Customer Reviews

Optimal Control Theory: A Course in Automatic Control Theory

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Automatic control theory is a vital and expanding area of mathematics with wide applications in many areas of modern technology, engineering and science. Students of engineering and applied mathematics will find a wealth of interesting material in this book, which elucidates the mathematical background, theory, applications and techniques essential to the understanding of optimal control theory.

The first part of the book (Chaps. 1-7) is devoted to a rapid and extremely clear presentation of the mathematical facts required in the modern theory of optimal control. Such topics as the theory of distributions, Fourier Transform, Laplace Transform. elements of probability theory, Markov chains and second-order stationary random processes are presented in terms of the most up-to-date vocabulary, the newest techniques and the most powerful theorems. The author's lucid expostion of such classic tools as Schwartz'distributions and harmonic analysis, make this an invaluable aid in the study of traditional automatic control.

The latter part of the book (Chaps. 8-18) is given over to a broad treatment of optimal control theory and its applications, including such newer developments as Pontryagin's principle. Since as important aspect of the book concerns optimization problems, chapters on linear and non-linear programming are included, comprising an invaluable basis for the study of optimization of dynamic systems. The final section of the book deals with the theory of random processes and associated optimization problems. --- from book's back cover

A lot of the old linear systems control books are thought to be antiques

since people have turned so much to microprocessor digital control.

What I thought was good about this book was that it started at topological vectors spaces

as Banach spaces and Frechet spaces and used that Mathematics to build a foundation for

systems control.

In about the middle of the book is takes a Fibonacci like sequence,

gets a polynomial for it,

does the Binet solution and then does the Laplace transforms to give

a serve system transfer function.

Then he generalizes that Cyclotomic types with roots less than or equal to one

can produce stable system control and stuff like Pisots and Salems

will produce quasi-stable control systems.

The result is that a lot of OEIS sequences of this sort based on Fibonacci like sequences

or polynomial expansions come off having applications

in control theory.

Since I found what I think of as an error in this same section of the book

I can't give the result my highest review,

but I like the book and hope to be able to get more out of it by study.