nonparametric system identification by kernel methods a new nonparametric estimate for nonlinear discrete time dynamic systems is considered the new algorithm is weakly consistent under a specific condition on the transition probability operator of a stationary markov process the estimate is applicable when a parametric state model of the system is difficult to choose

model reference adaptive control of time varying and stochastic systems the adaptive control of general delay linear time varying systems is addressed a simple model reference adaptive control law is devised it does not require a priori knowledge of the sign of the high frequency gain this control law coupled with the parameter estimation equations allows a simple representation of the closed loop system this greatly eases the stability and performance analysis and has potential for generalization to adaptive pole placement and other control laws suitable for nonminimum phase systems for the kalman filter parameter estimator coupled with this control law stability is obtained without persistence of excitation or knowledge of the sign of the high frequency gain performance results for the extended least squares algorithm are described

a new indirect adaptive control scheme for time varying plants structures are developed for the control and estimation parts of the indirect adaptive scheme which are more appropriate for time varying plants in contrast to the usual pointwise schemes the new controller structure can meet the control objective exactly for a wide class of plants with smooth but otherwise unrestricted parameter variations on the other hand the possibly available knowledge of the form or frequency of variation of the fast parameters is included in the new estimator structure so that for successful estimation the overall plant is not restricted to varying slowly with time the new estimator and control law are combined using the certainty equivalence principle to develop an indirect adaptive control scheme meeting the control objective for plants with time varying parameters whose fast varying parts are of known form and unknown parts are slow in the mean

analytic preconditioners for the electric field integral equation since the advent of the fast multipole method large scale electromagnetic scattering problems based on the electric field integral equation efie formulation are generally solved by a krylov iterative solver a well known fact is that the dense complex non hermitian linear system associated to the efie becomes ill conditioned especially in the high frequency regime as a consequence this slows down the convergence rate of krylov subspace iterative solvers in this work a new analytic preconditioner based on the combination of a finite element method with a local absorbing boundary condition is proposed to improve the convergence of the iterative solver for an open boundary some numerical tests precise the behaviour of the new preconditioner moreover comparisons are performed with the analytic preconditioner based on the calderon s relations for integral equations for several kinds of scatterers copyright 2004 john wiley sons ltd

exponential stability of general tracking algorithms tracking and adaptation algorithms are from a formal point of view nonlinear systems which depend on stochastic variables in a fairly complicated way the analysis of such algorithms is thus quite complicated a first step is to establish the exponential stability of these systems this is of interest in its own right and a prerequisite for the practical use of the algorithm it is also a necessary starting point to analyze the performance in terms of tracking and adaptation because that is how close the estimated parameters are to the time varying true ones in this paper we establish some general conditions for the exponential stability of a wide and common class of tracking algorithms this includes least mean squares recursive least squares and kalman filter based adaptation algorithms we show how stability of an averaged linear and deterministic equation and stability of the actual algorithm are linked to each other under weak conditions on the involved stochastic processes we also give explicit conditions for exponential stability of the most common algorithms the tracking performance of the algorithms is studied in a companion paper

identification of time varying systems in reproducing kernel hilbert spaces we consider a class of linear systems in state space form whose parameters evolve in time according to a continuous time gauss markov process our problem is to identify the system from a finite set of noisy output measurements we derive a connection between this problem and tikhonov regularization in reproducing kernel hilbert spaces relying upon this result conditions that ensure the existence of the maximum a posteriori estimate of the parameter trajectory are provided and an identification algorithm is worked out simulated data are used to test the goodness of the proposed approach

a measure of the tracking capability of recursive stochastic algorithms with constant gains a criterion is given for measuring the tracking capability of recursive algorithms when applied to slowly time varying systems the optimal gain for a given disturbance is also calculated this criterion is seen to have some connection with the fisher information matrix and allows us to select a priori the best algorithm for identifying a given unknown parameter which may be subject to smooth unknown disturbances examples of applications are given in the areas of identification theory and data communication theory

