional results include deterministic bounds on the identification error these results are illustrated with a practical example arising in the context of active vision

approaches to robust pole assignment abstract robust pole assignment is a non linear optimization problem in many variables we describe numerical methods for determining robust or well conditioned so lutions to the problem of pole assignment by state feedback the solutions are chosen to minimize various objective functions based on the condition number of the eigenvector matrix careful choice of parametrization and objective function avoids singularities and artificial variable constraints explicit formulae for the gradient and hessian permit rigorous stopping criteria and rapid local convergence several computational examples are included

new aspects of beurling lax shift invariant subspaces in terms of forward and backward shift invariant subspaces we characterize functions in hardy spaces or analytic signals in the terminology of signal analysis through multiplications between analytic and conjugate analytic signals as applications we give some necessary and sufficient conditions for solutions of the bedrosian equation h fg f hg when f or g is a bandlimited signal we also solve the band preserving problem by means of the shift invariant subspace method which establishes some necessary and sufficient conditions on the functions f that make fg have bandwidth within that of the function g

robust pole assignment for synthesizing feedback control systems using recurrent neural networks this paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback the problem is formulated as a pseudoconvex optimization problem with robustness measure i e the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment two coupled recurrent neural networks are applied for solving the formulated problem in real time in contrast to existing approaches the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

on asymptotic properties of hyperparameter estimators for kernel based regularization methods the kernel based regularization method has two core issues kernel design and hyperparameter estimation in this paper we focus on the second issue and study the properties of several hyperparameter estimators including the empirical bayes eb estimator two stein s unbiased risk estimators sure one related to impulse response reconstruction and the other related to output prediction and their corresponding oracle counterparts with an emphasis on the asymptotic properties of these hyperparameter estimators to this goal we first derive and then rewrite the first order optimality conditions of these hyperparameter estimators leading to several insights on these hyperparameter estimators then we show that as the number of data goes to infinity the two sures converge to the best hyperparameter minimizing the corresponding mean square error respectively while the more widely used eb estimator converges to another best hyperparameter minimizing the expectation of the eb estimation criterion this indicates that the two sures are asymptotically optimal in the corresponding mse senses but the eb estimator is not surprisingly the convergence rate of two sures is slower than that of the eb estimator and moreover unlike the two sures the eb estimator is independent of the convergence rate of t n to its limit where is the regression matrix and n is the number of data a monte carlo simulation is provided to demonstrate the theoretical results

deadzone compensation in motion control systems using neural networks a compensation scheme is presented for general nonlinear actuator deadzones of unknown width the compensator uses two neural networks nns one to estimate the unknown deadzone and another to provide adaptive compensation in the feedforward path the compensator nn has a special augmented form containing extra neurons whose activation functions provide a jump function basis set for approximating piecewise continuous functions rigorous proofs of closed loop stability for the deadzone compensator are provided and yield tuning algorithms for the weights of the two nns the technique provides a general procedure for using nns to determine the preinverse of an unknown right invertible function

a transformation approach to stochastic model reduction a new and direct approach to stochastic model reduction is developed the order reduction algorithm is obtained by establishing an equivalence between canonical correlation analysis and solutions to algebraic riccati equations also the concept of balanced stochastic realization bsr plays a fundamental role asymptotic stability of the reduced order realization is established and spectral domain interpretations for the bsr are given

the bedrosian identity for hp functions abstract we establish a necessary and sufficient condition for f h p r g h q r with p 1 q 1 1 to satisfy the bedrosian identity h f g f h g where h denotes the hilbert transform as applications we prove the bedrosian theorem for this identity and give a characterization of f satisfying the identity when g is a finite linear combination of complex sinusoids we also show that if f is of low fourier frequency then it is necessary for g to have high fourier frequency in order to satisfy the bedrosian identity

a smoothness priors state space modeling of time series with trend and seasonality abstract a smoothness priors modeling of time series with trends and seasonalities is shown an observed time series is decomposed into local polynomial trend seasonal globally stationary autoregressive and observation error components each component is characterized by an unknown variance white noise perturbed difference equation constraint the constraints or bayesian smoothness priors are expressed in state space model form trading day factors are also incorporated in the model a kalman predictor yields the likelihood for the unknown variances hyperparameters likelihoods are computed for different constraint order models in different subsets of constraint equation model classes akaike s minimum aic procedure is used to select the best model fitted to the data within and between the alternative model classes smoothing is achieved by using a fixed interval smoother algorithm examples are shown

brief a gradient flow approach to on line robust pole assignment for synthesizing output feedback control systems pole assignment is a basic design method for synthesis of feedback control systems in this paper a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems the proposed approach is shown to be capable of synthesizing linear output feedback control systems via on line robust pole assignment convergence of the gradient flow can be guaranteed moreover with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed loop control system based on the gradient flow is globally exponentially stable these desired properties make it possible to apply the proposed approach to slowly time varying linear control systems simulation results are shown to demonstrate the effectiveness and advantages of the proposed approach