analysis of a high order iterative learning control algorithm for uncertain nonlinear systems with state delays key words iterative learning control nonlinear systems convergence analysis high order scheme delay tracking abstract for a better learning transient along the iteration number direction a pid type iterative learning control algo rithm is proposed for a class of delayed uncertain nonlinear systems which perform a given task repeatedly the convergence conditions for the proposed high order learning control have been established the tracking error bound is proven to be a class k function of the bounds of reinitialization errors uncer tainties and disturbances to the systems it is also indicated that the time delays in the system states do not play a significant role in the ilc convergence property the e ectiveness of the high order ilc algorithm is demonstrated by simulation examples 1998 elsevier science ltd all rights reserved

iterative learning control for a class of nonlinear systems abstract for precise tracking control of a class of nonlinear systems over a finite time interval an iterative learning control method using the relative degree of a system is proposed the class of nonlinear systems where the iterative learning control is applied can be extended by using the proposed method a sufficient condition is derived for guaranteeing a uniform convergence of the output to the desired output the results obtained for a class of nonlinear systems are shown to be a generalization of the existing results for linear time invariant systems

brief terminal iterative learning control with an application to rtpcvd thickness control a special type of iterative learning control ilc problem is considered due to the insufficient measurement capability in many real control problems such as rapid thermal processing rtp it may happen that only the terminal output tracking error instead of the whole output trajectory tracking error is available in the rtp chemical vapor deposition cvd of wafer fab industry the ultimate control objective is to control the deposition thickness dt at the end of the rtp cycle the control profile for the next operation cycle has to be updated using the terminal dt tracking error alone a revised ilc method is proposed to address this terminal output tracking problem by parameterizing the control profile with a piecewise continuous functional basis the parameters are updated by a high order updating scheme a convergence condition is obtained for a class of uncertain discrete time time varying linear systems including the rtpcvd system as the subset simulation results for an rtpcvd thickness control problem are presented to demonstrate the effectiveness of the proposed iterative learning scheme

optimal selection of reduced rank estimators of high dimensional matrices we introduce a new criterion the rank selection criterion rsc for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models the corresponding rsc estimator minimizes the frobenius norm of the fit plus a regularization term proportional to the number of parameters in the reduced rank model the rank of the rsc estimator provides a consistent estimator of the rank of the coefficient matrix in general the rank of our estimator is a consistent estimate of the effective rank which we define to be the number of singular values of the target matrix that are appropriately large the consistency results are valid not only in the classic asymptotic regime when n the number of responses and p the number of predictors stay bounded and m the number of observations grows but also when either or both n and p grow possibly much faster than m we establish minimax optimal bounds on the mean squared errors of our estimators our finite sample performance bounds for the rsc estimator show that it achieves the optimal balance between the approximation error and the penalty term furthermore our procedure has very low computational complexity linear in the number of candidate models making it particularly appealing for large scale problems we contrast our estimator with the nuclear norm penalized least squares nnp estimator which has an inherently higher computational complexity than rsc for multivariate regression models we show that nnp has estimation properties similar to those of rsc albeit under stronger conditions however it is not as parsimonious as rsc we offer a simple correction of the nnp estimator which leads to consistent rank estimation we verify and illustrate our theoretical findings via an extensive simulation study

a survey on iterative learning control for nonlinear systems in this article we review the recent advances in iterative learning control ilc for nonlinear dynamic systems in the research field of ilc two categories of system nonlinearities are considered namely the global lipschitz continuous glc functions and local lipschitz continuous llc functions ilc for glc systems is widely studied and analysed using contraction mapping approach and the focus of recent exploration moves to application problems though a number of theoretical issues remain open ilc for llc systems is currently a hot area and the recent research focuses on ilc design and analysis by means of lyapunov approach the objectives of this article are to introduce recent development and advances in nonlinear ilc schemes highlight their effectiveness and limitations as well as discuss the directions for further exploration of nonlinear ilc

