Learning for Advanced Motion Control

Iterative Learning Control (ILC) can achieve perfect tracking performance for mechatronic systems. The aim of this paper is to present an ILC design tutorial for industrial mechatronic systems. First, a preliminary analysis reveals the potential performance improvement of ILC prior to its actual implementation. Second, a frequency domain approach is presented, where fast learning is achieved through noncausal model inversion, and safe and robust learning is achieved by employing a contraction mapping theorem in conjunction with nonparametric frequency response functions. The approach is demonstrated on a desktop printer. Finally, a detailed analysis of industrial motion systems leads to several shortcomings that obstruct the widespread implementation of ILC algorithms. An overview of recently developed algorithms, including extensions using machine learning algorithms, is outlined that are aimed to facilitate broad industrial deployment.Comment: 8 pages, 15 figures, IEEE 16th International Workshop on Advanced Motion Control, 202

Statistical Models for High Frequency Security Prices

This article studies two extensions of the compound Poisson process with iid Gaussian innovations which are able to characterize important features of high frequency security prices. The first model explicitly accounts for the presence of the bid/ask spread encountered in price-driven markets. This model can be viewed as a mixture of the compound Poisson process model by Press and the bid/ask bounce model by Roll. The second model generalizes the compound Poisson process to allow for an arbitrary dependence structure in its innovations so as to account for more complicated types of market microstructure. Based on the characteristic function, we analyze the static and dynamic properties of the price process in detail. Comparison with actual high frequency data suggests that the proposed models are sufficiently flexible to capture a number of salient features of financial return data including a skewed and fat tailed marginal distribution, serial correlation at high frequency, time variation in market activity both at high and low frequency. The current framework also allows for a detailed investigation of the ``market-microstructure-induced bias'' in the realized variance measure and we find that, for realistic parameter values, this bias can be substantial. We analyze the impact of the sampling frequency on the bias and find that for non-constant trade intensity, ``business'' time sampling maximizes the bias but achieves the lowest overall MSECompound Poisson Process; High Frequency Data; Market Microstructure; Characteristic Function; OU Process; Realized Variance Bias; Optimal Sampling

Sparse Iterative Learning Control with Application to a Wafer Stage: Achieving Performance, Resource Efficiency, and Task Flexibility

Trial-varying disturbances are a key concern in Iterative Learning Control (ILC) and may lead to inefficient and expensive implementations and severe performance deterioration. The aim of this paper is to develop a general framework for optimization-based ILC that allows for enforcing additional structure, including sparsity. The proposed method enforces sparsity in a generalized setting through convex relaxations using $\ell_1$ norms. The proposed ILC framework is applied to the optimization of sampling sequences for resource efficient implementation, trial-varying disturbance attenuation, and basis function selection. The framework has a large potential in control applications such as mechatronics, as is confirmed through an application on a wafer stage.Comment: 12 pages, 14 figure

Modelling realized variance when returns are serially correlated

This article examines the impact of serial correlation in high frequency returns on the realized variance measure. In particular, it is shown that the realized variance measure yields a biased estimate of the conditional return variance when returns are serially correlated. Using 10 years of FTSE-100 minute by minute data we demonstrate that a careful choice of sampling frequency is crucial in avoiding substantial biases. Moreover, we find that the autocovariance structure (magnitude and rate of decay) of FTSE-100 returns at different sampling frequencies is consistent with that of an ARMA process under temporal aggregation. A simple autocovariance function based method is proposed for choosing the “optimal” sampling frequency, that is, the highest available frequency at which the serial correlation of returns has a negligible impact on the realized variance measure. We find that the logarithmic realized variance series of the FTSE-100 index, constructed using an optimal sampling frequency of 25 minutes, can be modelled as an ARFIMA process. Exogenous variables such as lagged returns and contemporaneous trading volume appear to be highly significant regressors and are able to explain a large portion of the variation in daily realized variance. -- Dieser Artikel untersucht die Auswirkungen von autokorrelierten Erträgen auf das Maß der realisierten Varianz bei hochfrequenten Daten über die Erträge. Es wird gezeigt, dass die realisierte Varianz ein verzerrter Schätzer für die bedingte Varianz der Erträge bei Vorliegen von Autokorrelation ist. Unter Verwendung eines zehnjährigen Datensatzes von Minutendaten des FTSE-100 wird dargestellt, dass eine sorgfältige Auswahl der Stichprobenfrequenz unabdingbar zur Vermeidung von Verzerrungen ist. Eine einfache Methode zur Bestimmung der optimalen Stichprobenfrequenz, basierend auf der Autokovarianzfunktion, wird vorgeschlagen. Diese ergibt sich als die höchste Frequenz, bei der die vorhandene Autokorrelation noch einen vernachlässigbaren Einfluss auf das Maß der realisierten Varianz hat. Für den betrachteten Datensatz ergibt sich eine optimale Frequenz von 25 Minuten. Unter Verwendung dieser Frequenz können die logarithmierten Erträge des FTSE-100 als ARFIMA Prozess modelliert werden.High frequency data,realized return variance,market microstructure,temporal aggregation,long memory,bootstrap

