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 Izv. IMI UdGU, 2015, Issue 2(46), Pages 216–227 (Mi iimi322)

On properties of characteristics of attainability set for a control system

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: We continue to study the characteristics of a control system, which reflect uniform staying the attainability set of the system in a given set $\mathfrak M\doteq\{(t,x)\in [0,+\infty)\times\mathbb R^n: x\in M(t)\}$ during a finite time interval. In terms of Lyapunov functions and Clarke's derivative, we obtain conditions under which relative frequencies of absorption of attainability set for the control system can be estimated by similar characteristics defined for differential equations. We prove a theorem about evaluating and calculating of the relative frequencies for some multivalued functions. We get estimation for different characteristics of Bohr almost periodic functions. We show examples of calculations and estimations for the relative frequencies of staying graphs of functions in a given set.

Keywords: controllable systems, differential inclusions, attainability set, almost periodic functions.

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UDC: 517.958, 530.145.6
MSC: 34H05, 34H99, 93C10

Citation: A. H. Hammady, “On properties of characteristics of attainability set for a control system”, Izv. IMI UdGU, 2015, no. 2(46), 216–227

Citation in format AMSBIB
\Bibitem{Ham15} \by A.~H.~Hammady \paper On properties of characteristics of attainability set for a control system \jour Izv. IMI UdGU \yr 2015 \issue 2(46) \pages 216--227 \mathnet{http://mi.mathnet.ru/iimi322} \elib{http://elibrary.ru/item.asp?id=25030049}