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 H-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. Contents: Introduction - The problem of output
regulation - Introduction - Problem statement - Output regulation via
full information - Output regulation via full error feedback - A
particular case - Well-posedness and robustness - The construction of a
robust regulator - Disturbance attenuation via H-methods -
Introduction - Problem statement - A characterization of the L2-gain of
a linear system - Disturbance attenuation via full information -
Disturbance attenuation via measured feedback - Full information
regulators - Problem statement - Time-dependent control strategies -
Examples - Time-independent control strategies - The local case -
Nonlinear observers - Problem statement - Time-dependent observers -
Error feedback regulators - Examples - Nonlinear H-techniques -
Introduction - Construction of the saddle-point - The local scenario -
Disturbance attenuation via linearization - Matrix equations - Linear
matrix equations - Algebraic Riccati equations - Invariant manifolds -
Existence theorem - Outflowing manifolds - Asymptotic phase -
Convergence for T ¹ - A special case - Dichotomies and Lyapunov
functions - Hamilton-Jacobi-Bellman-Isaacs equation - Introduction -
Method of characteristics - The equation of Isaacs - The Hamiltonian
version of Isaacs' equation - Bibliography