on the numerical approximation of high frequency acoustic multiple scattering problems by circular cylinders the aim of this paper is to propose a numerical strategy for computing the solution of two dimensional time harmonic acoustic multiple scattering problems at high frequency the scatterers are assumed to be circular leading therefore to semi analytical representation formulae of the scattered field through the solution of a large linear system of equations taking advantage of the special block toeplitz structure of the matrix of the linear system a fast iterative and preconditioned numerical method yielding large memory savings is proposed several numerical experiments for general configurations are presented to show the efficiency of the numerical method

paper tracking error bounds of adaptive nonstationary filtering adaptive filtering with error gradient algorithm and constant step size is analyzed for a deterministic time variable optimum filtering vector the unrealistic assumption of independent observations is replaced by a bounded memory model largely justifiable in applications then the mean square tracking deviation msd between the optimum vector and the algorithm output is proved to include two contributions the stationary mode error characteristic of convergence accuracy which is proportional to the step size and the transient mode error reflecting the rapidity of tracking which is proportional to the squared ratio of the maximum optimum estimator increment to the step size this result agrees with the common intuition that there exists an optimum step size which compromises between convergence accuracy and tracking speed

nonparametric kernel algorithm for recovery of functions from noisy measurements with applications this note presents a kernel algorithm for recovery of a regression function from noisy data conditions are provided that assure pointwise convergence in the mean square and almost sure senses an application to a class of linear system identification problems is discussed

bounds on achievable performance in the identification and adaptive control of time varying systems treats the identification and adaptive control of time varying linear systems for linear systems with a gauss markov parameter process a global lower bound on the mean square error is obtained which is valid for any causal parameter estimator a similar lower bound is obtained for any causal one step ahead predictor these bounds are applied to the adaptive control of time varying systems to obtain a lower bound on closed loop mean square performance for any causal control law for a specific control law mean square stability is established and through simulations it is seen that the performance nearly meets the theoretical lower bound

adaptive stabilization of time varying discrete time linear systems we develop an adaptive control technique for the regulation of a class of linear discrete time time varying system the only a priori knowledge required is a bound of the varying component of the parameters the result is concerned with global behaviour

identification of discrete hammerstein systems using kernel regression estimates in this note a discrete time hammerstein system is identified the weighting function of the dynamical subsystem is recovered by the correlation method the main results concern estimation of the nonlinear memoryless subsystem no conditions concerning functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is presented the algorithm is a nonparametric kernel estimate of regression functions calculated from dependent data it is shown that the algorithm converges to the characteristic as the number of observations tend to infinity for sufficiently smooth characteristics the rate of convergence is o n 2 5 in probability

spectral and condition number estimates of the acoustic single layer operator for low frequency multiple scattering in dilute media the aim of this paper is to develop an analysis of the distribution of the eigenvalues of the acoustic single layer potential for various low frequency two dimensional multiple scattering problems the obstacles are supposed to be distant dilute media in cite thierrythesis it is shown that an approach based on the gershgorin disks provides limited spectral information we therefore introduce an alternative approach by applying the power iteration method to the limit matrix associated with the zero order spatial modes which results in satisfactory estimates all these approximations are built for circular cylinders and formally extended to ellipses and rectangles for linear boundary element methods with non uniform meshes this study is completed in cite antoinethierrypart2 by spectral estimates for the case of close obstacles

a robust adaptive minimum variance controller this paper addresses the twin questions of performance and robustness of an adaptive controller for single input single output linear stochastic systems the authors present an adaptive controller that has the following properties 1 attaining optimal regulation and tracking in the ideal minimum phase known upper bound on system order known sign and lower bound for the leading coefficient b 0 positive real condition on noise case and self tuning in a cesaro sense to a minimum variance regulator in the case of pure regulation 2 providing mean square stability when the system is of minimum phase with known upper bound on order but not necessarily satisfying a positive real condition on the noise 3 providing mean square stability when the system is in a graph topological neighborhood of computable size of an ideal plant as in 1 and the statistical properties of the disturbance are violated 4 continuing to stabilize the system when the adaptation gain is prevented from vanishing

