optimality approximation and complexity in set membership h sub spl infin identification investigates the set membership identification of time invariant discrete time exponentially stable possibly infinite dimensional linear systems from time or frequency domain data corrupted by deterministic noise the aim is to deliver not a single model but a set of models whose size in h sub spl infin norm measures the uncertainty in the identification the main focus of the note is on the optimality properties for finite data and on the tradeoff between optimality and complexity of approximated low order model sets a method is given for evaluating convergent and computationally efficient inner and outer approximations of the value set for a given frequency such approximations allow one to compute within any desired accuracy the identification error of any identified model and to evaluate an optimal model at any given number of frequencies by suitably approximating these values model sets with nominal models in rh sub spl infin are then derived whose order is selected by trading off between model set complexity and identification accuracy degradation this degradation is evaluated by computing the optimality level defined as the ratio between the reduced model identification error and the optimal one a numerical example demonstrates the effectiveness of the presented results

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

maximum likelihood estimators and worst case optimal algorithms for system identification abstract for system identification problems with stochastic noise maximum likelihood estimators are frequently used if noise is deterministic worst case optimal algorithms should be considered in this paper we study the following problem under what circumstances are maximum likelihood estimators optimal in the worst case

performance of the taylor series method for odes daes this paper revisits the use of the taylor series method for the numerical integration of odes and daes the numerical method is implemented using an efficient variable step variable order scheme several numerical tests comparing with well established numerical codes are presented

model quality evaluation in h sub 2 identification model quality evaluation in set membership identification is investigated in the recent literature two main approaches have been used to investigate this problem based on the concepts of n width and of radius of information in this paper it is shown that the n width is related to the asymptotic value of the conditional radius of information of the identification problem with noise free measurements upper and lower bounds of the conditional radius of information are derived for the h sub 2 identification of exponentially stable systems using approximating n dimensional models linear in the parameters in the presence of power bounded measurement errors the derived bounds are shown to be convergent to the radius for a large number of data and model dimensions moreover a formula for computing the worst case identification error for any linear algorithm is given in particular it is shown that the identification error of the least square algorithm may be increasing with respect to the model dimension peaking effect an almost optimal linear algorithm is presented that is not affected by this peaking effect and indeed is asymptotically optimal

hybrid numerical methods for exponential models of growth abstract a series of novel numerical methods for the exponential models of growth are proposed based on these methods hybrid predictor corrector methods are constructed the hybrid numerical methods can increase the accuracy and the computing speed obviously as well as enlarge the stability domain greatly

resolvability of the parameters of multiexponentials and other sum models it is shown that model fitting solutions for closely located nonlinear parameters of sums of functions of the same family such a multiexponentials are only distinct in a sub space of the euclidean space of the errors in the observations in the complementary space the solutions for two or more of the nonlinear parameters exactly coincide subspaces of the complementary space each correspond with the coincidence of the solutions for the parameters of specific terms of the sum model earlier studies concentrated on the case that the linear parameters such as the amplitudes of the exponentials are known and only two solutions for the nonlinear parameters coincide the analysis presented generalizes these results and extends them to include the solving for the linear parameters and multiple coincidence also a procedure is proposed for the computation of the errors that have minimum energy among all errors causing coincidence this minimum energy may be used as a simple scalar criterion to find out to what extent res olution is to be expected for assumed parameter values and er ror energy for least squares model fitting the proposed pro cedure is shown to be particularly simple

optimal sampling schedule for parameter estimation of linear models with unknown but bounded measurement errors the problem of optimal sampling design for parameter estimation when data are generated by linear models is addressed the measurements are assumed to be corrupted by an unknown but bounded additive noise the sampling design assumes that the number of samples is unconstrained and no replication is allowed two main results are shown 1 for particular classes of linear models the optimal number of measurements is equal to the number of parameters as in the statistical context 2 the uncertainty intervals of the parameter estimates are bounded from above by quantities that can be computer a priori knowing only the model and the error structure

brief paper state estimation in the presence of bounded disturbances this contribution proposes a robust recursive algorithm for the state estimation of linear models with unknown but bounded disturbances corrupting both the state and measurement vectors a novel approach based on state bounding techniques is presented the proposed algorithm can be decomposed into two steps time updating and observation updating that uses a switching estimation kalman like gain matrix particular emphasis will be given to the design of a weighting factor that ensures the stability of the estimation error

identification of probabilistic system uncertainty regions by explicit evaluation of bias and variance errors a procedure is developed for identification of probabilistic system uncertainty regions for a linear time invariant system with unknown dynamics on the basis of time sequences of input and output data the classical framework is handled in which the system output is contaminated by a realization of a stationary stochastic process given minor and verifiable prior information on the system and the noise process frequency response pulse response and step response confidence regions are constructed by explicitly evaluating the bias and variance errors of a linear regression estimate in the model parametrizations use is made of general forms of basis functions conservatism of the uncertainty regions is limited by focusing on direct computational solutions rather than on closed form expressions using an instrumental variable method for identification the procedure is suitable also for input output data obtained from closed loop experiments

