Nonlinear Phenomena in Complex Systems, 2013, Vol.16, No.4, pp.388-396

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2013, Vol.16, No.4, pp.388-396

Controllability and Number-Theoretic Properties of Dynamical Polysystems
Sergey M. Khryashchev

Control systems with a finite number of control parameters, i.e. dynamical polysystems, are considered. It is assumed that the control switchings occur at some discrete times. Controllability of these systems are studied. Methods of number theory are used. Existence of control switching times is established by analysis of Diophantine equations. The values of control switching times can be found by some numerical methods. The statements on controllability are proved. Some examples are considered.

Key words: control systems, dynamical polysystems, number theory

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