Controllability and Number-Theoretic Properties of Dynamical Polysystems

Abstract

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.