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

bounded error parameter estimation a sequential analytic center approach a sequential analytic center approach for bounded error parameter estimation is proposed the authors show that the analytic center minimizes the logarithmic average output error among all the estimates within the membership set and is a maximum likelihood estimator for a class of noise density functions which include parabolic densities and approximations of truncated gaussian they also show that the analytic center is easily computable for both offline and online problems with a sequential algorithm the convergence proof of this sequential algorithm is obtained and moreover it is shown that the complexity in terms of the maximum number of newton iterations is linear in the number of observed data points

finite horizon optimal control with pointwise cost functional a finite horizon discrete time optimal control problem is proposed and analyzed where the uncertainty affecting the system is modeled as an input variable disturbance that at any time instant is only known to belong to a given set the functional to be minimized is the highest instantaneous cost that may occur under the worst possible combination of disturbances a dynamic programming algoritm is proposed for the solution two simple but relevant examples of application the target set reachability problem and the control of a storage system are presented

an improved class of generalized runge kutta methods for stiff problems part ii the separated system case in order to study a generalization of the explicit p stage runge kutta methods we introduce a new family of p stage formulas for the numerical integration of some special systems of odes that provides better order and stability results with the same number of stages in our recent paper entitled an improved class of generalized runge kutta methods for stiff problems part i the scalar case we studied new schemes for the numerical integration of scalar autonomous odes in this second part we will show that it is possible to generalize our grk methods so that they can be applied to some non autonomous scalar odes and systems obtaining linearly implicit a stable and l stable methods these methods do not require jacobian evaluations in their implementation some numerical examples are discussed in order to show the good performance of the new schemes

risk adjusted set membership identification of wiener systems this technical note addresses the problem of set membership identification of wiener systems its main result shows that even though the problem is generically np hard it can be reduced to a tractable convex optimization through the use of risk adjusted methods in addition this approach allows for efficiently computing worst case bounds on the identification error finally we provide an analysis of the intrinsic limitations of interpolatory algorithms these results are illustrated with a non trivial problem arising in computer vision tracking a human in a sequence of frames where the challenge here arises from the changes in appearance undergone by the target and the large number of pixels to be tracked

on linear models for nonlinear systems best linear time invariant lti approximations are analysed for several interesting classes of discrete nonlinear time invariant systems these include nonlinear finite impulse response systems and a class of nonsmooth systems called bi gain systems the frechet derivative of a smooth nonlinear system is studied as a potential good lti model candidate the frechet derivative is determined for nonlinear finite memory systems and for a class of wiener systems most of the concrete results are derived in an signal setting applications to linear controller design to identification of linear models and to estimation of the size of the unmodelled dynamics are discussed

block recursive parallelotopic bounding in set membership identification in this paper a procedure for the recursive approximation of the feasible parameter set of a linear model with a set membership uncertainty description is provided approximating regions of parallelotopic shape are considered the new contribution of this paper consists in devising a general procedure allowing for block processing of q 1 measurements at each recursion step based on this several approximation strategies for polytopes are presented simulation experiments are performed showing the effectiveness of the algorithm as compared to the original algorithm processing one measurement at each step

experiment design in a bounded error context comparison with d optimality abstract the problem of optimal experiment design for linear regression models is addressed the measurement errors are supposed to be bounded with no other hypothesis on their distribution contrary to the classical statistical approach an experiment is considered here as optimal if it minimizes the volume of the set of all parameters that are consistent with the data the model structure and the noise bounds this new design policy is compared to the classical d optimal design used in a statistical context when the number of measurements is equal to the number of parameters to be estimated the new optimality criterion although relying on quite different hypotheses on the noise distribution is shown to lead to the same optimal policy as a d optimality criterion this is no longer true when more measurements are to be made depending on the shape of the admissible experimental domain it is sometimes possible to design optimal experiments without any calculations an algorithmic procedure is suggested to be used when this is not so

decoupling the linear and nonlinear parts in hammerstein model identification the main result of this paper is to show that the linear part can be made decoupled from the nonlinear part in hammerstein model identification therefore identification of the linear part for a hammerstein model becomes a linear problem and accordingly enjoys the same convergence and consistency results as if the unknown nonlinearity is absent

