Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation

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Huseyin A., Huseyin N.

APPLICATIONS OF MATHEMATICS, vol.59, no.3, pp.303-317, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.1007/s10492-014-0056-4
  • Journal Name: APPLICATIONS OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.303-317
  • Keywords: nonlinear Volterra integral equation, control system, integral constraint
  • Anadolu University Affiliated: Yes

Abstract

In this paper the control system with limited control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The admissible control functions are chosen from the closed ball centered at the origin with radius A mu in L (p) (p > 1). It is proved that the set of trajectories generated by all admissible control functions is Lipschitz continuous with respect to A mu for each fixed p, and is continuous with respect to p for each fixed A mu. An upper estimate for the diameter of the set of trajectories is given.