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

identification of composite local linear state space models using a projected gradient search an identification method is described to determine a weighted combination of local linear state space models from input and output data normalized radial basis functions are used for the weights

on the interpretation and identification of dynamic takagi sugeno fuzzy models dynamic takagi sugeno fuzzy models are not always easy to interpret in particular when they are identified from experimental data it is shown that there exists a close relationship between dynamic takagi sugeno fuzzy models and dynamic linearization when using affine local model structures which suggests that a solution to the multiobjective identification problem exists however it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes due to the multiobjective nature of the identification problem studied here special considerations must be made during model structure selection experiment design and identification in order to meet both objectives some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied these include constrained and regularized identification and locally weighted identification their usefulness in the present context is illustrated by examples

strong stability of a class of difference equations of continuous time and structured singular value problem abstract this article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters i i 1 2 k the characteristic quasipolynomial of such an equation is a multilinear function of e i s it is known that the characteristic quasipolynomial of any difference equation set in the form of one delay per scalar channel odpsc model is also in such a multilinear form however it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any odpsc difference equation set the equivalence between local strong stability the exponential stability of a fixed set of rationally independent delays and the stability for all positive delays is shown and relations with the structured singular value problem are presented a procedure to determine strong stability in the special case of up to three independent delay parameters in finite steps is developed this procedure means that the structured singular value problem in the case of up to three scalar complex uncertain blocks can be solved in finite steps

an algorithm of uniform ultimate boundedness for a class of switched linear systems uniform ultimate boundedness of a class of switched linear systems is studied a switched linear system in this class consists of m subsystems and none of the individual subsystems need to be stabilizable the switched linear system is shown to be uniformly ultimately bounded for any pre given bound if the union of individual controllable subspaces covers the entire state space an algorithm for guaranteeing uniform ultimate boundedness is given to provide the design of continuous controllers and the switching strategy

model structure selection by cross validation two criteria for choosing between different model structures are proposed their derivation is within a natural cross validatory assessment context and is fairly assumption free in particular the two criteria can be used for discriminating between non nested model structures and more importantly the true system is not required to belong to the considered set of models should the true system belong to the model set the two proposed criteria will asymptotically reduce to some well known structure selection criteria this is believed to be a desirable feature of our proposals on the other hand it provides a nice cross validation interpretation of some well known model structure selection rules also the cross validation interpretation helps one to choose which criteria to use in a given application the paper also has a second purpose somewhat decoupled from that mentioned above it contains an extensive survey of the literature that is useful in its own right

forward and backward least angle regression for nonlinear system identification a forward and backward least angle regression lar algorithm is proposed to construct the nonlinear autoregressive model with exogenous inputs narx that is widely used to describe a large class of nonlinear dynamic systems the main objective of this paper is to improve model sparsity and generalization performance of the original forward lar algorithm this is achieved by introducing a replacement scheme using an additional backward lar stage the backward stage replaces insignificant model terms selected by forward lar with more significant ones leading to an improved model in terms of the model compactness and performance a numerical example to construct four types of narx models namely polynomials radial basis function rbf networks neuro fuzzy and wavelet networks is presented to illustrate the effectiveness of the proposed technique in comparison with some popular methods

regularization aspects in continuous time model identification this paper presents an analysis of some regularization aspects in continuous time model identification the study particulary focuses on linear filter methods and shows that filtering the data before estimating their derivatives corresponds to a regularized signal derivative estimation by minimizing a compound criterion whose expression is given explicitly a new structure based on a null phase filter corresponding to a true regularization filter is proposed and allows to discuss the filter phase effects on parameter estimation by comparing its performances with those of the poisson filter based methods based on this analysis a formulation of continuous time model identification as a joint system input output signal and model parameter estimation is suggested in this framework two linear filter methods are interpreted and a compound criterion is proposed in which the regularization is ensured by a model fitting measure resulting in a new regularization filter structure for signal estimation

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

on tikhonov regularization bias and variance in nonlinear system identification abstract regularization is a general method for solving ill posed and ill conditioned problems traditionally ill conditioning in system identification problems is approached using regularization methods such as ridge regression and principal component regression in this work it is argued that the tikhonov regularization method is a powerful alternative for regularization of nonlinear system identification problems by introducing smoothness of the model as a prior its properties is discussed in terms of an analysis of bias and variance and illustrated by a semirealistic simulation example

asymptotic properties of least squares estimates of hammerstein wiener models this paper investigates the asymptotic properties of least squares estimates of hammerstein wiener model structures and in doing so establishes consistency and asymptotic normality under fairly mild conditions on the additive noise process the inputs and the static non linearities in relation to the asymptotic distributional results a consistent procedure for the estimation of the asymptotic variance of the parameter estimates is provided a key theme of this paper is to demonstrate how recent results from the econometrics literature may be employed in an engineering setting in this respect the hammerstein wiener model structure serves as a demonstration example a simulation study complements the theoretical findings

