Topics in Control Theory

by Knobloch, H. W.; Isidori, Alberto; Flockerzi, Dietrich

• ISBN13: 9780817629533
• ISBN10: 081762953X
• Format: Paperback
• Copyright: 1993-10-01
• Publisher: Birkhauser

Summary

One of the key concerns in modern control theory is the design of steering strategies. The implementation of such strategies is done by a regulator. Presented here is a self-contained introduction to the mathematical background of this type of regulator design. The topics selected address the matter of greatest interest to the control community at present, namely, when the design objective is the reduction of the influence of exogeneous disturbances upon the output of the system.
In a first scenario the disturbance signal is regarded as a deterministic time series with known dynamics but unknown parameters. The design objective is then the asymptotic disturbance compensation. In a second scenario, no information about the disturbance signal is available apart from some bounds. Here, in an [actual symbol not reproducible]-approach, control strategies are worked out which will prove efficient for all such disturbances.
The intention of this book is to present ideas and methods on such a level that the beginning graduate student will be able to follow current research. New results are included, especially for nonlinear control systems, and as a service to the reader, an extensive appendix presents topics from linear algebra, invariant manifolds and calculus of variations, information which is hardly to be found in standard textbooks.

Table of Contents

Introduction	p. 1
The problem of output regulation
Output regulation via full information	p. 9
Output regulation via error feedback	p. 13
A particular case	p. 22
Well-posedness and robustness	p. 26
The construction of a robust regulator	p. 29
Disturbance attenuation via [actual symbol not reproducible]-methods
A characterization of the [actual symbol not reproducible]-gain of a linear system	p. 45
Disturbance attenuation via full information	p. 49
Disturbance attenuation via measured feedback	p. 58
Full information regulators
Time-dependent control strategies	p. 72
Time-independent control strategies	p. 79
The local case	p. 79
Nonlinear observers
Time-dependent observers	p. 84
Error feedback regulators	p. 88
Nonlinear [actual symbol not reproducible]-techniques
Construction of the saddle-point	p. 100
The local scenario	p. 103
Disturbance attenuation via linearization	p. 108
A Matrix equations
Linear matrix equations	p. 113
Algebraic Riccati equations	p. 115
B Invariant manifolds
Existence theorem	p. 127
Outflowing manifolds	p. 131
Asymptotic phase	p. 134
Convergence for [actual symbol not reproducible]	p. 143
A special case	p. 150
Dichotomies and Lyapunov functions	p. 151
C Hamilton-Jacobi-Bellman-Isaacs equation
Method of characteristics	p. 154
The equation of Isaacs	p. 156
The Hamiltonian version of Isaacs' equation	p. 160
Bibliography	p. 163
Table of Contents provided by Blackwell. All Rights Reserved.