discrete time adaptive iterative learning control for high order nonlinear systems with unknown control directions an adaptive iterative learning control method is proposed for a class of nonlinear strict feedback discrete time systems with random initial conditions and iteration varying desired trajectories an n step ahead predictor approach is employed to estimate the future states in the control design discrete nussbaum gain method is utilised to deal with the lack of a priori knowledge of control directions the proposed control algorithm guarantees the boundedness of all the signals in the controlled system the tracking error converges to zero asymptotically along the iterative learning axis except for beginning states affected by random initial conditions the effectiveness of the proposed control scheme is verified through numerical simulation

random rates in anisotropic regression in the context of minimax theory we propose a new kind of risk normalized by a random variable measurable with respect to the data we present a notion of optimality and a method to construct optimal procedures accordingly we apply this general setup to the problem of selecting significant variables in gaussian white noise in particular we show that our method essentially improves the accuracy of estimation in the sense of giving explicit improved confidence sets in l2 norm links to adaptive estimation are discussed 1 introduction searching for significant variables is certainly one of the oldest and most popular problems in statistics one of the simplest models where the issue of selecting significant variables was first stated mathematically is linear regression a vast literature has been devoted to this topic since and different approaches have been proposed over the last forty years both for estimation and for hypothesis testing among many authors we refer to akaike 1 breiman and freedman 3 chernoff 5 csiszar and korner 6 dychakov 10 patel 42 renyi 46 freidlina 13 meshalkin 35 malyutov and tsitovich 34 schwarz 47 and stone 48 in classical parametric regression if we consider a linear model we first have to measure the possible gain of searching for a limited number of significant variables if the model comes from a specific field of application then only an adequate description together with its solution is relevant however from a mathematical point of view a theory of selecting significant variables does not lead at least asymptotically to a substantial improvement of the accuracy of estimation in a regular parametric model the classical n rate of convergence is not affected by the number of significant variables however even in this setup let us emphasize that asymptotically has to be understood as up to a constant and that the correct choice of significant variables may possibly improve this constant if instead of a linear model we consider a nonparametric regression model the search for significant variables becomes crucial for estimating the regression function the rate of convergence explicitly depends on the set of significant variables let us develop this statement with the following example of multivariate regression suppose we observe z n xi y i i 1 n in the model

superefficiency in nonparametric function estimation fixed parameter asymptotic statements are often used in the context of nonparametric curve estimation problems e g nonparametric density or regression estimation in this context several forms of superefficiency can occur in contrast to what can happen in regular parametric problems here every parameter point e g unknown density or regression function can be a point of superefficiency we begin with an example which shows how fixed parameter asymptotic statements have often appeared in the study of adaptive kernel estimators and how superefficiency can occur in this context we then carry out a more systematic study of such fixed parameter statements it is shown in four general settings how the degree of superefficiency attainable depends on the structural assumptions in each case

brief paper output feedback adaptive control of a class of nonlinear discrete time systems with unknown control directions in this paper output feedback adaptive control is investigated for a class of nonlinear systems in output feedback form with unknown control gains to construct output feedback control the system is transformed into the form of the narma nonlinear auto regressive moving average model based on which future output prediction is carried out with employment of the predicted future output a constructive output feedback adaptive control is given with the discrete nussbaum gain exploited to overcome the difficulty due to unknown control directions under the global lipschitz condition of the system functions the boundedness of all the closed loop signals and asymptotical output tracking are achieved by the proposed control simulation results are presented to show the effectiveness of the proposed approach

prediction based discrete time stochastic adaptive control a new step towards non linear growth rate in this paper we will study adaptive control of a class of discrete time parametric strict feedback non linear stochastic systems almost all the existing results for such systems need lipschitz condition the main purpose of this paper is to remove this restriction and to get some positive result under non linear growth condition the control law is designed based on weighted least squares wls algorithms and on recursive adaptive predictors global stability and tracking performance are established for the closed loop systems

adaptive output feedback design for a class of nonlinear discrete time systems we present adaptive output feedback schemes for a class of discrete time systems whose continuous time counterparts are the output feedback canonical form we first develop a systematic design procedure for the deterministic case global boundedness and convergence are achieved with no restriction imposed on the nonlinearities then we proceed to develop an analogous design procedure for the adaptive case depending on the characteristics of the nonlinearities global boundedness and convergence can be achieved with various update laws a rank condition is required to ensure such properties for nonlinearities which are not globally lipschitz

on robust stability of discrete time adaptive nonlinear control abstract we consider adaptive control of discrete time nonlinear systems with a single unknown parameter in this paper we demonstrate that the necessary and sufficient condition for the existence of a feedback stabilizer that is robust to bounded noise is that the nonlinear growth rate of the system dynamics is less than 4 this result further confirms the conclusion of guo on critical stability of discrete time adaptive nonlinear control ieee trans automat control 42 1997 1488 1499 which addresses unbounded noise in a stochastic setting also in our worst case approach we find that much simpler adaptive stabilizers can be constructed when the nonlinear growth rate is less than 4

