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 aimed primarily at advanced mathematics
and engineering students in various disciplines.
The topics covered include realization problems,
linear-quadratic optimal control, stability theory, stochastic
modeling and recursive estimation algorithms in communications and
control, and distributed system modeling. These topics have a wide
range of applicability, and provide background for further study in
the control and communications areas.
In the early chapters the basics of linear control systems as
well as the fundamentals of 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.
The approach here utilizes methods based on Wiener-Hopf integral
equations. 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 both the continuous
and discrete time cases, followed by a discussion of the (dual)
filtering problems. Later chapters treat the stationary regulator
and filtering problems with a Wiener-Hopf approach. This leads to
spectral factorization problems and useful iterative algorithms
that follow naturally from the methods employed. Theinterplay
between time and frequency domain approaches is emphasized.
General
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