generalised linear model selection by the predictive least quasi deviance criterion we consider the problem of selecting a model with the best predictive ability in a class of generalised linear models a predictive least quasi deviance criterion is proposed to measure the predictive ability of a model this criterion is obtained by applying the idea of the predictive minimum description length principle and the theory of quasi likelihood functions the resulting predictive quasi deviance function is an extension of the predictive stochastic complexity of the model under rather weak conditions the predictive least quasi deviance method is shown to be consistent in the sense that the probability of selecting the right model converges to one as the number of observations goes to infinity also we show that the selected model converges to the optimal model in expectation the method is then modified for finite sample applications examples and simulation results are presented

stabilization of singularly perturbed fuzzy systems this paper presents some novel results for stabilizing singularly perturbed sp nonlinear systems with guaranteed control performance by using takagi sugeno fuzzy model we construct the sp fuzzy spf systems the corresponding fuzzy slow and fast subsystems of the original spf system are also obtained two fuzzy control designs are explored in the first design method we propose the composite fuzzy control to stabilize the spf subsystem with h sup spl infin control performance based on the lyapunov stability theorem the stability conditions are reduced to the linear matrix inequality lmi problem the composite fuzzy control will stabilize the original sp nonlinear systems for all spl epsiv spl isin 0 spl epsiv sup and the upper bound spl epsiv sup can be determined for the second design method we present a direct fuzzy control scheme to stabilize the sp nonlinear system with h sup spl infin control performance by utilizing the lyapunov stability theorem the direct fuzzy control can guarantee the stability of the original sp nonlinear systems for a given interval spl epsiv spl isin spl epsiv spl epsiv the stability conditions are also expressed in the lmis two sp nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes

non linear observer design by transformation into a generalized observer canonical form an observer design method for a certain class of non linear single output systems is introduced the characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non linear system is approximated by a linear one the present paper deals with the derivation of a transformation of the considered non linear system into a generalized observer canonical form gocf which enables a systematic observer design similar to the linear one based on the well known linear observer canonical form to assign conditions for its existence the transformation into the gocf is carried out in two steps via a generalized observability canonical form gobcf in contrast to previous forms used for linear systems the two non linear canonical forms presented here also depend on the time derivatives of the input variables this means that the resulting observer has to be supplied not only with the input and output variables of the given system but also with deri

a sufficient condition for stability of a polytope of matrices abstract in this paper we study the stability of interval dynamical systems a sufficient condition for the stability of a polytope of matrices which is shown to be necessary and sufficient for a certain class of matrices is obtained the results developed can also be applied to the stability of a positive cone of matrices and sufficient conditions for the stability of interval dynamical systems are obtained a relationship between real parts of eigenvalues and matrix measures is also presented

recursive estimation of autoregressions this paper is concerned with the recursive estimation of autoregressive models in particular the realtime determination of the order of such a specification a model selection criterion based on the minimum description length principle due to rissanen is discussed and strong consistency in the stationary situation is shown alternative criteria are also considered and modifications required to introduce forgetting when the procedures are implemented in the non stationary case are presented some simulation evidence on the performance of the criteria when applied to stationary and non stationary processes is given

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

observers for lipschitz nonlinear systems this paper presents some fundamental insights into observer design for the class of lipschitz nonlinear systems the stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix the correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented these conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix the eigenvalues have to be located sufficiently far out into the left half plane and the eigenvectors also have to be sufficiently well conditioned for ensuring asymptotic stability based on these results a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

structure selection for bounded parameter models consistency conditions and selection criterion strong consistency conditions for structure selection in bounded parameter models are studied a certain robust selection criterion based on the volume of the exact parameter bounding polytope is proposed for linear regression models the effectiveness of the polytope volume criterion is demonstrated on a model nonlinear in its variables but linear in its parameters its strong consistency is proved for a large class of noise distributions the usual assumptions on the noise namely independence constant variance or martingale difference properties need not be made but asymptotic independence is assumed

model selection and the principle of minimum description length this article reviews the principle of minimum description length mdl for problems of model selection by viewing statistical modeling as a means of generating descriptions of observed data the mdl framework discriminates between competing models based on the complexity of each description this approach began with kolmogorov s theory of algorithmic complexity matured in the literature on information theory and has recently received renewed attention within the statistics community here we review both the practical and the theoretical aspects of mdl as a tool for model selection emphasizing the rich connections between information theory and statistics at the boundary between these two disciplines we find many interesting interpretations of popular frequentist and bayesian procedures as we show mdl provides an objective umbrella under which rather disparate approaches to statistical modeling can coexist and be compared we illustrate the mdl principle by considering problems in regression nonpar

