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Control Applications in Physics: From Control of Chaos to Quantum Control

Organizer:Fradkov Alexander, Institute for Problems of Mechanical Engineering, Russian Federation
Co-Organizer:  Nijmeijer Henk, Eindhoven Technical University, Netherlands
Sieniutycz Stanislaw, Warsaw Technical University, Poland
Topic2.3 Non-Linear Control Systems
Chair:Fradkov Alexander, Russian Academy of Sciences, Russian Federation
Time:09:00 - 13:00
Room:University Lecture Room 202b

Before the 1990s not much interaction between theoretical physics and control theory could be observed. A new avenue of research in the borderland between physics and control was opened by advances in control and synchronization of chaos. It was discovered by E.Ott, C.Grebogi and J.Yorke (1990) and their numerous successors that even small feedback action can dramatically change the behavior of a nonlinear system, e.g. turn chaotic motions into periodic ones and vice versa. An interest in control of chaos gained interaction between physics and control theory (cybernetics) in different areas. One of the most important ones is control of molecular and quantum systems. Its rapid development is motivated by applications in quantum computations and control of chemical reactions. Now, after a decade of vigorous development, "cybernetical physics" (the term was coined in 1999) related to both physics and control is still an emerging field.

In the tutorial a number of new application fields related to studying properties of physical systems by means of feedback will be exposed.

Firstly, the subject and methodology of cybernetical physics will be outlined. Methods of energy control in conservative and dissipative systems will be presented. Examples of transformation laws describing the excitability properties of dissipative systems will be presented and discussed. A number of applications in physics will be discussed: feedback resonance phenomenon in nonlinear oscillators, escape from potential wells, control and synchronization in oscillatory chains, etc.

In the second part the main ideas and results in the emerging field of controlling chaotic behavior, in which more than 3,000 papers in peer-reviewed journals were published from 1997 to 2003 will be presented. Among other methods, feedforward control by periodic signal, linearization of Poincare map (OGY method), and delayed feedback (Pyragas method) will be analyzed. Some open will be discussed. Examples of potential applications in different areas of science and technology will then be surveyed: control of turbulence, control of chaotic friction forces, control of chaos in lasers, attitude control of spacecrafts, control of microeconomical chaos.

In the third part the concepts and results related to controlled synchronization will be outlined, including general definitions, observer-based synchronization, synchronization of mechanical systems, applications in robotics and secure communications.

In the fourth part a brief exposition of control thermodynamics will be given with emphasis on methods and algorithms of optimal control that constitute theoretical and computational tools when evaluating extremum or optimal properties of thermodynamic systems. It will be demonstrated that thermodynamics helps to treat physical or economical problems of optimal control and behavior of physical or practical systems under prescribed external conditions can be predicted from suitable variational or extremum principles.

Finally, introductory exposition of the field related to control of molecular systems will be given based on both classical and quantum description of the controlled molecular motion.

Goal: to acquaint control
theorists and engineers with a number of new application fields
To acquaint control theorists and engineers with new application fields related to studying properties of physical systems by means of feedback

Subject and methodology of cybernetical physics (30 min)

Control of chaos (40 min) - A.Fradkov (Lab. Control of Complex Systems, Russian Academy of Sciences)

Controlled synchronization (40 min) - H.Nijmeijer (Dept. Mechanical Engineering, TU Eindhoven)

Control thermodynamics (40 min) - S.Sieniutycz (Dept. Chemical Engineering, TU Warsaw)

Molecular and quantum control (30 min) - A.Fradkov

The material of the tutorial is based on recent monographs:

Fradkov A.L., A.Yu.Pogromsky. Introduction to Control of Oscillations and Chaos. Singapore: World Scientific, 1998.
Fradkov A.L. Cybernetical Physics: Principles and Examples. St.Petersburg: Nauka, 2003 (in Russian).
Nijmeijer, H. /Rodriguez-Angeles, A.:Synchronization of Mechanical Systems. Singapore: World Scientific, 2003.
S. Berry, V.A. Kazakov, S. Sieniutycz, Z. Szwast, and A.M. Tsirlin. Thermodynamic Optimization of Finite Time Processes. Wiley 2000