identification of non linear systems using empirical data and prior knowledge an optimization approach abstract the choice of a parametric model structure in empirical and semi empirical non linear modeling is usually viewed as an important and critical step however it is known that by augmenting the least squares identification criterion with a term that imposes a penalty on the non smoothness of the model an optimal non parametric model can be found explicitly the optimal non parametric model will depend on the particular form of the penalty which can be looked upon as a priori knowledge or the desired properties of the model in this paper these results are extended in several directions i we show how useful types of prior knowledge other than smoothness can be included as a term in the criterion or as a constraint and how this influences the optimal model ii dynamic models and a general prediction error penalty are considered iii we present a practical numerical procedure for the identification of a close to optimal semi parametric model the numerical approach is motivated by the difficulty of deriving the optimal non parametric model if there are complicated constraints or penalty terms in the criterion and finally iv we discuss determination of the appropriate model complexity through selecting weights on the different penalties on the basis of empirical data since the optimal non parametric model is identified using an augmented optimization criterion and all prior knowledge and desired model properties may be specified through the augmented optimization criterion it is the choice of this criterion that is critical in this approach this elevates the empirical and semi empirical modeling problems to a more transparent and engineering friendly level than is achieved by directly specifying a parametric model structure hence our results shed some more light on modern non linear empirical modeling approaches like radial basis functions splines and neural networks in addition to providing a fundamental insight into the role of different kinds of prior knowledge this high level formulation is also attractive from a practical point of view as it lies closer to engineering thinking and less guesswork is required the flexibility and power of this approach are illustrated with a semi realistic simulation example

on singular fibres of lagrangian fibrations over holomorphic symplectic manifolds we classify singular fibres over general points of the discriminant locus of projective lagrangian fibrations over 4 dimensional holomorphic symplectic manifolds the singular fibre f is the following either one f is isomorphic to the product of an elliptic curve and a kodaira singular fibre up to finite unramified covering or f is a normal crossing variety consisting of several copies of a minimal elliptic ruled surface of which the dual graph is dynkin diagram of type a n tilde a n or tilde d n moreover we show all types of the above singular fibres actually occur

reachable set estimation for markov jump lpv systems with time delays abstract this paper investigates the reachable set estimation problem for discrete time markov jump lpv systems with time varying delays and bounded disturbance the main consideration is that under zero initial conditions how to obtain a bound set as small as possible that includes system states based on this by applying a novel summation inequality integrated with the reciprocally convex approach under the framework of the lyapunov functional method the delay dependent conditions are provided to guarantee the presence of an ellipsoid that bounds the system state in the existence of bounded disturbances some derived conditions expressed by linear matrix inequalities can be solved via utilizing different computational tools and the minimum possible ellipsoidal bound can also be determined additionally the obtained results are extensively used in the case with partially known transition probability and some conditions with more universality are derived finally a numerical example is given to illustrate the effectiveness of the results

on lagrangian fibrations by jacobians i let y p n be a flat family of reduced gorenstein curves such that the compactified relative jacobian x j d y p n is a lagrangian fibration we prove that x is a beauville mukai integrable system if n 3 4 or 5 and the curves are irreducible and non hyperelliptic we also prove that x is a beauville mukai system if n 3 d is odd and the curves are canonically positive 2 connected hyperelliptic curves

higher direct images of dualizing sheaves of lagrangian fibrations let f x s be a lagrangian fibration between projective varieties we prove that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i i s if s is smooth suppose that x is an irreducible symplectic manifold or a certain moduli space of semistable torsion free sheaves on a k 3 surface the hodge numbers satisfy h p q s h p q inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i where n dim s if s inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i and x is an irreducible symplectic manifold there exists a hypersurface m f of the kuranishi space of x such that every member of the kuranishi family over m f admits a lagrangian fibration over inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i

stability crossing set for systems with two scalar delay channels the characteristic function of a system with three scalar delay channels contains cross terms of different delays this article studies the parameterization and geometric structure of the stability crossing set the set of delay combinations with at least one characteristic root on the imaginary axis for such systems understanding the structure of this set is crucial to the identification of stable regions in the delay parameter space using the d subdivision method the presence of the cross terms significantly complicates the analysis and requires a quite different method than the case without these cross terms and it involves more numerical computation

on different facets of regularization theory this review provides a comprehensive understanding of regularization theory from different perspectives emphasizing smoothness and simplicity principles using the tools of operator theory and fourier analysis it is shown that the solution of the classical tikhonov regularization problem can be derived from the regularized functional defined by a linear differential integral operator in the spatial fourier domain state of the art research relevant to the regularization theory is reviewed covering occam s razor minimum length description bayesian theory pruning algorithms informational entropy theory statistical learning theory and equivalent regularization the universal principle of regularization in terms of kolmogorov complexity is discussed finally some prospective studies on regularization theory and beyond are suggested

