In this thesis, we investigate the global robust output regulation problem for nonlinear systems subject to time-varying or nonlinear exosystems. / One of the crucial issues in output regulation problem is the design of the appropriate internal model. Internal model is a dynamical compensator which possesses an essential ability of generating all possible steady-state input information asymptotically, and it should not only lead to a well-defined augmented system but also ensure the stabilizability of the augmented system. Besides, stabilization techniques for the augmented system should also be carefully chosen to meet the needs in different scenarios, e.g. the time-varying settings. Efforts are put on both sides throughout the thesis. / Output regulation problem, also known as servomechanism problem, is one of the central topics in control theory. The control objective is to design a feedback control law for the given plant so as to achieve asymptotic tracking for a class of reference signals and asymptotic rejection for a class of disturbance signals while maintaining the stability of closed-loop system. The reference or the disturbance signals are assumed to be generated from a dynamical system called the exosystem. Normally, the exosystem is a linear autonomous system, e.g. a harmonic oscillator, and the exogenous signals represent step or ramp signals, or sinusoidal signals contains finite number of harmonics. The extensions of the exosystem, from linear to nonlinear, autonomous to non-autonomous, significantly enlarge the categories of the exogenous signals, and more importantly, such extensions motivate the development of the output regulation theory in both scientific research and practical application. / Paying special attention to the appearance of time-varying or nonlinear exosystems, our research is mainly conducted under the general framework for tackling the output regulation problem. In general, first we convert the output regulation problem of the original plant into the stabilization problem of the augmented system which is composed of the plant and the designed internal model. Second, we achieve the global stabilization of the augmented system by robust and adaptive control approaches, according to both parameter uncertainty and dynamic uncertainty in either plant or the exosystem. / The main contributions of the thesis are outlined as follows. 1. A framework for handling the robust output regulation problem for general timevarying nonlinear systems subject to time-varying exosystem is proposed. Especially, certain existence conditions of a time-varying internal model is given, and problem conversion can be achieved. As an application of this framework, we give the solvability conditions of the output regulation problem for the time-varying nonlinear systems in output feedback form. Further, when parameter uncertainties occurred in the time-varying exosystem, we solve the corresponding adaptive robust output regulation problem resorting to some adaptive control methods. These results can also be applied to the time-varying nonlinear systems in lower triangular form. 2. The global robust output regulation problem for nonlinear systems subject to nonlinear exosystem is considered. A new class of internal models is introduced which relaxes the existence conditions of the former one. Also, this class of internal models has the merit that it is zero input globally asymptotically stable which greatly facilitates the global stabilization of the augmented system. Compared with the existing results, the new method solves the global robust output regulation problem without restrictions on the initial conditions or trajectory bounds of the exosystems, and the bound of the parameter uncertainties of the plant is not necessarily known. Moreover, utilizing the Nussbaum gain technique, the unknown control direction case can also be handled by modifying the control law. 3. The theoretical results have been applied to several practical control problems, such as the global disturbance rejection problem for FitzHugh-Nagumo model with Mathieu equation, the synchoniztion of periodically-forced pendulum with Rayleigh equation, etc .. / Yang, Xi. / Adviser: Jie Huang. / Source: Dissertation Abstracts International, Volume: 73-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 123-134). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

by Huang Liren. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1988. / Bibliography: leaves 92-97.

This thesis has two overall themes, both of which involve the word functional, albeit in different contexts. The theme that motivates two of the chapters is the development of methods that enable a deeper understanding of the variability of functional data. The theme of the final chapter is the development of methods that enable a deeper understanding of the landscape of functionality across the human genome in different human tissues. The first chapter of this thesis provides a framework for quantifying the variability of functional data and for analyzing the factors that affect this variability. We extend functional principal components analysis by modeling the variance of principal component scores. We pose a Bayesian model, which we estimate using variational Bayes methods. We illustrate our model with an application to a kinematic dataset of two-dimensional planar reaching motions by healthy subjects, showing the effect of learning on motion variability. The second chapter of this thesis provides an alternative method for decomposing functional data that follows a Poisson distribution. Classical methods pose a latent Gaussian process that is then linked to the observed data via a logarithmic link function. We pose an alternative model that draws on ideas from non-negative matrix factorization, in which we constrain both scores and spline coefficient vectors for the functional prototypes to be non-negative. We impose smoothness on the functional prototypes. We estimate our model using the method of alternating minimization. We illustrate our model with an application to a dataset of accelerometer readings from elderly healthy Americans. The third chapter of this thesis focuses on functional genomics, rather than functional data analysis. Here we pose a method for unsupervised clustering of functional genomics data. Our method is non-parametric, allowing for flexible modeling of the functional genomics data without binarization. We estimate our model using variational Bayes methods, and illustrate it by calculating genome-wide functional scores (based on a partition of our clusters into functional and non-functional clusters) for 127 different human tissues. We show that these genome-wide and tissue-specific functional scores provide state-of-the-art functional prediction.

