further results on least squares based adaptive minimum variance control based on the recently established results on self tuning regulators originally proposed by astrom and wittenmark this paper presents various novel and extended results on least squares based adaptive minimum variance control for linear stochastic systems these results establish self optimality self tuning property and the best possible convergence rate of the control law in a variety of situations of interest

cloaking via change of variables for the helmholtz equation the transformation optics approach to cloaking uses a singular change of coordinates which blows up a point to the region being cloaked this paper examines a natural regularization obtained by 1 blowing up a ball of radius rather than a point and 2 including a well chosen lossy layer at the inner edge of the cloak we assess the performance of the resulting near cloak as the regularization parameter tends to 0 in the context of dirichlet and neumann boundary measurements for the time harmonic helmholtz equation since the goal is to achieve cloaking regardless of the content of the cloaked region we focus on estimates that are uniform with respect to the physical properties of this region in three space dimensions our regularized construction performs relatively well the deviation from perfect cloaking is of order in two space dimensions it does much worse the deviation is of order 1 log in addition to proving these estimates we give numerical examples demonstrating their sharpness some authors have argued that perfect cloaking can be achieved without losses by using the singular change of variable based construction in our regularized setting the analogous statement is false without the lossy layer there are certain resonant inclusions depending in general on that have a huge effect on the boundary measurements 2010 wiley periodicals inc

adaptive control of parametric nonlinear autoregressive models via a new martingale approach the purpose of this note is to investigate the stability and the optimality of the adaptive tracking for a wide class of parametric nonlinear autoregressive models via a new martingale approach several asymptotic results for the standard least squares estimator of the unknown model parameter such as a central limit theorem a law of iterated logarithm and strong laws of large numbers are also provided

convergence rates in stochastic adaptive tracking abstract for stochastic control systems described by the armax model with unknown matrix coefficients the stochastic adaptive control is designed so that the parameter estimates converge to the true values with a rate of convergence o log n log log n c n a with a 0 c 1 and the tracking error tends to its minimum value at a speed of o n 1 2e with e 0

discrete time stochastic adaptive control this paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems it is shown that with probability one the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control thus asymptotically the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known

localization of multi constrained optima and avoidance of local optima in structural optimization problems abstract this paper describes two new methods of structural optimization the first method is seen primarily in conjunction with optimality criteria algorithms it proposes a new procedure for the solution of multi constrained optimization problems based on the calculation of partial optima the partial optima refer to solutions of the optimization problem only for part of the constraints in the simplest case only for a single constraint and can be easily determined by already known procedures the second method is a new mathematical programming method designed to combine a high convergence speed together with a high reliability with respect to the avoidance of local minima

nonlinearity estimation in hammerstein systems based on ordered observations the nonlinear subsystem of a hammerstein system is identified i e its characteristic is recovered from input output ohservations of the whole system the input and disturbance are white stochastic processes the identified characteristic satisfies a piecewise lipschitz condition only algorithms presented in the paper are calculated from ordered input output observations i e from pairs of observations arranged in a sequence in which input measurements increase in value the mean integrated square error converges to zero as the number of observations tends to infinity convergence rates are insensitive to the shape of the probability density of the input signal results of numerical simulation are also shown

adaptive control with recursive identification for stochastic linear systems this paper presents a stochastic adaptive control algorithm which is shown to possess the following properties when applied to a possibly unstable inverse stable linear stochastic system with unknown parameters whenever that system satisfies a certain positive real condition on its moving average noise dynamics 1 the adaptive control part of the algorithm stabilizes and asymptotically optimizes the behavior of the system in the sense that the limit of the sample mean square variation of the output around a given demand level equals that of a minimum variance control strategy implemented with known parameters this optimal behavior is subject to an offset 2where 2is the variance of a dither signal added to the control action in order to produce a continually disturbed control for mu 2 0 it is shown that the input output process satisfies a persistent excitation property and hence subject to a simple identifiability condition the next property holds 2 the observed input and output of the controlled system may be taken as inputs to an approximate maximum likelihood algorithm aml which generates strongly consistent estimates of the system s parameters results are presented for the scalar and multivariable cases

central limit theorem and law of iterated logarithm for least squares algorithms in adaptive tracking in autoregressive adaptive tracking we prove that the least squares and the weighted least squares algorithms possess the same asymptotic properties sharing the same central limit theorem and the same law of iterated logarithm we also obtain the same asymptotic behavior and show the limitations of these results in the autoregressive with moving average framework