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

adaptive blind source separation for virtually any source probability density function blind source separation bss aims to recover a set of statistically independent source signals from a set of linear mixtures of the same sources in the noiseless real mixture two source two sensor scenario once the observations are whitened decorrelated and normalized only a givens rotation matrix remains to be identified in order to achieve the source separation in this paper an adaptive estimator of the angle that characterizes such a rotation is derived it is shown to converge to a stable valid separation solution with the only condition that the sum of source kurtosis be distinct from zero an asymptotic performance analysis is carried out resulting in a closed form expression for the asymptotic probability density function of the proposed estimator it is shown how the estimator can be incorporated into a complete adaptive source separation system by combining it with an adaptive prewhitening strategy and how it can be useful in a general bss scenario of more than two signals by means of a pairwise approach a variety of simulations assess the accuracy of the asymptotic results display the properties of the estimator such as its robust fast convergence and compare this on line bss implementation with other adaptive bss procedures

necessary and sufficient conditions for robust identification of uncertain lti systems abstract robust identification of uncertain systems arises whenever a chosen family of models does not completely describe reality in these situations the issue of unmodeled dynamics gains significance in addition to random measurement noise to deal with such mixed stochastic deterministic settings we introduce a novel notion for robust consistency which requires that the expectation with respect to noise of the worst case with respect to unmodeled dynamics identification error asymptotically approach zero it turns out that this notion leads to transparent necessary and sufficient conditions we show that robust consistency holds if and only if there is an instrument input pair capable of annihilating the residual error as well as stochastic noise an extension of this result to the well known bounded but unknown noise model shows that if we were to remove a set of lebesgue measure zero the error bound asymptotically approaches zero

identification and application of bounded parameter models abstract the place of parameter bounding algorithms in identification methodology is discussed such algorithms provide a radical alternative to the computation of parameter point estimates and covariances instead of p d f or mean and covariance for the noise and prior parameter estimates they require bounds in an essentially deterministic model formulation the paper is a preliminary review of some standard tasks namely experiment design testing for outliers toleranced prediction and worst case control design in the context of parameter bounding identification computational requirements of these tasks are examined and the limitations of existing parameter bounding algorithms are noted

brief a set theoretic approach for time to contact estimation in dynamic vision this paper deals with the estimation of the time to contact in dynamic vision it is well known that differential invariants of the image velocity field can be used to characterize the shape changes of objects in the scene due to relative motion between the observer and the scene under the hypothesis of constant velocity along the optical axis the time to contact turns out to be a function of the area enclosed by the object contour and its time derivative in the paper a novel approach based on set membership estimation theory is proposed to estimate the variables involved in the computation of the time to contact both errors in the motion model and image measurement noise are described as unknown but bounded disturbances without requiring any statistical assumption the proposed technique allows for the computation of guaranteed bounds on the time to contact estimates in finite time a crucial issue in all problems where a robust evaluation of the time to contact is in order

optimal algorithms theory for robust estimation and prediction this paper deals with the theory of optimal algorithms for problems which cannot be solved exactly the theory developed allows for the derivation of new and interesting results in parameter estimation and in time series prediction in situations where no reliable statistical hypothesis can be made on the functions and modeling errors involved but only a bound on them is known in particular the derivation of computationally simple optimal algorithms for these two problems is investigated the practical effectiveness of the algorithms obtained is illustrated by several numerical examples

optimization with few violated constraints for linear bounded error parameter estimation in the context of linear constrained optimization we study the problem of finding an optimal solution satisfying all but k of the given n constraints a solution is obtained by means of an algorithm of the complexity min o n spl middot k sup d o n spl middot d sup k 1 where d is the dimension of the problem we then use these results to solve the problem of robust identification in the presence of outliers in the setting of bounded error parameter identification finally we show that the estimate obtained converges to the true but unknown parameter in the presence of outliers

input design in worst case system identification using binary sensors this technical note addresses system identification using binary valued sensors in a worst case set membership setting the main contribution is the solution of the optimal input design problem for identification of scalar gains which is instrumental to the construction of suboptimal input signals for identification of fir models of arbitrary order two different cost functions are considered for input design the maximum parametric identification error and the relative uncertainty reduction with respect to the minimum achievable error it is shown that in the latter case the solution enjoys the property of being independent of the length of the identification experiment and as such it can be implemented as an optimal recursive procedure over a time interval of arbitrary length

explicitly solving vectorial odes this paper concerns a new method for finding numerical solutions of multivariate ode flows where the flow field is not given explicitly the method is based on the existing implicit numerical methods such as euler backward and the implicit midpoint rule the main aspect is that the method as such is explicit but with the similar accuracy and stability properties as the original implicit methods a higher dimensional analysis is given of both stability and accuracy a couple of examples illustrate this analysis

