On Some Metric Characteristics of Polysystems with Control Switchings in Discrete Time

Abstract

Control systems with a finite number of control settings (dynamical polysystems) are considered. It is assumed that every polysystem functions in continuous time and switchings of control occur in certain discrete instants of time. A switching control in continuous time is interpreted as a limiting case of a switching control in discrete time. The control goal is to transfer the polysystem from an initial state to a final state. Controllability of switched systems in discrete time is studied. Probabilistic methods are applied and some metric characteristics of dynamical polysystems are defined. In these terms, the rate of convergence of a sequence of estimates of control times in discrete time is characterized. These estimates can be find by numerical methods. It is shown that the attainability sets of a continuous switched system and of a discrete switched system coincide up to a set of measure zero.