discrete time model reference adaptive control of nonlinear dynamical systems using neural networks a multilayer discrete time neural net nn controller is presented for the direct model reference adaptive control of a class of multi input multi output mim0 nonlinear dynamical systems the nonlinear dynamical system is assumed to be controllable and its state vector is available for measurement the nn controller exhibits learning while functioning features instead of learning then control so that control is immediate with no explicit learning phase needed the tracking error between the output of a nonlinear plant and an ideal linear model converges within a very short time persistence of excitation pe is not needed linearity in the parameters is not required and certainty equivalence is not used this overcomes several limitations of standard adaptive control the novel weight tuning paradigm for the nn controller is based on the well known delta rule but includes a modification to the learning rate parameter plus a correction term it guarantees tracking as well as bounded nn weights in non i

a robbins monro procedure for estimation in semiparametric regression models this paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model we implement a robbins monro procedure very efficient and easy to handle on the one hand we propose a stochastic algorithm similar to that of robbins monro in order to estimate the shift parameter a preliminary evaluation of the regression function is not necessary for estimating the shift parameter on the other hand we make use of a recursive nadaraya watson estimator for the estimation of the regression function this kernel estimator takes in account the previous estimation of the shift parameter we establish the almost sure convergence for both robbins monro and nadaraya watson estimators the asymptotic normality of our estimates is also provided

approximate cloaking for the helmholtz equation via transformation optics and consequences for perfect cloaking in this paper we study approximate cloaking of active devices for the helmholtz equation in the whole space of dimension 2 or 3 using the scheme introduced by kohn shen vogelius and weinstein more precisely we assess the degree of invisibility determine the limit of the field inside the cloaked and cloaking regions and show that the scheme is unstable with respect to the material parameters as a consequence we obtain some feasible properties of perfect cloaking 2011 wiley periodicals inc

stochastic adaptive prediction and model reference control guo and chen 1991 have recently shown how to establish the self optimality and mean square stability of a self tuning regulator the idea allows us to proceed with the development of a more comprehensive theory of stochastic adaptive filtering control and identification in adaptive filtering we examine both indirect and noninterlaced direct schemes for prediction using both least squares and gradient parameter estimation algorithms in addition to analyzing similar direct adaptive control algorithms we propose new generalized certainty equivalence adaptive model reference control laws with simultaneous disturbance rejection we also establish that the parameters converge to the null space of a certain matrix from this one may deduce the convergence of several adaptive controllers

almost sure rate of convergence of the parameter estimates in stochastic approximation algorithm this paper presents novel results on the almost sure convergence of the parameter estimates in stochastic approximation algorithm it is proved that this rate has the same order as the best one established for the least squares algorithm although we consider the case of self tuning controllers the presented results can easily be extended to some other adaptive processes

nonparametric estimation and adaptive control of functional autoregressive models this paper deals with nonparametric estimation and adaptive control of nonlinear systems of the form x n 1 f x n u n xi n 1 n in bkn where the state x n is observed f is an unknown function and the control un is chosen in order to track a given reference trajectory we estimate the function f using a nonparametric estimator and study two adaptive control laws built from this nonparametric estimator and derived from the self tuning control the first one can be used for open loop stable systems and requires an additional exciting noise the second one needs some a priori knowledge on function f but allows us to control open loop unstable systems we establish some general results on the nonparametric estimator of f like the uniform almost sure convergence over dilating sets and then prove that both adaptive control laws are asymptotically optimal in quadratic mean in addition we give a strongly consistent estimator of the covariance matrix of the unobservable white noise xi n

on feedback capability in a class of nonlinearly parameterized uncertain systems in this technical note we will investigate the maximum capability and limitations of the feedback mechanism in globally stabilizing a basic class of discrete time nonlinearly parameterized dynamical systems with multiple unknown parameters both possibility and impossibility theorems together with a fairly complete characterization on the capability of feedback will be presented it will be seen that to characterize the feedback capability the growth rates of the sensitivity functions of the nonlinear dynamics with respect to the uncertain parameters play a crucial role and a suitable decomposition of the family of the nonlinearly parameterized functions in question turns out to be necessary

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear 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 nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