worst case system identification in h sub spl infin validation of a priori information essentially optimal algorithms and error bounds resolves several important open issues pertaining to a worst case control oriented system identification problem known as identification in h sub spl infin first a method is presented for developing confidence that certain a priori information available for identification is not invalid this method requires the solution of a certain nondifferentiable convex program second an essentially optimal identification algorithm is constructed this algorithm is worst case strongly optimal to within a factor of two finally new upper and lower bounds on the optimal identification error are derived and used to estimate the identification error associated with the given algorithm interestingly the development of each of these results draws heavily upon the classical nevanlinna pick interpolation theory as such the authors results establish a clear link between the areas of system identification and optimal interpolation theory both the formulation and techniques in this paper are applicable to problems where the frequency data available for identification may essentially be arbitrarily distributed

a fast fixed point algorithm for independent component analysis we introduce a novel fast algorithm for independent component analysis which can be used for blind source separation and feature extraction we show how a neural network learning rule can be transformed into a fixedpoint iteration which provides an algorithm that is very simple does not depend on any user defined parameters and is fast to converge to the most accurate solution allowed by the data the algorithm finds one at a time all nongaussian independent components regardless of their probability distributions the computations can be performed in either batch mode or a semiadaptive manner the convergence of the algorithm is rigorously proved and the convergence speed is shown to be cubic some comparisons to gradient based algorithms are made showing that the new algorithm is usually 10 to 100 times faster sometimes giving the solution in just a few iterations

global attitude and gyro bias estimation based on set valued observers a b s t r a c t the problem of attitude and rate gyro bias estimation is addressed by resorting to measurements acquired from rate gyros and vector observations a set valued observer svo is proposed that has no singulari ties and that for any initial conditions provides a bounding set with guarantees of containing the actual unknown rotation matrix the sensor readings are assumed to be corrupted by bounded measurement noise and constant gyro bias conditions for the boundedness of the estimated sets are established and implementation details are discussed the feasibility of the technique is demonstrated in simulation

analytical methods for parameter space delimination and application to shallow lake phytoplankton dynamics modeling the first step in parameter estimation is to reduce the dimensionality of the problem by deriving estimates from independent experimentation and from the literature in addition insensitive parameters are either removed or fixed in the remaining lower dimensional problem parameter space delimitation is possible by analytical means three conjunctive methods are derived period average analysis extremum analysis and quasisteady state analysis the basic idea is to find conditions for the parameters that must be fulfilled in order to comply with average and extreme values in the observations the approach is applied to the modeling of the phytoplankton dynamics of lake balaton the analytical techniques prove to supply valuable insight into parameter interrelationships and model adequacy and can serve as satisfactory substitutes for formal parameter estimation techniques in the early stages of model development

adaptive online learning algorithms for blind separation maximum entropy and minimum mutual information there are two major approaches for blind separation maximum entropy me and minimum mutual information mmi both can be implemented by the stochastic gradient descent method for obtaining the demixing matrix the mi is the contrast function for blind separation the entropy is not to justify the me the relation between me and mmi is first elucidated by calculating the first derivative of the entropy and proving that the mean subtraction is necessary in applying the me and at the solution points determined by the mi the me will not update the demixing matrix in the directions of increasing the cross talking second the natural gradient instead of the ordinary gradient is introduced to obtain efficient algorithms because the parameter space is a riemannian space consisting of matrices the mutual information is calculated by applying the gram charlier expansion to approximate probability density functions of the outputs finally we propose an efficient learning algorithm that incorporates with an adaptive method of estimating the unknown cumulants it is shown by computer simulation that the convergence of the stochastic descent algorithms is improved by using the natural gradient and the adaptively estimated cumulants

computation of nonconservative stability perturbation bounds for systems with nonlinearly correlated uncertainties consideration is given to the problem of robust stability analysis of linear dynamic systems with uncertain physical parameters entering as polynomials in the state equation matrices a method is proposed giving necessary and sufficient conditions for computing the uncertain system stability margin in parameter space which provides a measure of maximal parameter perturbations preserving stability of the perturbed system around a known stable nominal system a globally convergent optimization algorithm that enables solutions to the problem to be obtained is presented using the polynomial structure of the problem the algorithm generates a convergent sequence of interval estimates of the global extremum these intervals provide a measure of the accuracy of the approximating solution achieved at each step of the iterative procedure some numerical examples are reported showing attractive features of the algorithm from the point of view of computational burden and convergence behavior