density estimation by stochastic complexity the results by p hall and e j hannan 1988 on optimization of histogram density estimators with equal bin widths by minimization of the stochastic complexity are extended and sharpened in two separate ways as the first contribution two generalized histogram estimators are constructed the first has unequal bin widths which together with the number of the bins are determined by minimization of the stochastic complexity using dynamic programming the other estimator consists of a mixture of equal bin width estimators each of which is defined by the associated stochastic complexity as the main contribution in the present work two theorems are proved which together extend the universal coding theorems to a large class of data generating densities the first gives an asymptotic upper bound for the code redundancy in the order of magnitude achieved with a special predictive type of histogram estimator which sharpens a related bound the second theorem states that this bound cannot be improved upon by any code whatsoever

testing the order of a model this paper deals with order identification for nested models in the i i d framework we study the asymptotic efficiency of two generalized likelihood ratio tests of the order they are based on two estimators which are proved to be strongly consistent a version of stein s lemma yields an optimal underestimation error exponent the lemma also implies that the overestimation error exponent is necessarily trivial our tests admit non trivial underestimation error exponents the optimal underestimation error exponent is achieved in some situations the overestimation error can decay exponentially fast with respect to a positive power of the number of observations these results are proved under mild assumptions by relating the underestimation resp overestimation error to large resp moderate deviations of the log likelihood process in particular it is not necessary that the classical cramer condition be satisfied namely the log densities are not required to admit every exponential moment three benchmark examples with specific difficulties location mixture of normal distributions abrupt changes and various regressions are detailed so as to illustrate the generality of our results

comment on on sufficient conditions for the stability of interval matrices abstract some new sufficient conditions for the stability of interval matrices were given by argoun 1986 these conditions however are incorrect

stochastic complexity and modeling on demontre un theoreme fondamental qui donne une borne inferieure pour la longueur de code et donc pour les erreurs de prediction on definit les notions d information a priori et d information utile dans les donnees

complexity of simple nonlogarithmic loss functions the loss complexity for nonlogarithmic loss functions is defined analogously to the stochastic complexity for logarithmic loss functions such that its mean provides an achievable lower bound for estimation the mean taken with respect to the worst case data generating distribution the loss complexity also provides a lower bound for the worst case mean prediction error for all predictors for the important spl alpha loss functions y spl circ y sup spl alpha where y y spl circ denotes the prediction or fitting error and spl alpha is in the interval an accurate asymptotic formula for the loss complexity is given

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

determining a portfolio of linear time series models on applique les concepts de degre d evidence suggeres par jeffreys 1961 au probleme de la determination de l ordre dans des modeles de series temporelles lineaires

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

relations between information criteria for model structure selection part 3 strong consistency of the predictive least squares criterion the strong consistency of the predictive least squares pls structure selection criterion is proved for arma processes the advantage of the pls criterion defined by rissanen and wertz 1985 over the bic or aic criteria is that it is an online information criterion obtained by simple calculation the strong consistency is proved for the case of the maximum likelihood estimator while in simulations the likelihood estimator is substituted by its recursive maximum likelihood estimator approximation repeated simulations show the small sample comparison of the pls and bic criteria

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

error exponents for ar order testing this paper is concerned with error exponents in testing problems raised by autoregressive ar modeling the tests to be considered are variants of generalized likelihood ratio testing corresponding to traditional approaches to autoregressive moving average arma modeling estimation in several related problems such as markov order or hidden markov model order estimation optimal error exponents have been determined thanks to large deviations theory ar order testing is specially challenging since the natural tests rely on quadratic forms of gaussian processes in sharp contrast with empirical measures of markov chains the large deviation principles ldps satisfied by gaussian quadratic forms do not always admit an information theoretic representation despite this impediment we prove the existence of nontrivial error exponents for gaussian ar order testing and furthermore we exhibit situations where the exponents are optimal these results are obtained by showing that the log likelihood process indexed by ar models of a given order satisfy an ldp upper bound with a weakened information theoretic representation

h synthesis of unknown input observers for non linear lipschitz systems the problem of unknown input observer design for non linear lipschitz systems is considered a new dynamic framework which is a generalization of previously used linear unknown input observers is introduced the additional degrees of freedom offered by this dynamic framework are used to deal with the lipschitz non linearity the necessary and sufficient condition that ensures asymptotic convergence of the new observer is presented and the equivalence between this condition and an h optimal control problem which satisfies the standard regularity assumptions in the h optimization theory is shown based on these results a design procedure that is solvable using commercially available software is presented a simulation example is given to illustrate the proposed design