Three essays on the econometric analysis of high frequency financial data.

This thesis is motivated by the observation that the time series properties of financial security prices can vary fundamentally with their sampling frequency. Econometric models developed for low frequency data may thus be unsuitable for high frequency data and vice versa. For instance, while daily or weekly returns are generally well described by a martingale difference sequence, the dynamics of intra-daily, say, minute by minute, returns can be substantially more complex. Despite this apparent conflict between the behavior of high and low frequency data, it is clear that the two are intimately related and that high frequency data carries a wealth of information regarding the properties of the process, also at low frequency. The objective of this thesis is to deepen our understanding of the way in which high frequency data can be used in financial econometrics. In particular, we focus on (i) how to model high frequency security prices, and (ii) how to use high frequency data to estimate latent variables such as return volatility. One finding throughout the thesis is that the choice of sampling frequency is of fundamental importance as it determines both the dynamics and the information content of the data. A more detailed description of the chapters follows below.Macroeconomics -- Models;

Bi-cropping fodder maize in an existing (grass)clover sward

Organic cultivation of fodder maize is still considered to be difficult. Weed pressure, soil structure degradation during harvest and low nutrient efficiency are some of the common problems. Directly sowing maize in a (grass)clover sward using special-ized drilling machines can solve these problems. In a bi-cropping experiment under organic conditions we found similar yields as the reference treatment (ploughing) when the maize was sown in a clover sward, the roots of the remaining sward were cut one week after sowing and an additional fertiliser was applied

Influence of motor imagery training on gait rehabilitation in sub-acute stroke: a randomized controlled trial

Objective: To evaluate the effect of mental practice on motor imagery ability and assess the influence of motor imagery on gait rehabilitation in sub-acute stroke. Design: Randomized controlled trial. Subjects: A total of 44 patients with gait dysfunction after first-ever stroke were randomly allocated to a motor imagery training group and a muscle relaxation group. Methods: The motor imagery group received 6 weeks of daily mental practice. The relaxation group received a muscle relaxation programme of equal duration. Motor imagery ability and lower limb function were assessed at baseline and after 6 weeks of treatment. Motor imagery ability was tested using a questionnaire and mental chronometry test. Gait outcome was evaluated using a 10-m walk test (near transfer) and the Fugl-Meyer assessment (far transfer). Results: Significant between-group differences were found, with the vividness of kinesthetic imagery and the walking test results improving more in the motor imagery group than in the muscle relaxation group. There was no group interaction effect for the far transfer outcome score. Conclusion: Motor imagery training may have a beneficial task-specific effect on gait function in sub-acute stroke; however, longer term confirmation is required

A blocking and regularization approach to high dimensional realized covariance estimation

We introduce a regularization and blocking estimator for well-conditioned high-dimensional daily covariances using high-frequency data. Using the Barndorff-Nielsen, Hansen, Lunde, and Shephard (2008a) kernel estimator, we estimate the covariance matrix block-wise and regularize it. A data-driven grouping of assets of similar trading frequency ensures the reduction of data loss due to refresh time sampling. In an extensive simulation study mimicking the empirical features of the S&P 1500 universe we show that the ’RnB’ estimator yields efficiency gains and outperforms competing kernel estimators for varying liquidity settings, noise-to-signal ratios, and dimensions. An empirical application of forecasting daily covariances of the S&P 500 index confirms the simulation results