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

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

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

on the usefulness of persistent excitation in arx adaptive tracking the usefulness of persistent excitation is well known in the control community thanks to a persistently excited adaptive tracking control we show that it is possible to avoid the strong controllability assumption recently proposed in the multidimensional arx framework we establish the almost sure convergence for both least squares and weighted least squares estimators of the unknown parameters a central limit theorem and a law of iterated logarithm are also provided all this asymptotical analysis is related to the schur complement of a suitable limiting matrix

indirect adaptive pole placement control of mimo stochastic systems self tuning results in this paper we consider indirect adaptive pole placement control appc of linear multivariable stochastic systems instead of the canonical representation often used in the literature we propose using a non minimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable armax model identification to identify the plant we use the weighted extended least squares wels algorithm a least squares method with slowly decreasing weights which was introduced in bercu 1995 the pole placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable we prove that with a reasonable amount of prior information the resulting appc scheme is globally stabilizing and asymptotically self tuning regardless of the degree of persistency of external excitation these results represent the most complete study of stochastic multivariable appc systems to this date

identification of iir nonlinear systems without prior structural information in this paper we propose a kernel method for identification of infinite impulse response iir nonlinear systems without prior structural information the main result of the paper is to establish the conditions for asymptotic convergence in terms of the input to output exponential stability the performance of the method is tested on real world applications and computer simulations the results obtained show the efficacy of the method

weighted estimation and tracking for branching processes with immigration for branching processes with immigration we propose an approach which allows us to consistently estimate the means m spl lambda and the variances spl sigma sup 2 b sup 2 of the offspring and immigration distributions respectively generally statistical results for branching processes are established under the well known trichotomy m 1 for example no parameters of the immigration distribution can be consistently estimated if m 1 the purpose of the paper is to obtain through the introduction of a suitable adaptive control strongly consistent estimators for all the parameters m spl lambda spl sigma sup 2 and b sup 2 without any restriction on the range of m central limit theorems and laws of iterated logarithm are also provided

well posedness study for a time domain spherical cloaking model in this paper we study a time domain spherical cloaking model recently introduced by zhao and hao 2009 this model is quite complicated and is composed of four coupled differential equations here we first prove the existence and uniqueness of a solution for this model then we obtain a stability result which analysis is quite involved due to the coupling between the four variables to our best knowledge this is the first well posedness study carried out for the time domain cloaking model with metamaterials

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

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

asymptotically efficient self tuning regulators this paper studies the problem of adaptive regulation of linear systems with white noise disturbances the apparent dilemma between the control objective and the need of information for parameter estimation is resolved by occasional use of white noise probing inputs and by a reparametrization of the model insights into the question concerning how often and when such probing inputs should be introduced are provided by the concept of asymptotic efficiency which quantifies the asymptotically minimal cost due to parameter ignorance or equivalently due to the infeasibility of using the optimal regulator that assumes knowledge of the system parameters asymptotically efficient adaptive regulators are constructed by making use of certain basic properties of adaptive predictors involving recursive least squares for the reparametrized model

a parallel structural optimization method and its implementation on a transtech paramid abstract this paper presents a parallel structural optimization method and its implementation on a distributed memory multiple instruction multiple data parallel computer the proposed strategy does not require the formation or solution of global system equations instead each processor of the parallel computer stores only the data relevant to one structural element or substructure and generates its local stiffness matrix a parallel conjugate gradient procedure using the optimality criterion approach is employed to compute the displacements and modified design for each element or substructure an implementation of the parallel structural optimization method on a transtech paramid parallel computer is discussed the speedup and efficiency of this method being demonstrated by numerical examples

on convergence of the recursive identification algorithms the paper is concerned with identification of a linear dynamic system through recursive algorithms of the approximate maximum likelihood aml method in all papers on the convergence of the recursive aml procedure no matter what method of analysis is used a certain rather restrictive positive real condition is imposed on the model of disturbance in this work it is shown that recursive aml algorithms converge with probability one under a fairly broad also positive real condition which significantly expands the aml application area the well known principle of averaging from physics is used as a tool of analysis a sketch of the proof of the principle of averaging for stochastic difference equations is given

weighted estimation and tracking for armax models for complex multivariate armax models the author studies the weighted least squares algorithm which offers by the choice of suitable weightings the advantages of both the extended least squares and the stochastic gradient algorithms concerning adaptive tracking problems the strong consistency of the estimator and control optimality are both ensured almost sure rates of convergence are also provided

adaptive tracking control of linear systems with binary valued observations and periodic target this technical note studies the adaptive control for linear systems with set valued observations to track a given periodic target based on the system parameters accessorial parameters with the same order as that of the tracking targets are introduced and estimated considering the system parameters are unknown and set valued observations can supply only limited information each time a two scale adaptive control algorithm is designed each control input is designed at the large time scale and lasts for a holding time small scale during which the parameter estimation algorithm is constructed from the estimate of accessorial parameters the control signal is updated at the large time scale by the certainty equivalence principle as the holding time goes to infinity the algorithm can be proved to be asymptotically efficient in a certain sense meanwhile the adaptive tracking algorithm is shown to be asymptotically optimal a numerical example is given to demonstrate the effectiveness of the algorithms and the main results obtained