on the use of constraints in least squares estimation and control in this article we examine the effect of constraints on estimation and control methods based on quadratic penalty functions we begin with estimation theory and analyze how constraints alter the statistical properties of the least squares estimates it is shown that constraints can be used to formulate maximum likelihood mle and maximum a posteriori map estimators for a variety of unimodal distributions this provides greater flexibility over the assumption of normality inherent in the mle and map interpretation of traditional least squares we discuss how these ideas apply to state space models of dynamic systems possible applications for controllers that handle constraints are also discussed a parameter estimation example is given to demonstrate the potential for improved performance over unconstrained least squares

unboundedness for the euler bernoulli beam equation with a fractional boundary dissipation we consider the euler bernoulli beam problem with some boundary controls involving a fractional derivative the fractional derivative here represents a fractional dissipation of lower order than one we prove that the classical energy associated to the system is unbounded in presence of a polynomial nonlinearity in fact it will be proved that the energy will grow up as an exponential function as time goes to infinity

numerical approximations for population growth models this paper aims to introduce a comparison of adomian decomposition method and sinc galerkin method for the solution of some mathematical population growth models from the computational viewpoint the comparison shows that the adomian decomposition method is efficient and easy to use

h sub spl infin identification of multivariable systems by tangential interpolation methods the purpose of this paper is to present an extension to some of the current work on worst case identification problems to multivariable systems we consider an h sub spl infin identification problem for a class of linear shift invariant multi input multi output systems our main results are an interpolatory algorithm and a number of bounds on the identification error this algorithm operates on available input and output data in the time domain and is constructed by solving an extended matrix tangential caratheodory fejer problem similar to its counterpart for scalar systems this interpolatory algorithm possesses certain desirable optimality properties and can be obtained via standard convex programming methods

robust estimation and filtering in the presence of bounded noise optimal algorithms for robust estimation and filtering are constructed the noise is considered a deterministic variable belonging to a set described by a norm previous results obtained for complete one to one and approximate information by m milanese and r tempo ibid vol 30 p 730 8 1985 are extended to partial and approximate information this information is considered useful in dealing with dynamic systems not completely identifiable and or with two different sources of noise such as process and measurement noise for different norms characterizing the noise optimal algorithms in a min max sense are shown in particular for hilbert norms a linear optimal algorithm is the well known minimum variance estimator for l sub infinity norm an optimal algorithm computable by linear programming is presented state estimation is formalized in the context of the general theory for stable systems an approximate state estimation is obtained by neglecting higher order powers an upper bound determining the approximation introduced is derived a numerical example illustrates the application of the theory

persistent identification of time varying systems identification of time varying systems especially slowly time varying systems is of importance in the development of a comprehensive theory of adaptation the persistent identification measures employed in this paper capture a main characterization in such identification problems namely one input signal must be used for identification of all possible observation windows this paper establishes several essential features in persistent identification problems which highlight their potential utility in adaptation 1 they have computable upper and lower bounds for typical classes of prior uncertainty sets 2 any full rank n periodic signals are optimal and the simple least squares estimates are optimal identification algorithms 3 optimal probing inputs can be approximately generated in a closed loop configuration when the plant and the controller are slowly time varying and 4 n periodic signals are asymptotically optimal for slowly time varying systems the main results of this paper have been successfully combined with a certain slow h sup spl infin design to derive an adaptive stabilization scheme

optimal inner bounds of feasible parameter set in linear estimation with bounded noise some problems arising in parameter estimation theory with unknown but bounded measurement errors are discussed in this theory a key role is played by the feasible parameter set i e the set of all parameter values consistent with the system model and the error bounds if a linear relationship between parameters and measurements is assumed this set is a polytope an exact representation of this polytope may be too complex for practical use and approximate descriptions in terms of simple shaped sets contained in the feasible parameter set inner bounds have shown to be useful in several applications balls in l sub infinity norms boxes l sub 2 norms ellipsoids and l sub 1 norms diamonds are used as bounding sets results are given on the computation of maximal balls when their shape is either known or partially free a numerical example is given in which the results of a computation of inner boxes of fixed shape and fixed orientation are given and compared

parameter bounds for discrete time hammerstein models with bounded output errors in this note we present a two stage procedure for deriving parameters bounds in hammerstein models when the output measurement errors are bounded first using steady state input output data parameters of the nonlinear part are tightly bounded then for a given input transient sequence we evaluate tight bounds on the unmeasurable inner signal which together with noisy output measurements are used for bounding the parameters of the linear dynamic block