spectral and condition number estimates of the acoustic single layer operator for low frequency multiple scattering in dense media the aim of this paper is to derive spectral and condition number estimates of the single layer operator for low frequency multiple scattering problems this work extends to dense media the analysis initiated in antoine and thierry in press 19 estimates are obtained first in the case of circular cylinders by fourier analysis and are next formally adapted to disks ellipses and rectangles in the framework of boundary element methods numerical simulations validating the approach are also given

the limiting behavior of lms a realization oriented analysis is given of the gradient noise misadjustment and lag misadjustment performance of the lms least mean square algorithm new formulas are given for both of these components of excess mean square error it is shown that the traditional formula for lag misadjustment needs to be modified by adding further terms due to gradient noise and noise variance to perform the analysis it is necessary to study the convergence with probability one of the noise free fixed parameter lms algorithm convergence is found under simple conditions that improve on those previously obtained

nonparametric algorithm for identification of weakly nonlinear static distributed parameter systems an algorithm for identification of a nonlinear characteristic in a static distributed parameter system is proposed the algorithm is nonparametric in the sense that only smooth requirements are imposed on the unknown characteristic and that the number of terms in its orthogonal series expansion is not fixed in advance depending on the number of measurements the idea borrowed from statistics computational simplicity of the algorithm is obtained by restricting its applications to the identification of only weakly nonlinear static systems which allows applying perturbation theory it is shown that if the unknown characteristic in the system equation is replaced by its estimator then the resulting state converges to the true system state in the mean square sense

stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses in this paper the stochastic optimal control of linear networked control system ncs with uncertain system dynamics and in the presence of network imperfections such as random delays and packet losses is derived the proposed stochastic optimal control method uses an adaptive estimator ae and ideas from q learning to solve the infinite horizon optimal regulation of unknown ncs with time varying system matrices next a stochastic suboptimal control scheme which uses ae and q learning is introduced for the regulation of unknown linear time invariant ncs that is derived using certainty equivalence property update laws for online tuning the unknown parameters of the ae to obtain the q function are derived lyapunov theory is used to show that all signals are asymptotically stable as and that the estimated control signals converge to optimal or suboptimal control inputs simulation results are included to show the effectiveness of the proposed schemes the result is an optimal control scheme that operates forward in time manner for unknown linear systems in contrast with standard riccati equation based schemes which function backward in time

global stability of adaptive pole placement algorithms this paper presents direct and indirect adaptive control schemes for assigning the closed loop poles of a single input single output system in both the continuous and discrete time cases the resulting closed loop system is shown to be globally stable when driven by an external reference signal consisting of a sum of sinusoids in particular persistent excitation of the potentially unbounded closed loop input output data and hence convergence of a sequential least squares identification algorithm is proved the results are applicable to standard sequential least squares and least squares with covariance reset

self convergence of weighted least squares with applications to stochastic adaptive control a recursive least squares algorithm with slowly decreasing weights for linear stochastic systems is found to have self convergence property i e it converges to a certain random vector almost surely irrespective of the control law design such algorithms enjoy almost the same nice asymptotic properties as the standard least squares this universal convergence result combined with a method of random regularization then easily can be applied to construct a self convergent and uniformly controllable estimated model and thus may enable us to form a general framework for adaptive control of possibly nonminimum phase autoregressive moving average with exogenous input armax systems as an application we give a simple solution to the well known stochastic adaptive pole placement and linear quadratic gaussian lqg control problems in the paper

robust model reference adaptive control we propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed loop adaptive control system with respect to unmodeled plant uncertainties the robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law the extra a priori information needed to design the adaptive law are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function

