Synergetic Control Theory and Vibro-Mechanics: a Conceptual Relation

Abstract

The paper established a deep conceptual relation between the vibro-mechanics and the synergetic control theory. This conceptual relation is revealed in the emergence of new phenomena in the complex systems, namely: expansion and compression of the phase flow; transition of the point representing system into the internal attracting manifolds, on which new dynamic properties of the system are formed. In vibro-mehanics the control actions are carried out usually as a function of time by selecting the corresponding vibration actions, but the synergetic theory of the control actions is synthesized in the feedback function, ensuring the desired oscillation and vibration processes. These new research areas complement each other in meeting today's major technological challenges of controlling complex objects of different nature. We prove that with an example of a complete solution of the famous P. L. Kapitza's problem of "the inverted pendulum stabilization".