L1 Control Theoretic Smoothing Splines

In this paper, we propose control theoretic smoothing splines with L1 optimality for reducing the number of parameters that describes the fitted curve as well as removing outlier data. A control theoretic spline is a smoothing spline that is generated as an output of a given linear dynamical system. Conventional design requires exactly the same number of base functions as given data, and the result is not robust against outliers. To solve these problems, we propose to use L1 optimality, that is, we use the L1 norm for the regularization term and/or the empirical risk term. The optimization is described by a convex optimization, which can be efficiently solved via a numerical optimization software. A numerical example shows the effectiveness of the proposed method.Comment: Accepted for publication in IEEE Signal Processing Letters. 4 pages (twocolumn), 5 figure

Compressive Sampling for Remote Control Systems

In remote control, efficient compression or representation of control signals is essential to send them through rate-limited channels. For this purpose, we propose an approach of sparse control signal representation using the compressive sampling technique. The problem of obtaining sparse representation is formulated by cardinality-constrained L2 optimization of the control performance, which is reducible to L1-L2 optimization. The low rate random sampling employed in the proposed method based on the compressive sampling, in addition to the fact that the L1-L2 optimization can be effectively solved by a fast iteration method, enables us to generate the sparse control signal with reduced computational complexity, which is preferable in remote control systems where computation delays seriously degrade the performance. We give a theoretical result for control performance analysis based on the notion of restricted isometry property (RIP). An example is shown to illustrate the effectiveness of the proposed approach via numerical experiments

L1ノルム最適化に基づくセルオートマトンモデル同定法の研究

13301甲第4736号博士（工学）金沢大学博士論文要旨Abstrac

Sparsity Methods for Systems and Control

The method of sparsity has been attracting a lot of attention in the fields related not only to signal processing, machine learning, and statistics, but also systems and control. The method is known as compressed sensing, compressive sampling, sparse representation, or sparse modeling. More recently, the sparsity method has been applied to systems and control to design resource-aware control systems. This book gives a comprehensive guide to sparsity methods for systems and control, from standard sparsity methods in finite-dimensional vector spaces (Part I) to optimal control methods in infinite-dimensional function spaces (Part II). The primary objective of this book is to show how to use sparsity methods for several engineering problems. For this, the author provides MATLAB programs by which the reader can try sparsity methods for themselves. Readers will obtain a deep understanding of sparsity methods by running these MATLAB programs. Sparsity Methods for Systems and Control is suitable for graduate level university courses, though it should also be comprehendible to undergraduate students who have a basic knowledge of linear algebra and elementary calculus. Also, especially part II of the book should appeal to professional researchers and engineers who are interested in applying sparsity methods to systems and control

Intuitive Interaktion durch videobasierte Gestenerkennung

Hinter der Forschung an videobasierter Handgestenerkennung steht die Vision, Interaktion zwischen Mensch und Computer losgelöst von klassischen Eingabegeräten wie Maus und Tastatur zu realisieren. Das Ziel dieser Arbeit ist die Entwicklung von echtzeitfähigen Verfahren, die eine robuste und fehlerarme Erkennung menschlicher Handgesten realisieren und so die Bedienung eines Computersystems auch für technisch unerfahrene Anwender nutzbar machen. In dieser Arbeit werden vier Verfahren entwickelt, die unterschiedliche Arten der Interaktion durch videobasierte Handgestenerkennung realisieren.The vision behind research on video based hand gesture recognition is to realise a new kind of interaction between humans and computer beyond the classical input devices such as mouse and keyboard. The aim of this thesis is to develop new video based realtime algorithms, which enable a robust and accurate recognition of human hand gestures and allow interaction with the computer even for technically unversed users. In this thesis four different algorithms are developed that can be used for intuitive interaction purposes depending on the demands and needs of different scenario applications