Cybernetical Physics: From Control of Chaos to Quantum Control

In this book a number of ideas and results related to the ?eld of cybern- ical physics – the scienti?c area aimed at the study of physical systems by cybernetical means – are presented. Although some publications in physical journals related to control problems appeared long ago, formation of a se- rateself-sustainedareastartedaslateasinthe1990sduetotheexplosion-like developmentofresearchincontrolofchaos,quantumcontrol,andotherareas. The number of publications has reached several thousands by the end of the century and it continues to grow very rapidly. This book is, perhaps, the ?rst attempt to present a uni?ed exposition of the subject and methodology of cybernetical physics as well as solutions to some of its problems. A part of this book presents the limits of system transformation by means of control both for conservative and for dissipative systems based on Hamiltonian description of system dynamics. A survey of various control applications in physics is given: control of chaos, controlled synchronization, control of spatiotemporal systems, control ofmolecularandquantumsystems.Anapproachforbuildingmodelsofsystem dynamics based on control methods is discussed. The presented methods and results are illustrated by examples of new approaches to classical problems: Stephenson–Kapitsa pendulum, escape from a potential well, synchronization of coupled oscillators, control of chemical reaction with phase transition, c- trolled dissociation of molecules, controlled oscillations of complex crystalline lattices. Controlled pendulums appear in many parts of the book since p- dulum models can be thought of as the “atoms of nonlinear physics”.

The control of complex systems is one of the most important aspects in dealing with systems exhibiting nonlinear behaviour or similar features that defy traditional control techniques. This specific subject is gradually becoming known as cybernetical physics, borrowing methods from both theoretical physics and control engineering.

This book is, perhaps, the first attempt to present a unified exposition of the subject and methodology of cybernetical physics as well as solutions to some of its problems. Emphasis of the book is on the examination of fundamental limits on energy transformation by means of control procedures in both conservative and dissipative systems. A survey of application in physics includes the control of chaos, synchronisation of coupled oscillators, pendulum chains, reactions in physical chemistry and of quantum systems such as the dissociation of diatomic molecules.

This book has been written having researchers from various backgrounds in physics, mathematics and engineering in mind and is thus also suitable as introduction to graduate students working on the understanding of a broad range of complex systems in the natural sciences.