penalized least squares regression methods and applications to neuroimaging the goals of this paper are to review the most popular methods of predictor selection in regression models to explain why some fail when the number p of explanatory variables exceeds the number n of participants and to discuss alternative statistical methods that can be employed in this case we focus on penalized least squares methods in regression models and discuss in detail two such methods that are well established in the statistical literature the lasso and elastic net we introduce bootstrap enhancements of these methods the be lasso and be enet that allow the user to attach a measure of uncertainty to each variable selected our work is motivated by a multimodal neuroimaging dataset that consists of morphometric measures volumes at several anatomical regions of interest white matter integrity measures from diffusion weighted data fractional anisotropy mean diffusivity axial diffusivity and radial diffusivity and clinical and demographic variables age education alcohol and drug history in this dataset the number p of explanatory variables exceeds the number n of participants we use the be lasso and be enet to provide the first statistical analysis that allows the assessment of neurocognitive performance from high dimensional neuroimaging and clinical predictors including their interactions the major novelty of this analysis is that biomarker selection and dimension reduction are accomplished with a view towards obtaining good predictions for the outcome of interest i e the neurocognitive indices unlike principal component analysis that are performed only on the predictors space independently of the outcome of interest

stability of learning control with disturbances and uncertain initial conditions the authors investigate the effects of state disturbances output noise and errors in initial conditions on a class of learning control algorithms they present a simple learning algorithm and exhibit via a concise proof bounds on the asymptotic trajectory errors for the learned input and the corresponding state and output trajectories furthermore these bounds are continuous functions of the bounds on the initial condition errors state disturbances and output noise and the bounds are zero in the absence of these disturbances

regularization of wavelet approximations in this paper we introduce nonlinear regularized wavelet estimators for estimating nonparametric regression functions when sampling points are not uniformly spaced the approach can apply readily to many other statistical contexts various new penalty functions are proposed the hard thresholding and soft thresholding estimators of donoho and johnstone are specific members of nonlinear regularized wavelet estimators they correspond to the lower and upper envelopes of a class of the penalized least squares estimators necessary conditions for penalty functions are given for regularized estimators to possess thresholding properties oracle inequalities and universal thresholding parameters are obtained for a large class of penalty functions the sampling properties of nonlinear regularized wavelet estimators are established and are shown to be adaptively minimax to efficiently solve penalized least squares problems nonlinear regularized sobolev interpolators nrsi are proposed as initial estimators wh

decentralized iterative learning control for a class of large scale interconnected dynamical systems the problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered in this paper it is assumed that the considered large scale dynamical systems are linear time varying and the interconnections between each subsystem are unknown for such a class of uncertain large scale interconnected dynamical systems a method is presented whereby a class of decentralized local iterative learning control schemes is constructed it is also shown that under some given conditions the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process finally as a numerical example the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes

adaptive iterative learning control for nonlinearly parameterised systems with unknown time varying delays and input saturations in this work an adaptive iterative learning control ailc scheme is proposed to address a class of nonlinearly parameterised systems with both unknown time varying delays and input saturations by incorporating a saturation function a novel iterative learning control mechanism is constructed with a feedback term in the time domain and a fully saturated adaptive learning term in the iteration domain which is used to estimate the unknown time varying system uncertainty a new time weighted lyapunov krasovskii like composite energy function lkl cef is designed for the convergence analysis where time weighted inputs states and estimates of system uncertainty are all considered despite the existence of time varying parametric uncertainties time varying delays input saturations and local lipschitz nonlinearities the learning convergence is guaranteed with rigorous mathematical analysis simulation results verify the correctness and effectiveness of the proposed method further

brief paper noise tolerant iterative learning control for a class of continuous time systems the paper proposes a noise tolerant iterative learning control ilc for a class of linear continuous time systems which achieves high precision tracking for uncertain plants by iteration of trials in the presence of heavy measurement noise the robustness against measurement noise is achieved through i projection of continuous time i o signals onto a finite dimensional parameter space ii using error data of all past iterations via an integral operation in the learning law and iii noise reduction by h 2 optimization subject to a specified convergence speed of the ilc

