Statistic Methods for Control of Dynamical Polysystems

Abstract

Control systems with a finite number of control parameters (dynamical polysystems) are considered. It is assumed that the control switchings occur at some discrete times. Controllability of the systems is studied. Statistic methods of number theory are applied. Existence of integer control times is established by analysis of Diophantine inequalities. The values of control times can be found by some numerical methods. The statements on controllability are proved. Some examples are considered.