Extending H-infinity Control to Nonlinear Systems: Control of Nonlinear Systems to Achieve Performance Objectives (Advances in Design and Control, Series Number 1)

✍ Scribed by J. William Helton, Matthew R. James

• Publisher: Society for Industrial and Applied Mathematics
• Year: 1987
• Tongue: English
• Leaves: 356
• Category: Library

✦ Synopsis

H-infinity control originated from an effort to codify classical control methods, where one shapes frequency response functions for linear systems to meet certain objectives. H-infinity control underwent tremendous development in the 1980s and made considerable strides toward systematizing classical control. This book addresses the next major issue of how this extends to nonlinear systems. At the core of nonlinear control theory lie two partial differential equations (PDEs). One is a first-order evolution equation called the information state equation, which constitutes the dynamics of the controller. One can view this equation as a nonlinear dynamical system. Much of this volume is concerned with basic properties of this system, such as the nature of trajectories, stability, and, most important, how it leads to a general solution of the nonlinear H-infinity control problem.

✦ Table of Contents

Advances in Design and Control
ISBN 0-89871-440-0
Contents
Preface
Notation
1 Introduction


3 Information States
4 Information State Control

6 Storage Functions
7 Special Cases
8 Factorization
9 The Mixed Sensitivity Problem
Part II Singular Information States and Stability
10 Singular Information States
11 Stability of the Information State Equation
12 Time Varying Systems
Appendix A Differential Equations and Stability
Appendix B Nonlinear PDE and Riccati Equations
Appendix C Max-Plus Convergence
Bibliography
Index