This thesis uses methods from functional data analysis (FDA) to solve problems from three scientific areas of study. While the areas of application are quite distinct, the common thread of functional data analysis ties them together. The first chapter describes interactive open-source software for explaining and disseminating results of functional data analyses. Chapters two and three use curve alignment, or registration, to solve common problems in accelerometry and neuroimaging, respectively. The final chapter introduces a novel regression method for modeling functional outcomes that are trajectories over time. The first chapter of this thesis details a software package for interactively visualizing functional data analyses. The software is designed to work for a wide range of datasets and several types of analyses. This chapter describes that software and provides an overview ofFDA in different contexts. The second chapter introduces a framework for curve alignment, or registration, of exponential family functional data. The approach distinguishes itself from previous registration methods in its ability to handle dense binary observations with computational efficiency. Motivation comes from the Baltimore Longitudinal Study on Aging, in which accelerometer data provides valuable insights into the timing of sedentary behavior. The third chapter takes lessons learned about curve registration from the second chapter and use them to develop methods in an entirely new context: large multisite brain imaging studies. Scanner effects in multisite imaging studies are non-biological variability due to technical differences across sites and scanner hardware. This method identifies and removes scanner effects by registering cumulative distribution functions of image intensities values. In the final chapter the focus shifts from curve registration to regression. Described within this chapter is an entirely new nonlinear regression framework that draws from both functional data analysis and systems of ordinary equations. This model is motivated by the neurobiology of skilled movement, and was developed to capture the relationship between neural activity and arm movement in mice.

My research studies algebras of holomorphic functions from $d$-tuples of $n\times n$- matrices, $M_n(\bC)^d$, to $M_n(\bC)$. In particular, I study the holomorphic functions that can be approximated by \emph{polynomial matrix concomitants}, that is polynomial maps from $M_n(\bC)^d$ to $M_n(\bC)$ that satisfy the relationship \[ f(g^{-1}\fz g) = g^{-1}f(\fz)g \] for every $\fz \in M_n(\bC)^d$ and $g\in GL_n(\bC)$. In a sense, these are the polynomial maps that “remember” the structure of the $d$-tuple $\fz$. My first result is that these holomorphic matrix concomitants can be identified with holomorphic cross sections of certain matrix bundles. A holomorphic matrix bundle is a fibred space in which every fibre is $M_n(\bC)$ and the fibres are glued together in such a way that the total space has a holomorphic structure. Once the identification between holomorphic cross sections and holomorphic concomitants is established, the structure of the matrix bundle is used to endow the algebra of continuous cross sections with a $C^*$-algebra structure. Then we study the subalgebra of cross sections that can be approximated by polynomial concomitants. By identifying the matrix concomitants with cross sections, we are able to prove interesting results about these algebras.

The current study evaluated the effectiveness of delivering behavioral assessment and treatment to reduce challenging behavior shown by Korean children with ASD by using in-home telehealth from the U.S. The participants were five young children diagnosed with autism who lived in Korea and displayed challenging behavior. The children’s mothers, who had no previous experience in functional analysis (FA) and functional communication training (FCT) procedures, implemented all procedures with coaching provided by a behavior consultant during assessment and treatment sessions via telehealth. The results of the current study showed that functional analyses conducted via telehealth from the U.S. to the children’s homes in Korea were effective in identifying the function of challenging behavior for each participant. Furthermore, the results also showed that challenging behavior was reduced by 100% across all children by the end of treatment. These results suggest that telehealth can be an effective and efficient way to deliver behavior analytic services for underserved populations in countries like Korea.

No description available.

The following thesis is divided into two main parts. In the first part we study the problem of characterizing algebras of functions living on analytic varieties. Specifically, we consider the restrictions M_V of the multiplier algebra M of Drury-Arveson space to a holomorphic subvariety V of the unit ball as well as the algebras A_V of continuous multipliers under the same restriction. We find that M_V is completely isometrically isomorphic to cM_W if and only if W is the image of V under a biholomorphic automorphism of the ball. In this case, the isomorphism is unitarily implemented. Furthermore, when V and W are homogeneous varieties then A_V is isometrically isomorphic to A_W if and only if the defining polynomial relations are the same up to a change of variables. The problem of characterizing when two such algebras are (algebraically) isomorphic is also studied. In the continuous homogeneous case, two algebras are isomorphic if and only if they are similar. However, in the multiplier algebra case the problem is much harder and several examples will be given where no such characterization is possible. In the second part we study the triangular subalgebras of UHF algebras which provide new examples of algebras with the Dirichlet property and the Ando property. This in turn allows us to describe the semicrossed product by an isometric automorphism. We also study the isometric automorphism group of these algebras and prove that it decomposes into the semidirect product of an abelian group by a torsion free group. Various other structure results are proven as well.

Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Jon S. Bailey, Florida State University, College of Arts and Sciences, Dept. of Psychology. Title and description from dissertation home page (viewed June 16, 2004). Includes bibliographical references.

Thesis (Ph. D. in Biomedical Engineering)--Vanderbilt University, 2003. / Title from PDF title screen. Includes bibliographical references.