an approach to identification for robust control given measured data generated by a discrete time linear system we propose a model consisting of a linear time invariant system affected by norm bounded perturbation under mild assumptions the plants belonging to the resulting uncertain family form a convex set the approach depends on two key parameters an a priori given bound of the perturbation and the input used to generate the data it turns out that the size of the uncertain family can be reduced by intersecting the model families obtained by making use of different inputs the model validation problem in this identification scheme is analyzed for a given energy level the invalidation problem yields the family of those models which can never be invalidated for any possible input of fixed energy and any possible perturbation this leads to the intersection of all uncertain families a consequence of the invalidation problem is that for finite length measurements not all models can be invalidated using fixed energy inputs

convergence results of the analytic center estimator the analytic center approach for bounded error parameter estimation was recently proposed as an alternative to the well known least squares and chebyshev estimates in this paper we show the asymptotic performance of this approach and prove that the analytic center converges to the true parameter under mild conditions

nonlinear least absolute values and minimax model fitting abstract up to now the least absolute values l 1 and minimax l criteria have seldom been used in model fitting even if they are preferable for theoretical reasons their non differentiability causes numerical and analytical difficulties fortunately a recent reformulation of l 1 and l as equivalent constrained differentiable problems enables one to numerically solve them using standard nonlinear programming software this paper exploits this reformulation for analytical purposes in particular limits are derived concerning the ability of l 1 and l to resolve highly similar nonlinearly parametric terms from error corrupted observations examples are exponentials of nearly equal decay in compartmental models and almost coinciding peaks in spectroscopy

the decomposition method for continuous population models for single and interacting species the adomian decomposition method is applied to continuous population models for both single and interacting species in comparison with existing techniques the decomposition method is highly effective in terms of accuracy and rapid convergence analytical and numerical studies are presented

set membership prediction of nonlinear time series in this paper a prediction method for nonlinear time series based on a set membership sm approach is proposed the method does not require the choice of the functional form of the model used for prediction but assumes a bound on the rate of variation of the regression function defining the model at the contrary most of the existing prediction methods need the choice of a functional form of the regression function or of state equations piecewise linear quadratic etc and this choice is usually the result of heuristic searches these searches may be quite time consuming and lead only to approximate model structures whose errors may be responsible of bad propagation of prediction errors especially for the multistep ahead prediction moreover the method proposed in this paper assumes only that the noise is bounded in contrast with statistical approaches which rely on noise assumptions such as stationarity ergodicity uncorrelation type of distribution etc the validity of these assumptions may be difficult to be reliably tested in many applications and is certainly lost in presence of approximate modeling in the present sm approach using a result developed in a previous paper the values of the bounds on the gradient of the regression function and on the noise can be suitably assessed to verify the validity tests two almost optimal prediction algorithms are then derived the second one having improved optimal properties over the first one at the expense of an increased computational complexity the method is tested and compared with other literature methods on the well known wolf sunspot numbers series widely used in the time series literature as a benchmark test and on the prediction of vertical dynamics of vehicles with controlled suspensions a simulation example is also presented to investigate how much conservative the sm approach may be in the most adverse situation where data are generated by a linear autoregressive ar model driven by i i d gaussian white noise and the sm prediction is compared with the optimal statistical predictor which makes use of the exact assumptions

blind separation using convex functions in this paper the problem of how to conveniently estimate independence from observations is addressed random variables rvs are transformed by their respective distribution functions and quantized then the uniformity of the joint probability of the obtained discrete rvs is evaluated using a strictly convex function an infinite class of new independence measures named quasientropy qe is thus proposed unbiased estimates of the values of the distribution functions at the observations are directly utilized in estimating qe the linear instantaneous blind source separation bss algorithm based on qe can separate signals with arbitrary continuous distributions

optimality of central and projection algorithms for bounded uncertainty this paper investigates optimality properties of central and projection algorithms for linear problems in the field of system identification in a context in which uncertainty is described in a deterministic rather than statistical way particular attention is devoted to least squares algorithms when the measurement noise is assumed to be unknown but bounded in a hilbert norm a major contribution of this paper consists in proving that least squares algorithms enjoy strong optimality properties on the contrary it is pointed out that these properties do not hold for other frequently used projection algorithms such as least absolute values or minimax algorithms corresponding to a description of the measurement error in h or l norm respectively

model quality evaluation in set membership identification abstract identification from corrupted input output measurements of systems that do not necessarily belong to the model class used is investigated this leads to a nonstandard set membership sm identification problem the goodness of different model classes is measured by the conditional radius of information a generalization of the radius in standard sm identification theory giving a measure of the minimal worst case modeling error upper and lower bounds on the radius are derived for linearly parameterized model classes specific formulas for the upper and lower bounds are given for the case of h 2 identification of exponentially stable systems in the presence of powerbounded noise the bounds are shown to coincide with the conditional radius when the model space dimension is equal to the number of output measurements an almost optimal identification algorithm is derived giving identification error within the range of the derived bounds