a recurrent self evolving fuzzy neural network with local feedbacks and its application to dynamic system processing this paper proposes a recurrent self evolving fuzzy neural network with local feedbacks rsefnn lf for dynamic system processing a rsefnn lf is composed of zero order or first order takagi sugeno kang tsk type recurrent fuzzy if then rules the recurrent structure in a rsefnn lf comes from locally feeding the firing strength of a fuzzy rule back to itself a rsefnn lf is constructed on line via simultaneous structure and parameter learning in structure learning an efficient rule and fuzzy set generation algorithm is proposed to generate fuzzy rules on line and reduce the number of fuzzy sets in each dimension in parameter learning the consequent part parameters are learned through a varying dimensional kalman filter algorithm whose input dimension varies with structure learning the antecedent part and feedback loop parameters are learned using a gradient descent algorithm the rsefnn lf is applied to dynamic system identification chaotic sequence prediction and speech recognition problems this paper also compares the performance of the rsefnn lf with other recurrent fuzzy neural networks

analysis of the kalman filter based estimation algorithm an orthogonal decomposition approach in this paper we shall provide new analysis on some fundamental properties of the kalman filter based parameter estimation algorithms using an orthogonal decomposition approach based on the excited subspace a theoretical analytical framework is established based on the decomposition of the covariance matrix which appears to be very useful and effective in the analysis of a parameter estimation algorithm with the existence of an unexcited subspace the sufficient and necessary condition for the boundedness of the covariance matrix in the kalman filter is established the idea of directional tracking is proposed to develop a new class of algorithms to overcome the windup problem based on the orthogonal decomposition approach two kinds of directional tracking algorithms are proposed these algorithms utilize a time varying covariance matrix and can keep stable even in the case of unsufficient and or unbounded excitation

persistence of excitation properties for time varying autoregressive systems it is well known that a crucial property for the effective identification of time varying systems is that the data carry continual information on the parameters to be estimated as a matter of fact only in this case can the identification algorithm rely on fresh information in forming a reliable estimate of the current value of these parameters this concept has been formalized in the system identification literature under the name of persistence of excitation in this paper the persistence of excitation property is studied for a class of time varying systems that includes the standard autoregressive model as a particular case and conditions for it to hold are derived

a carleson type condition for interpolation in bergman spaces an analogue of the notion of uniformly separated sequences expressed in terms of canonical divisors is shown to yield a necessary and sufficient condition for interpolation in the bergman space ap 0 0 such that j j 6 k zj zk 1 zjzk for all k 1 carleson s result can be extended to the hardy space h which for 0 p consists of the functions f analytic in d with f php sup 0 r 1 1 2 2 0 f rei pd we say that is interpolating for h if the interpolation problem f zj aj has a solution f h for every sequence aj with aj 1 zj 2 1 p shapiro and shields 15 proved that 1 is necessary and sufficient for to be interpolating for h 1 p and kab ila 10 obtained the same result for 0 p 1 consider now the bergman space a which is the set of functions f analytic in d with f p 1 d f z pda z where da denotes lebesgue area measure is interpolating for a if for every sequence aj satisfying aj 1 zj 2 2 p there is an f a with f zj aj interpolation sequences for the growth space a n as well as for a have been characterized completely in 13 using a density condition which will be defined shortly the purpose of this paper is to identify a condition for interpolation in the bergman spaces which though less 1991 mathematics subject classification 30h05 46e15

the aastrom wittenmark self tuning regulator revisited and els based adaptive trackers although considerable progress has been made in stochastic adaptive control the problem concerning the convergence of the original self tuning regulator proposed by k j aastrom and b wittenmark 1973 is still open since it is attractive in theory and important in applications this problem is examined and a rigorous proof of its stability and optimality is given related problems such as convergence of the extended least squares els based adaptive tracker are also considered

a smoothness priors time varying ar coefficient modeling of nonstationary covariance time series a smoothness priors time varying ar coefficient model approach for the modeling of nonstationary in the covariance time series is shown smoothness priors in the form of a difference equation constraint excited by an independent white noise are imposed on each ar coefficient the unknown white noise variances are hyperparameters of the ar coefficient distribution the critical computation is of the likelihood of the hyperparameters of the bayesian model this computation is facilitated by a state space representation kalman filter implementation the best difference equation order best ar model order best hyperparameter model locally in time is selected using the minimum aic method also an instantaneous spectral density is defined in terms of the instantaneous ar model coefficients and a smoothed estimate of the instantaneous time series variance an earthquake record is analyzed the changing spectral analysis of the original data and of simulations from a time varying ar coefficient model of that data are shown

