A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.

The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.

The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.

Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.

Contents:

• The Mathematics of Nonlinear Control
• The Mathematics of Oscillations and Chaos
• Methods of Nonlinear and Adaptive Control of Oscillations
• Control of Oscillatory and Chaotic Systems
• Applications

"... should be a welcome addition to the library of anyone interested in chaos and nonlinear control. It also should be useful to engineers who are developing algorithms for the control of oscillatory and chaotic dynamical systems and perhaps to researchers interested in controlling the chaotic behavior of economic systems."

"The book is an excellent collection of some valuable techniques for adaptive control with respect to oscillations in particular. It is a mathematically rigorous and well-edited volume with many good examples, suitable for both professionals and graduates as a handy reference book."