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

observer design for systems with multivariable monotone nonlinearities globally convergent observers are designed for a class of systems with multivariable nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a state dependent multivariable nonlinearity we first extend an earlier design automatica 37 12 2001 1923 to multivariable nonlinearities satisfying an analog of the scalar nondecreasing property next we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system this relaxed design renders the feasibility conditions less restrictive and widens the applicability of the observer as illustrated with examples finally output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters

a method for autoregressive moving average estimation summary the problem considered is that of estimating an autoregressive moving average system including estimating the degrees of the autoregressive and moving average lag operators the basic method is that introduced by hannan rissanen 1982 however that method may sometimes overestimate the degrees and modifications are here introduced to correct this the problem is itself due to the use of a long autoregression of order clog t when t is large in the first stage of the process the effect of this is investigated and in particular its effect on the speed of convergence of the estimates

strongly consistent estimation of the order of stochastic control systems carma model abstract in this paper a variant of the plc predictive least squares criterion for order estimation is combined with an adaptive control strategy and applied to multidimensional carma systems it is shown that with this combination we can estimate recursively and in a strongly consistent way both the order and coefficients of the controlled system while achieving asymptotically optimal cost

nonlinear state observation using h sub spl infin filtering riccati design the authors propose an observer for continuous time nonlinear systems the observer gain is computed by a riccati differential equation similar to the extended kalman filter they prove that under certain conditions the proposed observer is an exponential observer by choosing an appropriate lyapunov function furthermore the authors explore some important relations of the proposed observer to robust control theory and h sub spl infin filtering to examine the practical usefulness of the proposed observer they applied it to an induction motor for the estimation of the rotor flux and the angular velocity

ar infinity estimation and nonparametric stochastic complexity let h be the transfer function of a linear stochastic system such that h and its inverse are in h sup infinity d writing the system as an ar infinity system the best ar k approximation of the system is estimated using the method of least squares a useful representation theorem for the parameter estimation error is presented the effect of undermodeling and parameter uncertainty due to estimation on honest prediction and the optimal choice of k are questioned this question is answered and the result is applied to the ar approximation of arma systems the excess of the mean of the nonparametric stochastic complexity with respect to the ar class of an arma system with zeros less than 1 beta in moduli is found asymptotically to be less than sigma sup 2 log sup 2 n log beta after n samples

recursive estimation of linear systems on compare par simulation deux algorithmes bien connus avec une methode liee a l algorithme de hannan et rissanen 1982

a note on observer design for one sided lipschitz nonlinear systems in this note observer design of a class of nonlinear systems is considered based on the one sided lipschitz condition sufficient conditions for the existence of observers of the class of nonlinear systems are presented a design method of the observer that is dependent on the solution of the linear matrix inequality is then presented furthermore a gain matrix of the observer is given the method given in this note makes the applicable class larger than that given in the literature it should be noticed that the proposed method is applicable not only to the monotone nonlinearities and lipschitz nonlinearities but also to the one sided lipschitz nonlinearities which are neither monotone nonlinearities nor usual lipschitz nonlinearities finally we use the proposed method to design observers for three simulative examples and the effect of each state trajectory tracking is very satisfactory

stability tests of interval time delay systems abstract this paper presents some sufficient conditions for robust stability independent of delay and decaying rate for uncertain time delay systems the obtained robustness results are extended to cover the class of interval time delay systems sufficient conditions are also derived for checking the instability of this class of systems the results are given in terms of norm and matrix measure easy to check a comparison between the derived conditions is given numerical computations are performed to illustrate the results

accumulated prediction errors information criteria and optimal forecasting for autoregressive time series the predictive capability of a modification of rissanen s accumulated prediction error ape criterion ape n is investigated in infinite order autoregressive ar oo models instead of accumulating squares of sequential prediction errors from the beginning ape n is obtained by summing these squared errors from stage n n where n is the sample size and 1 n n 1 1 n may depend on n under certain regularity conditions an asymptotic expression is derived for the mean squared prediction error mspe of an ar predictor with order determined by ape n this expression shows that the prediction performance of ape n can vary dramatically depending on the choice of n another interesting finding is that when n approaches 1 at a certain rate ape n can achieve asymptotic efficiency in most practical situations an asymptotic equivalence between ape n and an information criterion with a suitable penalty term is also established from the mspe point of view this offers new perspectives for understanding the information and prediction based model selection criteria finally we provide the first asymptotic efficiency result for the case when the underlying ar oo model is allowed to degenerate to a finite autoregression

