A.L. Fradkov, Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia


Before the 1990s not much interaction between physical and control-theoretical studies was observed. New avenue of research in physics was opened by results 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 cybernetics (control theory). Now, after a decade of vigorous development, "cybernetical physics" related both to physics and to control is still an emerging field. The aim of cyberphysical investigation is studying a physical system by means of controlling it. Conventional conservation laws of physics give up their place to the transformation laws of cyberphysics.

In the talk the possibilities of investigating physical systems by means of feedback will be discussed. Firstly, the subject and methodology of cybernetical physics will be outlined. Secondly, examples of transformation laws describing the excitability properties of dissipative systems will be presented and discussed. The feedback resonance phenomenon in nonlinear oscillators will be introduced and its consequences for physics will be described.

The material of the talk is based on recently published monographs: Fradkov A.L., A.Yu.Pogromsky. Introduction to Control of Oscillations and Chaos. Singapore, World Scientific, 1998. Fradkov A.L., Miroshnik I.V., Nikiforov V.O. Nonlinear and Adaptive Control of Complex Systems. Ch.9, Physics and Control. Dordrecht: Kluwer Academic Publ., 1999. and subsequent papers.