Foundations of Deterministic and Stochastic Control

Control theory has applications to a number of areas in engineering
and communication theory. This introductory text on the subject is
fairly self-contained, and consists of a wide range of topics that
include realization problems, linear-quadratic optimal control,
stability theory, stochastic modeling and recursive estimation
algorithms in communications and control, and distributed system
modeling.
In the early chapters methods based on Wiener--Hopf integral
equations are utilized. The fundamentals of both linear control
systems as well as stochastic control are presented in a unique way so
that the methods generalize to a useful class of distributed parameter
and nonlinear system models. The control of distributed parameter
systems (systems governed by PDEs) is based on the framework of linear
quadratic Gaussian optimization problems.
Additionally, the important notion of state space modeling of
distributed systems is examined. Basic results due to Gohberg and
Krein on convolution are given and many results are illustrated with
some examples that carry throughout the text.
The standard linear regulator problem is studied in the continuous
and discrete time cases, followed by a discussion of (dual) filtering
problems. Later chapters treat the stationary regulator and filtering
problems using a Wiener--Hopf approach. This leads to spectral
factorization problems and useful iterative algorithms that follow
naturally from the methods employed. The interplay between time and
frequency domain approaches is emphasized.
"Foundations of Deterministic and Stochastic Control" is geared
primarily towards advanced mathematics and engineering students in
various disciplines.