nonparametric identification of quasi stationary systems abstract recursive estimates of a regression function based on the parzen rosenblatt kernels are applied for identification of quasi stationary systems it is shown that these estimates do not lose their asymptotic properties even if the data are not stationary conditions for weak and strong pointwise consistency are given

a globally convergent adaptive pole placement algorithm without a persistency of excitation requirement this paper presents an indirect adaptive control scheme for deterministic plants which are not necessarily minimum phase global convergence is established for the scheme in the sense that the closed loop poles are asymptotically assigned for the given data sequence and the system input and output remain bounded for all time a key feature of the scheme is that no persistency of excitation condition is required the algorithm uses recursive least squares with variable forgetting factor normalized regression vectors and a matrix gain with constant trace

a self evolving interval type 2 fuzzy neural network with online structure and parameter learning this paper proposes a self evolving interval type 2 fuzzy neural network seit2fnn with online structure and parameter learning the antecedent parts in each fuzzy rule of the seit2fnn are interval type 2 fuzzy sets and the fuzzy rules are of the takagi sugeno kang tsk type the initial rule base in the seit2fnn is empty and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space to avoid generating highly overlapping fuzzy sets in each input variable an efficient fuzzy set reduction method is also proposed this method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated for parameter learning the consequent part parameters are tuned by the rule ordered kalman filter algorithm for high accuracy learning performance detailed learning equations on applying the rule ordered kalman filter algorithm to the seit2fnn consequent part learning with rules being generated online are derived the antecedent part parameters are learned by gradient descent algorithms the seit2fnn is applied to simulations on nonlinear plant modeling adaptive noise cancellation and chaotic signal prediction comparisons with other type 1 and type 2 fuzzy systems in these examples verify the performance of the seit2fnn

on line identification of time varying systems by nonparametric techniques a nonparametric algorithm based on orthogonal series is proposed for real time identification of nonstationary systems it is proved that the algorithm converges in the mean square sense the convergence conditions are closely related to those in dupac 2

estimating time varying parameters by the kalman filter based algorithm stability and convergence convergence and stability properties of the kalman filter based parameter estimator are established for linear stochastic time varying regression models the main features are both the variances and sample path averages of the parameter tracking error are shown to be bounded the regression vector includes both stochastic and deterministic signals and no assumptions of stationarity or independence are requires and the unknown parameters are only assumed to have bounded variations in an average sense

on the spectrum of the electric field integral equation and the convergence of the moment method existing convergence estimates for numerical scattering methods based on boundary integral equations are asymptotic in the limit of vanishing discretization length and break down as the electrical size of the problem grows in order to analyse the efficiency and accuracy of numerical methods for the large scattering problems of interest in computational electromagnetics we study the spectrum of the electric field integral equation efie for an infinite conducting strip for both the tm weakly singular kernel and te polarizations hypersingular kernel due to the self coupling of surface wave modes the condition number of the discretized integral equation increases as the square root of the electrical size of the strip for both polarizations from the spectrum of the efie the solution error introduced by discretization of the integral equation can also be estimated away from the edge singularities of the solution the error is second order in the discretization length for low order bases with exact integration of matrix elements and is first order if an approximate quadrature rule is employed comparison with numerical results demonstrates the validity of these condition number and solution error estimates the spectral theory offers insights into the behaviour of numerical methods commonly observed in computational electromagnetics copyright 2001 john wiley sons ltd

