Chain-Scattering Approach to H?Control

by Hidenori Kimura

Overview

Through its rapid progress in the last decade, HOOcontrol became an established control technology to achieve desirable performances of control systems. Several highly developed software packages are now avail­ able to easily compute an HOOcontroller for anybody who wishes to use HOOcontrol. It is questionable, however, that theoretical implications of HOOcontrol are well understood by the majority of its users. It is true that HOOcontrol theory is harder to learn due to its intrinsic mathematical nature, and it may not be necessary for those who simply want to apply it to understand the whole body of the theory. In general, how­ ever, the more we understand the theory, the better we can use it. It is at least helpful for selecting the design options in reasonable ways to know the theoretical core of HOOcontrol. The question arises: What is the theoretical core of HOO control? I wonder whether the majority of control theorists can answer this question with confidence. Some theorists may say that the interpolation theory is the true essence of HOOcontrol, whereas others may assert that unitary dilation is the fundamental underlying idea of HOOcontrol. The J­ spectral factorization is also well known as a framework of HOOcontrol. A substantial number of researchers may take differential game as the most salient feature of HOOcontrol, and others may assert that the Bounded Real Lemma is the most fundamental building block.

Product Details

ISBN-13:	9781461286424
Publisher:	Birkhäuser Boston
Publication date:	10/14/2011
Series:	Systems & Control: Foundations & Applications
Edition description:	1997
Pages:	246
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

About the Author

Hidenori Kimura is a Director of the RIKEN BSI-Toyota Collaboration Center, a Council Member of IFAC representing Japan, an associate member of Scientific Council of Japan, and Principal Fellow of the Center for Research and Development Strategy, Japan Science and Technology Agency. He is a Fellow of SICE, IEEE, and IFAC, and has been awarded SICE paper awards four times, the IFAC Paper Prize twice, and the George Axelby Award in 1984. Most recently, he has received the 2011-14 Giorgio Quazza Medal from IFAC.

Table of Contents

1 Introduction.- 1.1 Impacts of H?Control.- 1.2 Theoretical Background.- 2 Elements of Linear System Theory.- 2.1 State-Space Description of Linear Systems.- 2.2 Controllability and Observability.- 2.3 State Feedback and Output Insertion.- 2.4 Stability of Linear Systems.- 3 Norms and Factorizations.- 3.1 Norms of Signals and Systems.- 3.2 Hamiltonians and Riccati Equations.- 3.3 Factorizations.- 4 Chain-Scattering Representations of the Plant.- 4.1 Algebra of Chain-Scattering Representation.- 4.2 State-Space Forms of Chain-Scattering Representation.- 4.3 Dualization.- 4.4 J-Lossless and (J, J?)-Lossless Systems.- 4.5 Dual (J, J?)-Lossless Systems.- 4.6 Feedback and Terminations.- 5 J-Lossless Conjugation and Interpolation.- 5.1 J-Lossless Conjugation.- 5.2 Connections to Classical Interpolation Problem.- 5.3 Sequential Structure of J-Lossless Conjugation.- 6 J-Lossless Factorizations.- 6.1 (J, J?)-Lossless Factorization and Its Dual.- 6.2 (J, J?)-Lossless Factorization by J-Lossless Conjugation.- 6.3 (J, J?)-Lossless Factorization in State Space.- 6.4 Dual (J, J?)-Lossless Factorization in State Space.- 6.5 Hamiltonian Matrices.- 7 H? Control via (J, J?)-Lossless Factorization.- 7.1 Formulation of H? Control.- 7.2 Chain-Scattering Representations of Plants and H? Control.- 7.3 Solvability Conditions for Two-Block Cases.- 7.4 Plant Augmentations and Chain-Scattering Representations.- 8 State-Space Solutions to H? Control Problems.- 8.1 Problem Formulation and Plant Augmentation.- 8.2 Solution to H? Control Problem for Augmented Plants.- 8.3 Maximum Augmentations.- 8.4 State-Space Solutions.- 8.5 Some Special Cases.- 9 Structure of H? Control.- 9.1 Stability Properties.- 9.2 Closed-Loop Structure of H? Control.- 9.3 Examples.