Probabilistic Methods for Switching Control in Discrete Time

Abstract

Control systems with a finitely many of control settings, i. e. dynamical polysystems, are considered. It is assumed that a polysystem functions in continuous time and switchings of control occur in some discrete instants of time. The control goal is a transition of a polysystem from an initial state to a final state. Controllability of the polysystems is studied. Probabilistic methods are applied. Some probability characteristics of dynamical polysystems are defined. It is shown that under the rank condition, the switching controls always exist and the estimates of control times can be find by numerical methods. The rate of convergence of estimates of control times is established. The scale of the rates of convergence is described.