estimation theory for nonlinear models and set membership uncertainty this chapter studies the problem of estimating a given function of a vector of unknowns called the problem element by using measurements depending non linearly on the problem element and affected by unknown but bounded noise assuming that both the solution sought and the measurements depend polynomially on the unknown problem element a method is given to compute the axis aligned box of minimal volume containing the feasible solution set i e the set of all unknowns consistent with the actual measurements and the given bound on the noise the center of this box is a point estimate of the solution which enjoys useful optimality properties the sides of the box represent the intervals of possible variation of the estimates important problems like parameter estimation of exponential models time series prediction with arma models and parameter estimates of discrete time state space models can be formalized and solved by using the developed theory

a class of inverse runge kutta schemes for the numerical integration of singular problems a class of methods for the numerical solution of initial value problems whose solution has singular point s shall be discussed they are a and l stable and were found to perform efficiently well when faced with singularity problem but perform poorly when applied to non singular problems

on worst case approximation of feasible system sets via orthonormal basis functions this note deals with the approximation of sets of linear time invariant systems via orthonormal basis functions this problem is relevant to conditional set membership identification where a set of feasible systems is available from observed data and a reduced complexity model must be estimated the basis of the model class is made of impulse responses of linear filters the objective of the note is to select the basis function poles according to a worst case optimality criterion suboptimal conditional identification algorithms are introduced and tight bounds are provided on the associated identification errors

tracking and identification of regime switching systems using binary sensors this work is concerned with tracking and system identification for time varying parameters the parameters are markov chains and the observations are binary valued with noise corruption to overcome the difficulties due to the limited measurement information wonham type filters are developed first then based on the filters two popular estimators namely mean squares estimator msq and maximum posterior map estimator are constructed for the mean squares estimator we derive asymptotic normality in the sense of weak convergence and in the sense of strong approximation the asymptotic normality is then used to derive error bounds when the markov chain is infrequently switching we derive error bounds for map estimators when the markovian parameters are fast varying we show that the averaged behavior of the parameter process can be derived from the stationary measure of the markov chain and that can be estimated using empirical measures upper and lower error bounds on estimation errors are also established

stochastic and deterministic fault detection for randomized gossip algorithms this paper addresses the problem of detecting faults in linear randomized gossip algorithms where the selection of the dynamics matrix is stochastic a fault is a disturbance signal injected by an attacker to corrupt the states of the nodes we propose the use of set valued observers svos to detect if the state observations are compatible with the system dynamics for the worst case in a deterministic setting the concept of stochastic set valued observers ssvos is also introduced to construct a set that is guaranteed to contain all possible states with at least a pre specified desired probability the proposed algorithm is stable in the sense that it requires a finite number of vertices to represent polytopic sets and it allows for the computation of the largest magnitude of the disturbance that an attacker can inject in the network without being detected results are presented to reduce the computational cost of this approach and in particular by considering only local information and representing the remainder of the network as a disturbance the case of a consensus algorithm is discussed leading to the conclusion that by using the proposed svos finite time consensus is achieved in non faulty environments a novel algorithm is proposed that produces less conservative set valued state estimates by having nodes exchanging local estimates the algorithm inherits all the previous properties and also enables finite time consensus computation regardless of the value of the horizon

brief paper convergence properties of the membership set in this paper we study the convergence properties of the membership set for system identification in the presence of unknown but bounded noise besides the classical pointwise noise model we also analyze the so called window and average models two different scenarios are considered 1 the bound tight or overestimated is known 2 the bound is unknown and has to be estimated from measurement data under some probabilistic assumptions on the noise sequence and with the persistent excitation regressor in the first case we prove that the diameter of the associated membership sets converges to zero with probability one if the noise bound is tight if the bound is overestimated we compute upper bounds for the diameter which are stated in terms of the difference between the true and the over estimated bound in the second case we show that the estimates of the bound converge to the true but unknown noise bound

properties of least squares estimates in set membership identification the properties of the least square algorithm in the identification of linear time invariant discrete time systems in the presence of unknown but bounded errors are investigated it is known that the least squares algorithm enjoys strong optimality properties in the case of power bounded l 2 errors while it may be far from optimal in the case of pointwise l bounded errors exact expressions of the local and global worst case errors of the least squares estimates are derived using these results general conditions assuring convergence to zero of the global worst case error are given it is also shown that the least squares algorithm may be optimal in l 1 and l identification of fir systems with pointwise bounded errors