a new approach to stochastic adaptive control the principal techniques used up to now for the analysis of stochastic adaptive control systems have been 1 super martingale often called stochastic lyapunov methods and 2 methods relying upon the strong consistency of some parameter estimation scheme optimal stochastic control and filtering methods have also been employed although there have been some successes the extension of these techniques to a broader class of adaptive control problems including the case of time varying parameters has been difficult in this paper a new approach is adopted if an underlying markovian state space system for the controlled process is available and if this process possesses stationary transition probabilities then the powerful ergodic theory of markov processes may be applied subject to technical conditions such as stability one may deduce 1 the existence of an invariant measure for the process and 2 the convergence almost surely of the sample averages of a function of the state process and of its expectation to its conditional expectation the technique is illustrated by an application to a previously unsolved problem involving a linear system with unbounded random time varying parameters

on critical stability of discrete time adaptive nonlinear control in this paper we examine the global stability and instability problems for a class of discrete time adaptive nonlinear stochastic control the systems to be controlled may exhibit chaotic behavior and are assumed to be linear in unknown parameters but nonlinear in output dynamics which are characterized by a nonlinear function say f x it is found and proved that in the scalar parameter case there is a critical stability phenomenon for least squares ls based adaptive control systems to be specific let the growth rate of f x be f x o spl par x spl par sup 6 with b spl ges 0 then it is found that b 4 is a critical value for global stability i e the closed loop adaptive system is globally stable if b 4 and is unstable in general if b spl ges 4 as a consequence we find an interesting phenomenon that the linear case does not have for some ls based certainty equivalence adaptive controls even if the ls parameter estimates are strongly consistent the closed loop systems may still be unstable this paper also indicates that adaptive nonlinear stochastic control that is designed based on e g taylor expansion or weierstrass approximation for nonlinear models may not be feasible in general

convergence and logarithm laws of self tuning regulators abstract this paper starts with a survey of some recent results on least squares ls and ls based self tuning regulators str several long standing problems concerning the basic properties of ls based str such as stability optimality consistency and the best convergence rate are solved within a unified framework some previously related results are also subsumed and extended various new techniques for analysing ls based adaptive tracking systems are presented which may also be useful for analysing other adaptive control problems

stochastic adaptive control and martingale limit theory recently s p meyn and p e caines ibid vol ac 32 p 220 6 1987 have used ergodic theory for markov processes to give the first asymptotic stability analysis of a nontrivial stochastic adaptive control problem by nontrivial is meant a stochastic adaptive control problem whose parameter variation has finite nonzero power they correctly observed that the stochastic lyapunov function methods fail here because there is no almost sure parameter convergence it is shown here how martingale asymptotics can be used to produce many results close to those of meyn and caines as well as to supply some new observations strengths and weaknesses of both approaches are discussed

optimization of adaptive identification for time varying filters adaptive identification in a time varying context is studied when controlled by the lms algorithm with constant gain under the assumption of correlated successive input vectors it is well known by experience that the tracking mean square error mse epsilon mu results from the tradeoff between the gradient part which is increasing and the lag contribution which is decreasing in this note we clarify the relative roles of the gradient and lag errors by proving their decoupled character this property relies upon independence between the additive noise at the output of the plant to be identified and the information vector at the plant input convergence of the mse is established rather than assumed quantitative evaluations of upper and lower bounds allow an approximate optimization of the gain in two important cases the optimum is exact one of these cases is slow variations it is defined in a quantitative manner thanks to the ratio of the variation noise to the output additive noise

sampling sets and sufficient sets for a abstract we give new characterizations of the subsets s of the unit disc d of the complex plane such that the topology of the space a of holomorphic functions of polynomial growth on d coincides with the topology of space of the restrictions of the functions to the set s these sets are called weakly sufficient sets for a our approach is based on a study of the so called p q sampling sets which generalize the a p sampling sets of seip a characterization of p q sampling and weakly sufficient rotation invariant sets is included it permits us to obtain new examples and to solve an open question of khoi and thomas

sampling measures for bergman spaces on the unit disk we provide a characterization of the sampling measures for the bergman spaces these are the positive measures mu on the unit disk bbb d for which there exists a constant c 0 such that