extended bayesian information criteria for model selection with large model spaces summary the ordinary bayesian information criterion is too liberal for model selection when the model space is large in this paper we re examine the bayesian paradigm for model selection and propose an extended family of bayesian information criteria which take into account both the number of unknown parameters and the complexity of the model space their consistency is established in particular allowing the number of covariates to increase to infinity with the sample size their performance in various situations is evaluated by simulation studies it is demonstrated that the extended bayesian information criteria incur a small loss in the positive selection rate but tightly control the false discovery rate a desirable property in many applications the extended bayesian information criteria are extremely useful for variable selection in problems with a moderate sample size but with a huge number of covariates especially in genome wide association studies which are now an active area in genetics research

technical communique limit or limit superior observations on the convergence of some iterative learning control schemes in this paper we survey the convergence properties of a number of iterative learning control schemes from the past decade we observe a common technical error that appeared in these papers point out how the results should be corrected and finally consider the significance of these corrections with regard to the effectiveness of the schemes concerned

robust optimal design and convergence properties analysis of iterative learning control approaches in this paper we address four major issues in the field of iterative learning control ilc theory and design the first issue is concerned with ilc design in the presence of system interval uncertainties targeting at time optimal fastest convergence and robustness properties concurrently we formulate the ilc design into a min max optimization problem and provide a systematic solution for linear type ilc consisting of the first order and higher order ilc schemes inherently relating to the first issue the second issue is concerned with the performance evaluation of various ilc schemes convergence speed is one of the most important factors in ilc a learning performance index q factor is introduced which provides a rigorous and quantified evaluation criterion for comparing the convergence speed of various ilc schemes we further explore a key issue how does the system dynamics affect the learning performance by associating the time weighted norm with the supreme norm we disclose the dynamics impact in ilc which can be assessed by global uniform bound and monotonicity in iteration domain finally we address a rather controversial issue in ilc can the higher order ilc outperform the lower order ilc in terms of convergence speed and robustness by applying the min max design which is robust and optimal and conducting rigorous analysis we reach the conclusion that the q factor of ilc sequences of lower order ilc is lower than that of higher order ilc in terms of the time weighted norm

effectively categorical abelian groups abstract we study effective categoricity of computable abelian groups of the form i h where h is a subgroup of q such groups are called homogeneous completely decomposable it is well known that a homogeneous completely decomposable group is computably categorical if and only if its rank is finite we study n 0 categoricity in this class of groups for n 1 we introduce a new algebraic concept of s independence which is a generalization of the well known notion of p independence we develop the theory of s independent sets we apply these techniques to show that every homogeneous completely decomposable group is 3 0 categorical we prove that a homogeneous completely decomposable group of infinite rank is 2 0 categorical if and only if it is isomorphic to the free module over the localization of z by a computably enumerable set of primes p with the semi low complement within the set of all primes we apply these results and techniques to study the complexity of generating bases of computable free modules over localizations of integers including the free abelian group

technical communique on the disturbance properties of high order iterative learning control algorithms the disturbance properties of high order iterative learning control ilc algorithms are considered an error equation is formulated and using statistical models of the load and measurement disturbances an equation for the covariance matrix of the control error vector is derived the results are exemplified by analytic derivation of the covariance matrix for a second order ilc algorithm

sparse regularization techniques provide novel insights into outcome integration processes abstract by exploiting information that is contained in the spatial arrangement of neural activations multivariate pattern analysis mvpa can detect distributed brain activations which are not accessible by standard univariate analysis recent methodological advances in mvpa regularization techniques have made it feasible to produce sparse discriminative whole brain maps with highly specific patterns furthermore the most recent refinement the graph net explicitly takes the 3d structure of fmri data into account here these advanced classification methods were applied to a large fmri sample n 70 in order to gain novel insights into the functional localization of outcome integration processes while the beneficial effect of differential outcomes is well studied in trial and error learning outcome integration in the context of instruction based learning has remained largely unexplored in order to examine neural processes associated with outcome integration in the context of instruction based learning two groups of subjects underwent functional imaging while being presented with either differential or ambiguous outcomes following the execution of varying stimulus response instructions while no significant univariate group differences were found in the resulting fmri dataset l1 regularized sparse classifiers performed significantly above chance and also clearly outperformed the standard l2 regularized dense support vector machine on this whole brain between subject classification task moreover additional l2 regularization via the elastic net and spatial regularization by the graph net improved interpretability of discriminative weight maps but were accompanied by reduced classification accuracies most importantly classification based on sparse regularization facilitated the identification of highly specific regions differentially engaged under ambiguous and differential outcome conditions comprising several prefrontal regions previously associated with probabilistic learning rule integration and reward processing additionally a detailed post hoc analysis of these regions revealed that distinct activation dynamics underlay the processing of ambiguous relative to differential outcomes together these results show that l1 regularization can improve classification performance while simultaneously providing highly specific and interpretable discriminative activation patterns