characteristic foliation on the discriminant hypersurface of a holomorphic lagrangian fibration we give a kodaira type classification of general singular fibers of a holomorphic lagrangian fibration in fujiki s class c our approach is based on the study of the characteristic vector field of the discriminant hypersurface which naturally arises from the defining equation of the hypersurface via the symplectic form as an application we show that the characteristic foliation of the discriminant hypersurface has algebraic leaves which are either rational curves or smooth elliptic curves

a weighted view on the partial least squares algorithm in this paper it is shown that the partial least squares pls algorithm for univariate data is equivalent to using a truncated cayley hamilton polynomial expression of degree email protected email protected r for the matrix inverse x tx email protected r r x r which is used to compute the least squares ls solution furthermore the a coefficients in this polynomial are computed as the optimal ls solution minimizing parameters to the prediction error the resulting solution is non iterative the solution can be expressed in terms of a matrix inverse and is given by b p l s k a k a tx txk a 1k a tx ty where k email protected r r x a is the controllability krylov matrix for the pair x tx x ty the iterative pls algorithm for computing the orthogonal weighting matrix w a as presented in the literature is shown here to be equivalent to computing an orthonormal basis using e g the qr algorithm for the column space of k a the pls solution can equivalently be computed as b p l s w a w a tx txw a 1w a tx ty where w a is the q orthogonal matrix from the qr decomposition k a w ar furthermore we have presented an optimal and non iterative truncated cayley hamilton polynomial ls solution for multivariate data the free parameters in this solution is found as the minimizing solution of a prediction error criterion

on distributed delay in linear control laws part i discrete delay implementations this note proposes two approaches to approximate distributed delay in linear control laws and furthermore to implement it in the z domain and in the s domain the h sup spl infin norm of the approximation error converges to 0 when the number n of approximation steps approaches spl infin hence the instability problem due to the approximation error which has been widely studied in recent years does not exist provided that n is large enough moreover the static gain is guaranteed so that no extra efforts are needed to retain the steady state performance as by products two new formulas for the forward and backward rectangular rules are obtained these formulas are more accurate than the conventional ones when the integrand has an exponential term

stability analysis for delayed neural networks with an improved general free matrix based integral inequality this paper revisits the problem of stability analysis for neural networks with a time varying delay an improved general free matrix based fmb integral inequality is proposed with an undetermined number m compared with the conventional fmb ones the improved inequality involves a much smaller number of free matrix variables in particular the improved fmb integral inequality is expressed in a concrete form for any value of m by employing the new inequality with a properly constructed lyapunov krasovskii functional a new stability condition is derived for neural networks with a time varying delay two commonly used numerical examples are given to show strong competitiveness of the proposed approach in both the conservatism and computation burdens

l2 l consensus of stochastic delayed multi agent systems with adt switching interaction topologies abstract this paper investigates the l 2 l consensus for a class of stochastic delayed multi agent systems subject to switching interaction topologies via utilizing an observer based control protocol the switching between the interaction topologies is assumed to have the average dwell time adt constraint with the aid of a simple model transformation the l 2 l consensus issue is transformed into the problem of weighted stochastic l 2 l control analysis results on the weighted stochastic l 2 l control are proposed by constructing lyapunov krasovskii functional and employing stochastic analysis methods then an approach is developed to determine the desired observer based consensus protocol finally an illustrative numerical example is given to show the usefulness of our design method

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography part ii for imaging problems in which numerical solutions need to be computed for both the inverse and the underlying forward problems discretization can be a major factor that determines the accuracy of imaging in this work we analyze the effect of discretization on the accuracy of fluorescence diffuse optical tomography we model the forward problem by a pair of diffusion equations at the excitation and emission wavelengths and consider a finite element discretization method for the numerical solution of the forward problem for the inverse problem we use an optimization framework which allows incorporation of a priori information in the form of zeroth and first order tikhonov regularization terms next we convert the inverse problem into a variational problem and use galerkin projection to discretize the inverse problem following the discretization we analyze the error in reconstructed images due to the discretization of the forward and inverse problems and present two theorems which point out the factors that may lead to high error such as the mutual dependence of the forward and inverse problems the number of sources and detectors their configuration and their positions with respect to fluorophore concentration and the formulation of the inverse problem finally we demonstrate the results and implications of our error analysis by numerical experiments in the second part of the paper we apply our results to design novel adaptive discretization algorithms

a homotopy approach to improving pem identification of armax models homotopy methods are applied to the non convex optimization problem that arises in prediction error estimation using armax model structures a concrete algorithm is proposed and its performance is studied by monte carlo simulation

identification of parameters in distributed parameter systems by regularization identification of spatially varying parameters in distributed parameter systems from noisy data is an ill posed problem the concept of regularization widely used in solving linear fredholm integral equations is developed for the identification of parameters in distributed parameter systems a general regularization identification theory is first presented and then applied to the identification of parabolic systems the performance of the regularization identification method is evaluated by numerical experiments on the identification of a spatially varying diffusivity in the diffusion equation