correcting argoun s approach for the stability of interval matrices recently xu and shao 1989 pointed out that the approach of argoun 1986 for the stability of interval matrices is incorrect this note corrects his approach so that it can be used to check the stability of linear continuous time systems with perturbations

a note on observers for lipschitz nonlinear systems this note deals with the design of reduced order observers for lipschitz nonlinear systems it shows that the conditions under which a full order observer exists also guarantee the existence of a reduced order observer a design method of the reduced order observer that is dependent on the solution of the riccati equation is then presented and an example is given to illustrate effects of the design method

observer with linear error dynamics for nonlinear multi output systems based upon nonlinear state coordinate transformations and a condensed dual brunovsk form for multi output systems a method for designing nonlinear state observers with linear error dynamics is presented necessary and sufficient conditions are provided for identifying the class of nonlinear systems for which state observers with linear error dynamics can be obtained

observability and observers for nonlinear systems this paper deals with observability and observers for general nonlinear systems in the non control affine case we characterize systems that are observable independently of the inputs an exponential observer for these systems is also exhibited

observers for a class of lipschitz systems with extension to h performance analysis abstract in this paper observer design for a class of lipschitz nonlinear dynamical systems is investigated one of the main contributions lies in the use of the differential mean value theorem dmvt which allows transforming the nonlinear error dynamics into a linear parameter varying lpv system this has the advantage of introducing a general lipschitz like condition on the jacobian matrix for differentiable systems to ensure asymptotic convergence in both continuous and discrete time systems such sufficient conditions expressed in terms of linear matrix inequalities lmis are established an extension to h filtering design is obtained also for systems with nonlinear outputs a comparison with respect to the observer method of gauthier et al a simple observer for nonlinear systems applications to bioreactors ieee trans automat control 37 6 1992 875 880 is presented to show that the proposed approach avoids high gain for a class of triangular globally lipschitz systems in the last section academic examples are given to show the performances and some limits of the proposed approach the last example is introduced with the goal to illustrate good performances on robustness to measurement errors by avoiding high gain

on sufficient conditions for the stability of interval matrices using gershgorin s diagonal dominance theorem new sufficient conditions for the stability of interval matrices are obtained the new conditions remove a restriction in heinen s 1983 analysis and are applicable to a wider class of problems than previously possible

a strong tracking extended kalman observer for nonlinear discrete time systems the authors show how the extended kalman filter used as an observer for nonlinear discrete time systems or extended kalman observer eko becomes a useful state estimator when the arbitrary matrices namely r sub k and q sub k are adequately chosen as a first step we use the linearization technique given by boutayed et al 1997 which consists of introducing unknown diagonal matrices to take the approximation errors into account it is shown that the decreasing lyapunov function condition leads to a linear matrix inequality lmi problem which points out the connection between a good convergence behavior of the eko and the instrumental matrices r sub k and q sub k in order to satisfy the obtained lmi a particular design of q sub k is given high performances of the proposed technique are shown through numerical examples under the worst conditions

structure identification of parameter bounding models by use of noise structure bounds the selection of a model for a given set of records is discussed for the case when the output error is required to be always within some specified bounds a new selection criterion is proposed the model should be the simplest giving sufficiently unstructured output errors the lack of structure is specified by requiring the candidate model to be capable of giving sufficiently small sample autocorrelations of the model output errors over a range of lags computational algorithms to apply the criterion are presented and illustrated by tests on ar processes

greedy sparse rls starting from the orthogonal greedy least squares method we build an adaptive algorithm for finding online sparse solutions to linear systems the algorithm belongs to the exponentially windowed recursive least squares rls family and maintains a partial orthogonal factorization with pivoting of the system matrix for complexity reasons the permutations that bring the relevant columns into the first positions are restrained mainly to interchanges between neighbors at each time moment the storage scheme allows the computation of the exact factorization implicitly working on indefinitely long vectors the sparsity level of the solution i e the number of nonzero elements is estimated using information theoretic criteria in particular bayesian information criterion bic and predictive least squares we present simulations showing that for identifying sparse time varying fir channels our algorithm is consistently better than previous sparse rls methods based on the norm regularization of the rls criterion we also use our sparse greedy rls algorithm for computing linear predictions in a lossless audio coding scheme and obtain better compression than mpeg4 als using an rls lms cascade

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example