Precompactness of the Set of Trajectories of the Controllable System Described by a Nonlinear Volterra Integral Equation

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Huseyin A., Huseyin N.

MATHEMATICAL MODELLING AND ANALYSIS, vol.17, no.5, pp.686-695, 2012 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 17 Issue: 5
  • Publication Date: 2012
  • Doi Number: 10.3846/13926292.2012.736088
  • Journal Name: MATHEMATICAL MODELLING AND ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.686-695
  • Keywords: nonlinear Volterra integral equation, controllable system, integral constraint, set of trajectories
  • Open Archive Collection: AVESIS Open Access Collection
  • Anadolu University Affiliated: Yes

Abstract

In this paper the controllable system whose behaviour is described by a nonlinear Volterra integral equation, is studied. The set of admissible control functions is the closed ball of the space L-p (p > 1) with radius mu(0) and centered at the origin. It is shown that the set of trajectories of the system is a bounded and pre-compact subset of the space of continuous functions.