brief paper a new concept of strong controllability via the schur complement for arx models in adaptive tracking we propose a new concept of strong controllability related to the schur complement of a suitable limiting matrix this new notion allows us to extend the previous convergence results associated with multidimensional arx models in stochastic adaptive tracking on the one hand we carry out a sharp analysis of the almost sure convergence for both least squares and weighted least squares algorithms on the other hand we also provide a central limit theorem and a law of iterated logarithm for these two algorithms

persistence of excitation in extended least squares in least squares parameter estimation schemes persistency of excitation conditions on the plant states are required for consistent estimation in the case of extended least squares the persistency conditions are on the state estimates here these persistency of excitation conditions are translated into sufficiently rich conditions on the plant noise and inputs in the case of adaptive minimum variance control schemes the sufficiently rich conditions are on the noise and specified output trajectory with sufficiently rich input signals guaranteed convergence rates of prediction errors improve and it is conjectured that the algorithms are consequently more robust

efficient optimum design of structures program dddu abstract an efficient optimization algorithm is developed for engineering structures subject to multiple constraints this highly non linear and implicit problem is reduced to a combination of a sequence of quasi linear constraints and explicit problems of the statically determined structures the method is based on the kuhn tucker necessary conditions for optimality associated with a simple quadratic programme designed simultaneously to determine the lagrange multipliers and to delete non active constraints a number of examples including trusses and wing structures show that the method is efficient when compared with other competing techniques

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

nonlinear adaptive tracking using kernel estimators estimation and test for linearity we present some statistical results on nonlinear adaptive control using kernel estimators we are concerned with a nonlinear autoregressive model of the form x n 1 f x n u n xi n 1 hskip 0 4cm n in mathbb n controlled using a nonparametric estimator of the unknown function f and derived from a tracking control policy we prove an almost sure convergence result for the noise density estimator a pointwise central limit theorem for f and a test for linearity of the driving function f

adaptive control with the stochastic approximation algorithm geometry and convergence new geometric properties possessed by the sequence of parameter estimates are exhibited which yield valuable insight into the behavior of the stochastic approximation based algorithm as it is used in minimum variance adaptive control in particular these geometric properties together with certain probabilistic arguments prove that if the system does not have a reduced order minimum variance controller then the parameter estimates converge to a random multiple of the true parameter an explicit expression for the limiting parameter estimate is also available with strictly positive probability the limiting parameter estimate is not the true parameter and in some cases differs from the true parameter with probability one if the system possesses reduced order minimum variance controllers then convergence to a minimum variance controller in a cesaro sense is shown the geometry of the limit set is described sufficient conditions are also given for some of these results to hold for parameter estimation schemes other than stochastic approximation

nonparametric function estimation involving time series consider a stationary time series mathbf x t y t t 0 pm 1 ldots with mathbf x t being mathbb r d valued and y t real valued the conditional mean function is given by theta mathbf x 0 e y 0 mid mathbf x 0 under appropriate regularity conditions a local average estimator of this function based on a finite realization mathbf x 1 y 1 ldots mathbf x n y n can be chosen to achieve the optimal rate of convergence n 1 2 d both pointwise and in l 2 norms restricted to a compact and it can also be chosen to achieve the optimal rate of convergence n 1 log n 1 2 d in l infty norm restricted to a compact similar results hold for local median estimators of the conditional median function which is given by theta mathbf x 0 operatorname med y 0 mid mathbf x 0

kernel density estimation and goodness of fit test in adaptive tracking we investigate the asymptotic properties of a recursive kernel density estimator of the driven noise of multivariate armax models in adaptive tracking we provide an almost sure pointwise and uniform strong law of large numbers as well as a pointwise and multivariate central limit theorem we also carry out a goodness of fit test together with some simulation experiments

cloaking via change of variables for the helmholtz equation in the whole space this paper is devoted to the study of a cloaking device that is composed of a standard near cloak based on a regularization of the transformation optics i e a change of variables that blows up a small ball to the cloaked region and a fixed lossy layer for the helmholtz equation in the whole space of dimension 2 or 3 with the outgoing condition at infinity we establish a degree of near invisibility which is independent of the content inside the cloaked region for this device we also show that the lossy layer is necessary to ensure the validity of the degree of near invisibility when no constraint on physical properties inside the cloaked region is imposed 2010 wiley periodicals inc