one step sparse estimates in nonconcave penalized likelihood models fan and li propose a family of variable selection methods via penalized likelihood using concave penalty functions the nonconcave penalized likelihood estimators enjoy the oracle properties but maximizing the penalized likelihood function is computationally challenging because the objective function is nondifferentiable and nonconcave in this article we propose a new unified algorithm based on the local linear approximation lla for maximizing the penalized likelihood for a broad class of concave penalty functions convergence and other theoretical properties of the lla algorithm are established a distinguished feature of the lla algorithm is that at each lla step the lla estimator can naturally adopt a sparse representation thus we suggest using the one step lla estimator from the lla algorithm as the final estimates statistically we show that if the regularization parameter is appropriately chosen the one step lla estimates enjoy the oracle properties with good initial estimators computationally the one step lla estimation methods dramatically reduce the computational cost in maximizing the nonconcave penalized likelihood we conduct some monte carlo simulation to assess the finite sample performance of the one step sparse estimation methods the results are very encouraging

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

brief paper novel iterative learning controls for linear discrete time systems based on a performance index over iterations an optimal iterative learning control ilc is proposed to optimize an accumulative quadratic performance index in the iteration domain for the nominal dynamics of linear discrete time systems properties of stability convergence robustness and optimality are investigated and demonstrated in the case that the system under consideration contains uncertain dynamics the proposed ilc design can be applied to yield a guaranteed cost ilc whose solution can be found using the linear matrix inequality lmi technique simulation examples are included to demonstrate feasibility and effectiveness of the proposed learning controls

a robust high order p type iterative learning controller using current iteration tracking error a high order p type updating law in which the current iteration tracking error cite is employed is proposed for iterative learning control ilc of a class of uncertain nonlinear repetitive systems uniform boundedness of the tracking error is established in the presence of uncertainty disturbance and initialization error the bound and the ilc convergence rate can be adjusted by tuning the learning gain of the cite

fixed point theorem based iterative learning control for ltv systems with input singularity in this paper we address a challenging and open problem how to design a suitable iterative learning control ilc system in the presence of input singularity which is incurred by the singularities of the system direct feed through term considering two typical types of input singularities we first revise the ilc operators accordingly by adding a forgetting factor and incorporating a time varying learning gain in the sequel guarantee ilc operators to be contractible next using the banach fixed point theorem we demonstrate that the output sequence can either enter and remains ultimately in a designated neighborhood of the target trajectory or is bounded by a class k function finally an illustrative example is presented

an iterative learning control approach for linear systems with randomly varying trial lengths this technical note addresses an iterative learning control ilc design problem for discrete time linear systems where the trial lengths could be randomly varying in the iteration domain an ilc scheme with an iteration average operator is introduced for tracking tasks with non uniform trial lengths which thus mitigates the requirement on classic ilc that all trial lengths must be identical in addition the identical initialization condition can be absolutely removed the learning convergence condition of ilc in mathematical expectation is derived through rigorous analysis as a result the proposed ilc scheme is applicable to more practical systems in the end two illustrative examples are presented to demonstrate the performance and the effectiveness of the averaging ilc scheme for both time invariant and time varying linear systems

