Series on Stability, Vibration and Control of Systems, Series A - Vol. 6
MATHEMATICAL PROBLEMS OF CONTROL THEORY
An Introduction
by Gennady A Leonov (St. Petersburg State University, Russia)
This book shows clearly how the study of concrete control systems has motivated the development of the mathematical tools needed for solving such problems. In many cases, by using this apparatus, far-reaching generalizations have been made, and its further development will have an important effect on many fields of mathematics.
In the book a way is demonstrated in which the study of the Watt flyball governor has given rise to the theory of stability of motion. The criteria of controllability, observability, and stabilization are stated. Analysis is made of dynamical systems, which describe an autopilot, spacecraft orientation system, controllers of a synchronous electric machine, and phase-locked loops. The Aizerman and Brockett problems are discussed and an introduction to the theory of discrete control systems is given.
Contents:
- The Watt Governor and the Mathematical Theory of Stability of
Motion
- Linear Electric Circuits. Transfer Functions and Frequency Responses of Linear Blocks
- Controllability, Observability, Stabilization
- Two-Dimensional Control Systems. Phase Portraits
- Discrete Systems
- The Aizerman Conjecture. The Popov Method
Readership: Applied mathematicians and mechanical engineers.
"... one has here a light introduction proposing paths that bring together motivating applications, important known facts and methods as well as open problems. Instead of imposing a point of view, the reader will build a working knowledge, and his creativity will be stimulated so that he can develop his own perspective."
"The very readable book addresses primarily readers with an engineering background, without however relinquishing mathematical exactness."
| 180pp |
Pub. date: Nov 2001 |
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