unified set membership theory for identification prediction and filtering of nonlinear systems the problem of making inferences from data measured on nonlinear systems is investigated within a set membership sm framework and it is shown that identification prediction and filtering can be treated as specific instances of the general presented theory the sm framework presents an alternative view to the parametric statistical ps framework more widely used for studying the above specific problems in particular in the sm framework a bound only on the gradient of the model regression function is assumed at difference from ps methods which assume the choice of a parametric functional form of the regression function moreover the sm theory assumes only that the noise is bounded in contrast with ps approaches which rely on noise assumptions such as stationarity uncorrelation type of distribution etc the basic notions and results of the general inference making theory are presented moreover some of the main results that can be obtained for the specific inferences of identification prediction and filtering are reviewed concluding comments on the presented results are also reported focused on the discussion of two basic questions what may be gained in identification prediction and filtering of nonlinear systems by using the presented sm framework instead of the widely diffused ps framework why sm methods could provide stronger results than the ps methods requiring weaker assumptions on system and on noise

a state set estimation algorithm for linear systems in the presence of bounded disturbances this paper concerns the problem of state set estimation for discrete time linear systems the linear system is given in state space form and the system s uncertainty is described by bounded scalar variations we present a recursive algorithmic procedure of computing guaranteed estimated state sets in particular a polyhedron variation algorithm is presented the new algorithm is based on linear programming and sensitivity analysis techniques for improved computational efficiency and practicability

complete mathematical analysis of predator prey models with linear prey growth and beddington deangelis functional response the dynamics of a predator prey model with a beddington deangelis functional response and linear intrinsic growth rate of the prey population is fully analyzed conditions on local and global stability of the interior equilibrium are established the equilibria type are determined all possible global asymptotic behaviors of the system are considered including the determination of the extinction conditions and existence of periodic orbits it is shown that mutual interference between predators can alone stabilize predator prey interactions even when only a linear intrinsic growth rate of the prey population is considered in the mathematical model additional biological implications and a set of numerical simulations supporting the analysis are also presented

recursive computation of inner bounds for the parameters of linear models minimum volume ellipsoidal outer bounds on the parameters of linear regression type models with bounded model output error can be computed by an established algorithm a complementary algorithm to compute maximum volume ellipsoidal inner bounds is derived it is little more complicated than the existing outer bounding algorithm in conjunction with that algorithm it allows parameter values to be classified as acceptable dubious or unacceptable it is also found to be effective in determining output error bounds by trial and error during development of parameter bounding models

on optimal e to e filtering abstract in this paper we consider the problem of finding a filter that minimizes the worst case magnitude l of the estimation error in the case of linear time invariant systems subjected to unknown but magnitude bounded l inputs these inputs consist of process and observation noise as well as initial conditions also the optimization problem is considered over an infinite time horizon taking a model matching approach suboptimal solutions are presented that stem from the resulting l induced norm minimization problem

estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors linear families of models and estimators the problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available of suitable but only a bound on them is known in the present paper only linear parametrizations and estimators are considered very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals estimates uncertainty intervals parameter uncertainty intervals the relationships between the eui s and the pui s are established and the solution to the problem of the minimum uncertainty intervals estimator is given the latter can be obtained by means of a simple linear programming algorithm

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

h sub spl infin identification and model quality evaluation set membership h sub spl infin identification is investigated using time domain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors the problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error called radius of information is solved for classes of models affine in the parameters the radius of information is obtained as function of the h sub spl infin norm of the unmodeled dynamics a method is given for estimating this norm from the available data and some general a priori information on the unmodeled dynamics thus allowing the actual evaluation of the radius of information the radius represents a measure of the predictive ability of the considered class of models and it is then used for comparing the quality of different classes of models and for the order selection of their parametric part the effectiveness of the proposed procedure is tested on some numerical examples and compared with standard statistical criteria for model order selection

asymptotically convergent modified recursive least squares with data dependent updating and forgetting factor for systems with bounded noise continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances an algorithm which eliminates these difficulties is investigated based on a set theoretic assumption the algorithm yields modified least squares estimates with a forgetting factor it updates the estimates selectively depending on whether the observed data contain sufficient information the information evaluation required at each step involves very simple computations in addition the parameter estimates are shown to converge asymptotically at an exponential rate to a region around the true parameter

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

optimal induced norm and set membership state smoothing and filtering for linear systems with bounded disturbances in this paper a unified framework founded on information based complexity is introduced to study set membership and optimal induced norm state estimation problems for linear systems subject to norm bounded process noise and measurement errors the proposed approach leads to a clean geometric picture of the problem allowing for a straightforward derivation of several existing results moreover it permits to tackle new estimation problems in which both induced norm optimization and consistency of the estimate with the noise bound are required