a nonparametric algorithm for identification of linear dynamic siso systems of unknown order a new nonparametric algorithm is presented for estimation of the weighting function of linear dynamic single input single output systems the behavior of the mean squared error of the proposed estimate is examined finally the optimal parameter is found for the best speed of uniform mean squared consistency

brief paper on the lower smoothing bound in identification of time varying systems in certain applications of nonstationary system identification the model based decisions can be postponed i e executed with a delay this allows one to incorporate in the identification process not only the currently available information but also a number of future data points the resulting estimation schemes which involve smoothing are not causal assuming that the infinite observation history is available the paper establishes the lower steady state estimation bound for any noncausal estimator applied to a linear system with randomly drifting coefficients under gaussian assumptions this lower bound complements the currently available one which is restricted to causal estimators

adaptive control of time varying linear systems the authors present a global bounded input bounded state stability theory for a class of continuously adapting controllers applied to time varying linear systems this gives theoretical support to the application of many of the algorithms used in practice a key feature of the analysis is that no persistence of excitation requirement is needed

adaptive control for systems with bounded disturbances the authors present an identification algorithm that can be used to design globally stable indirect adaptive controllers for minimum and nonminimum phase systems subject to bounded disturbances the parameter estimation scheme is a least squares algorithm with dead zone the dead zone is such that the estimates converge and make it possible to define projected estimates having the same convergence properties as the original estimates in the minimum phase case the projection facility can be used to ensure that the leading coefficient projected estimate is greater than or equal to the true leading coefficient in absolute value the projection procedure can also be used to avoid pole zero cancellations in an adaptive pole placement algorithm

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

convergence rate of least squares identification and adaptive control for stochastic systems the strong consistency and the convergence rate of least squares identification for the multidimensional armax model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied the parameter identification results are applied to adaptive control systems with a quadratic loss function the rate of convergence of the loss function to its minimum is also obtained

extended least squares and their applications to adaptive control and prediction in linear systems herein strong consistency of recursive extended least squares is established under considerably weaker assumptions than previously assumed in the literature the argument used to establish consistency also leads to certain basic properties of adaptive predictors based on these recursive estimators making use of these properties of the adaptive predictors simple modifications of the astrom wittenmark self tuning regulator are proposed and shown to be asymptotically optimal

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

reformulation of the parameter identification problem for systems with bounded disturbances abstract the problem of deriving parameter identification algorithms that incorporate prior knowledge of a bound on the disturbance is studied particular emphasis is given to the following aspects firstly to motivate from geometrical and optimization considerations the modifications dead zones required to cope with the disturbances secondly to guarantee the convergence properties which are essential in the establishment of stability of identification based adaptive control systems projection and least squares algorithms are studied in both cases an interpretation is given to the new dead zone that has proven to be a key ingredient in recent robustness studies e g goodwin et al 1986 automatica 22 199 207 kreisselmeier and anderson 1985 ieee trans aut control 31 127 133 and lozano leal and ortega 1986 2nd ifac workshop on adapt syst in control and signal proc lund sweden

robust adaptive regulation with minimal prior knowledge a robust adaptive regulator is designed under minimal prior knowledge namely the order of a nominal plant model in a well defined sense the involved robustness means that the closed loop stability is guaranteed in the presence of some class of time varying parameters and unmodeled dynamics the main design feature of the proposed adaptive regulator consists in its self excitation capability together with an appropriate identification stabilization time splitting unlike in the available literature concerning robust adaptive control the involved self excitation is established independently of the parameter estimator properties the use of the robustness oriented modifications as deadzone and parameter projection or contraction which are aimed at achieving the parameter estimates boundedness is no longer required beforehand thereby reducing the underlying prior knowledge