multiscale testing of qualitative hypotheses suppose that one observes a process y on the unit interval where dy t n1 2f t dt dw t with an unknown function parameter f given scale parameter n 1 sample size and standard brownian motion w we propose two classes of tests of qualitative nonparametric hypotheses about f such as monotonicity or concavity these tests are asymptotically optimal and adaptive in a certain sense they are constructed via a new class of multiscale statistics and an extension of levy s modulus of continuity of brownian motion

adaptive nn control for a class of discrete time non linear systems in this paper adaptive neural network nn control is investigated for a class of single input single output siso discrete time unknown non linear systems with general relative degree in the presence of bounded disturbances firstly the systems are transformed into a causal state space description adaptive state feedback nn control is presented based on lyapunov s stability theory then by converting the systems into a causal input output representation adaptive output feedback nn control is given finally adaptive nn observer design and observer based adaptive control are presented under the assumption of persistent excitation pe all the control schemes avoid the so called controller singularity problem in adaptive control by suitably choosing the design parameters the closed loop systems are proven to be semi globally uniformly ultimately bounded sguub simulation studies show the effectiveness of the newly proposed schemes

adaptive prediction and estimation in linear regression with infinitely many parameters the problem of adaptive prediction and estimation in the stochastic linear regression model with infinitely many parameters is considered we suggest a prediction method that is sharp asymptotically minimax adaptive over ellipsoids in 2 the method consists in an application of blockwise stein s rule with weakly geometrically increasing blocks to the penalized least squares fits of the first n coefficients to prove the results we develop oracle inequalities for a sequence model with correlated data

risk bounds for model selection via penalization performance bounds for criteria for model selection are devel oped using recent theory for sieves the model selection criteria are based on an empirical loss or contrast function with an added penalty term moti vated by empirical process theory and roughly proportional to the number of parameters needed to describe the model divided by the number of ob servations most of our examples involve density or regression estimation settings and we focus on the problem of estimating the unknown density or regression function we show that the quadratic risk of the minimum penal ized empirical contrast estimatoris bounded by an index of the accuracy of the sieve this accuracy index quanties the trade off among the candidate models between the approximation error and parameter dimension relative to sample size if we choose a list of models which exhibit good approximation prop erties with respect to different classes of smoothness the estimator can be simultaneously minimax rate optimal in each of those classes this is what is usually called adaptation the type of classes of smoothness in which one gets adaptation depends heavily on the list of models if too many models are involved in order to get accurate approximation of many wide classes of functions simultaneously it may happen that the estimator is only approx

adaptive confidence interval for pointwise curve estimation we present a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around f x 0 in either a white noise model or a regression setting a suitable modification in the truncation rule for wavelets allows construction of confidence intervals that achieve optimal coverage accuracy up to a logarithmic factor the procedure does not require knowledge of the regularity of the unknown function f it is also efficient for functions with a low degree of regularity

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

active identification for discrete time nonlinear control ii strict feedback systems the problem of controlling nonlinear systems with unknown parameters has received a great deal of attention in the continuous time case in contrast its discrete time counterpart remains largely unexplored primarily due to the difficulties associated with utilizing lyapunov design techniques in a discrete time framework existing results impose restrictive growth conditions on the nonlinearities to yield global stability in this paper we propose a novel approach which removes this obstacle and yields global stability and tracking for systems that can be transformed into an output feedback canonical form in which the nonlinearities depend only on the measured output but are otherwise arbitrary the main novelties of our design are i the temporal and algorithmic separation of the parameter estimation task from the control task and ii the development of an active identification procedure which uses the control input to actively drive the system state to points in the state space that allow the orthogonalized projection estimator to acquire all the necessary information about the unknown parameters we prove that our algorithm guarantees complete for control purposes identification in a finite time interval whose maximum length we compute thus the traditional structure of concurrent online estimation and control is replaced by a two phase control strategy first use active identification and then utilize the acquired parameter information to implement any control strategy as if the parameters were known

on line parameter estimator derived from modified matrix pseudoinverse abstract a method based on the matrix pseudoinverse is considered for on line parameter identification of discrete time nonlinear systems a recursive scheme was previously reported but assuming some restrictions on the input output data by resorting to the formulae developed for modified matrix pseudoinverse an iterative algorithm is derived in this work this algorithm applies to the general class of proposed systems while keeping well known desired properties for parameter identification

wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra we derive minimax rates for estimation in anisotropic smoothness classes this rate is attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale parameter for every dimension it is shown that this basis is superior to its one scale multiresolution analog if different degrees of smoothness in different directions are present as an important application we introduce a new adaptive wavelet estimator of the time dependent spectrum of a locally stationary time series using this model which was resently developed by dahlhaus we show that the resulting estimator attains nearly the rate which is optimal in gaussian white noise simultaneously over a wide range of smoothness classes moreover by our new approach we overcome the difficulty of how to choose the right amount of smoothing i e how to adapt to the appropriate resolution for reconstructing the local structure of the evolutionary spectrum in the time frequency plane

dead beat controllability of polynomial systems symbolic computation approaches state and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the quantifier elimination by partial cylindrical algebraic decomposition qepcad symbolic computation program the method is unified for a very large class of systems and can handle one or two sided control constraints families of minimum time state output dead beat controllers are obtained the computational complexity of the test is prohibitive for general polynomial systems but by constraining the structure of the system we may beat the curse of complexity a computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented necessary and sufficient conditions are given they are still very difficult to check therefore a number of easier to check sufficient conditions are also provided the latter are based on the grobner basis method and qepcad it is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system

optimal spatial adaptation to inhomogeneous smoothness an approach based on kernel estimates with variable bandwidth selectors a new v ria e 1 s e 0r estimation is proposed the application of this bandwidth selector leads to kernel estimates that achieve optimal rates of convergence over b 3 sses this implies that the procedure adapts to spatially inhomogeneous s noothness in particu lar the estimates share optimality properties with wavelet estimates based on thresholding of empirical wavelet coefficients 1 introduction in nonparametric curve estimation the statistical anal ysis may focus on the inference of the qualitative structure of the analyzed curve often interesting features of the curve are connected with spatially inhomogeneous smoothness in this case curve estimates that are spatially adaptlve ar e appropriaie a variety of such procedures have been proposed in the literature in breiman friedman olshen and stone 1983 piecewise constant least squares estimates are considered with a data adaptive choice of the pieces cart more generally friedman and silverman 1989 friedman 1991 and luo and wahba 1995 use variable knot splines mars knot points are added removed and allocated recursively using cross validation techniques these methods have shown good performance in simulations and real data examples however no asymptotic theory is available mammen and van de geer 1997 discuss penalized least squares curve estimation for spatially inhomogeneous curves they propose penalty terms which allow more spatial inhomogeneity than the usual l2 norms of deriva tives of the curve the estimates turn out to be variable knot splines see also mammen 1991 results on rates of convergence and a pointwise asymptotic distribution theory are given miiller and stadtmiiller 1987 staniswalis 1989 and brockmann gasser and hermann 1993 propose kernel estimation with locally variable band width selectors the calculation of local bandwidths is based on pilot estima tion of local smoothness characteristics an asymptotic analysis is available

smoothing spline anova for exponential families with application to the wisconsin epidemiological study of diabetic retinopathy the 1994 neyman memorial lecture let y i i 1 n be independent observations with the density of y i of the form h y i f i exp y i f i b f i c y i where b and c are given functions and b is twice continuously differentiable and bounded away from 0 let i t f t i where t t 1 t d t 1 t d t the t are measurable spaces of rather general form and f is an unknown function on t with some assumed smoothness properties given y i t i i 1 n it is desired to estimate f t for t in some region of interest contained in t we develop the fitting of smoothing spline anova models to this data of the form f t c f t f t t the components of the decomposition satisfy side conditions which generalize the usual side conditions for parametric anova the estimate of f is obtained as the minimizer in an appropriate function space of l y f j f j f where l y f is the negative log likelihood of y y 1 y n given f the j j are quadratic penalty functionals and the anova decomposition is terminated in some manner there are five major parts required to turn this program into a practical data analysis tool 1 methods for deciding which terms in the anova decomposition to include model selection 2 methods for choosing good values of the smoothing parameters 3 methods for making confidence statements concerning the estimate 4 numerical algorithms for the calculations and finally 5 public software in this paper we carry out this program relying on earlier work and filling in important gaps the overall scheme is applied to bernoulli data from the wisconsin epidemiologic study of diabetic retinopathy to model the risk of progression of diabetic retinopathy as a function of glycosylated hemoglobin duration of diabetes and body mass index it is believed that the results have wide practical application to the analysis of data from large epidemiologic studies

direct adaptive control for a class of mimo nonlinear systems using neural networks in this note direct adaptive neural network nn control is studied for a class of multiple input multiple output nonlinear systems based on input output discrete time model with unknown interconnections between subsystems by finding an orthogonal matrix to tune the nn weights the closed loop system is proven to be semiglobally uniformly ultimately bounded the control performance of the closed loop system is guaranteed by suitably choosing the design parameters