an iterative learning control theory for a class of nonlinear dynamic systems abstract an iterative learning control scheme is presented for a class of nonlinear dynamic systems which includes holonomic systems as its subset the control scheme is composed of two types of control methodology a linear feedback mechanism and a feedforward learning strategy at each iteration the linear feedback provides stability of the system and keeps its state errors within uniform bounds the iterative learning rule on the other hand tracks the entire span of a reference input over a sequence of iterations the proposed learning control scheme takes into account the dominant system dynamics in its update algorithm in the form of scaled feedback errors in contrast to many other learning control techniques the proposed learning algorithm neither uses derivative terms of feedback errors nor assumes external input perturbations as a prerequisite the convergence proof of the proposed learning scheme is given under minor conditions on the system parameters

optimality of first order ilc among higher order ilc higher order iterative learning control ho ilc algorithms use past system control information from more than one past iterative cycle this class of ilc algorithms have been proposed aiming at improving the learning efficiency and performance this paper addresses the optimality of ho ilc in the sense of minimizing the trace of the control error covariance matrix in the presence of a class of uncorrelated random disturbances it is shown that the optimal weighting matrices corresponding to the control information associated with more than one cycle preceding the current cycle are zero that is an optimal ho ilc does not add to the optimality of standard first order ilc in the sense of minimizing the trace of the control error covariance matrix the system under consideration is a linear discrete time varying systems with different relative degree between the input and each output

an iterative learning control law for dynamical systems abstract this paper is concerned with an iterative learning control law which enables us to find a control input that generates the desired output exactly over a finite time interval through the repetition of trials we derive a sufficient condition for nonlinear systems to achieve the desired output by the iterative learning control based on this result we show that the direct transmission term of the plant plays a crucial role in the error convergence of the learning process further we identify the class of plants to which the learning control law is applicable

recursive labelling systems and stability of recursive structures in hyperarithmetical degrees we show that under certain assumptions of recursiveness in 2t the recursive structure 2t is ao stable for ca w we need to deal with limit ordinals and we frame an analogous result proposition 2 for yn systems where yn is an increasing sequence of ordinals propositions 1 and 2 are then established by the

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

high dimensional variable selection this paper explores the following question what kind of statistical guarantees can be given when doing variable selection in high dimensional models in particular we look at the error rates and power of some multi stage regression methods in the first stage we fit a set of candidate models in the second stage we select one model by cross validation in the third stage we use hypothesis testing to eliminate some variables we refer to the first two stages as screening and the last stage as cleaning we consider three screening methods the lasso marginal regression and forward stepwise regression our method gives consistent variable selection under certain conditions

exponential convergence of a learning controller for robot manipulators the proof for the exponential convergence of a class of learning and repetitive control algorithms for robot manipulators is given the learning process involves the identification of the robot inverse dynamics function by having the robot execute a set of tasks repeatedly using the concepts of functional persistence of excitation and functional uniform complete observability it is shown that when a training task is selected for the robot which is persistently exciting the learning controllers are globally exponentially stable repetitive controllers are always exponentially stable

parameter optimization in iterative learning control in this paper parameter optimization through a quadratic performance index is introduced as a method to establish a new iterative learning control law with this new algorithm monotonic convergence of the error to zero is guaranteed if the original system is a discrete time lti system and it satisfies a positivity condition if the original system is not positive two methods are derived to make the system positive the effect of the choice of weighting parameters in the performance index on convergence rate is analysed as a result adaptive weights are introduced as a method to improve the convergence properties of the algorithm a high order version of the algorithm is also derived and its convergence analysed the theoretical findings in this paper are highlighted with simulations

iterative learning control design based on composite energy function with input saturation in this work an iterative learning control scheme is designed for a class of nonlinear uncertain systems with input saturation the analysis of convergence in the iteration domain is based on composite energy function which consists of both input and state information along the time and iteration axes through rigorous analysis the learning convergence in the iteration domain can be guaranteed under the input saturation provided the desired trajectory is realizable within the saturation bound

more comments on c p we discuss the interpretation of c p plots and show how they can be calibrated in several ways we comment on the practice of using the display as a basis for formal selection of a subset regression model and extend the range of application of the device to encompass arbitrary linear estimates of the regression coefficients for example ridge estimates