analytic representations in quantum mechanics various euclidean hyperbolic and elliptic analytic representations are introduced and relations among them are discussed the bargmann analytic representation in the complex plane is considered and its relation to other phase space methods for the harmonic oscillator is reviewed the general theory that relates the growth of analytic functions with the density of their zeros is applied to bargmann functions and it leads to theorems on the completeness of sequences of glauber coherent states two hyperbolic analytic representations in the unit disc based on su 1 1 coherent states and also on phase states are introduced a third analytic representation in the complex plane based on barut girardello states is also considered and transformations which relate it to the other ones are studied in the case of systems with finite dimensional hilbert space an elliptic analytic representation in the extended complex plane and also another analytic representation based on theta functions are introduced the berezin formalism in the euclidean hyperbolic and elliptic cases is discussed contour analytic representations in these three cases are also presented

boundedness properties of simple indirect adaptive control systems examining adaptive controllers for a class of first order linear continuous time plants with different estimators and control laws the authors obtain explicit solutions completely describing the nonlinear behavior of the resultant adaptive systems some of these adaptive systems exhibit either finite time escapes or other forms of unbounded behavior due to a loss of stabilizability of the estimated model some fixes for the loss of stabilizability problem are analyzed implications of these results for the general indirect adaptive control case are discussed

towards understanding the capability of adaptation for time varying systems the information uncertainty coupled with the structural complexity is more pertinent than the rate of parameter changes in characterizing the capability of adaptation for time varying systems

hammerstein system identification by non parametric regression estimation a discrete time multiple input non linear hammerstein system is identified the dynamical subsystem is recovered using the standard correlation method the main results concern estimation of the non linear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a non parametric kernel estimate of the regression function calculated from the dependent data it is shown that the algorithm converges to the characteristic of the subsystem in the pointwise as well as the global sense for sufficiently smooth characteristics the rate of convergence is o n 1 2 d in probability where d is the dimension of the input variable

beurling type density theorems in the unit disk we consider two equivalent density concepts for the unit disk that provide a complete description of sampling and interpolation ina n the banach space of functionsf analytic in the unit disk with 1 z 2 n f z bounded this study reveals a nyquist density a sequence of points is roughly speaking a set of sampling if and only if its density in every part of the disk is strictly larger thann and it is a set of interpolation if and only if its density in every part of the disk is strictly smaller thann similar density theorems are also obtained for weighted bergman spaces

convergence of adaptive control schemes using least squares parameter estimates the stability convergence asymptotic optimality and self tuning properties of stochastic adaptive control schemes based on least squares estimates of the unknown parameters are examined it is assumed that the additive noise is i i d and gaussian and that the true system is of minimum phase the bayesian embedding technique is used to show that the recursive least squares parameter estimates converge in general the normal equations of least squares are used to establish that all stable control law designs used in a certainty equivalent i e indirect procedure generally yield a stable adaptive control system four results are given to characterize the limiting behavior precisely a certainty equivalent self tuning regulator is shown to yield strongly consistent parameter estimates when the delay is strictly greater than one even without any excitation in the reference trajectory

bounded error identification of time varying parameters by rls techniques the performance of the recursive least squares algorithm with constant forgetting factor in the identification of time varying parameters is studied in a stochastic framework it is shown that the mean square tracking error keeps bounded if and only if the so called covariance matrix of the algorithm is l sup 1 bounded then a feasibility range for the forgetting factor is worked out in correspondence of which the covariance matrix and therefore the tracking error keeps bounded

performance analysis of general tracking algorithms a general family of tracking algorithms for linear regression models is studied it includes the familiar least mean square gradient approach recursive least squares and kalman filter based estimators the exact expressions for the quality of the obtained estimates are complicated approximate and easy to use expressions for the covariance matrix of the parameter tracking error are developed these are applicable over the whole time interval including the transient and the approximation error can be explicitly calculated

uniform densities of regular sequences in the unit disk the upper and lower uniform densities of some regular sequences are computed these densities are used to determine sets of sampling and interpolation for bergman spaces of the unit disk

on almost sure convergence of adaptive algorithms we present an extension of the furstenberg kesten theorem on the convergence of random matrices this extension is applied to the study of almost sure convergence of certain adaptive algorithms in particular we establish that the nlms algorithm is almost surely convergent under extremely weak necessary and sufficient conditions we also discuss the relationship of sufficient conditions that have appeared in the literature with our results