On the continuity property of L-P balls and an application

Guseinov K. G., Nazlipinar A. S.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.335, no.2, pp.1347-1359, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 335 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1016/j.jmaa.2007.01.109
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1347-1359
  • Keywords: L-p space, set-valued map, control system, attainable set, ATTAINABLE SETS, CONTROL-SYSTEMS, MINIMUM ENERGY, TIME
  • Anadolu University Affiliated: No

Abstract

In this paper continuity properties of the set-valued map p -> B-p(mu(0)), p is an element of (1, +infinity), are considered where B-p (mu(0)) is the closed ball of the space L-p ([t(0), theta]; R-m) centered at the origin with radius mu(0). It is proved that the set-valued map p -> B-p(mu(0)), p is an element of (1, +infinity), is continuous. Applying obtained results, the attainable set of the nonlinear control system with integral constraint on the control is studied. The admissible control functions are chosen from B-p (mu(0)). It is shown that the attainable set of the system is continuous with respect to p. (c) 2007 Elsevier Inc. All rights reserved.