Approximation of the Sections of the Set of Trajectories of the Control System Described by a Nonlinear Volterra Integral Equation


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HÜSEYİN A. , HÜSEYİN N. , Guseinov K. G.

MATHEMATICAL MODELLING AND ANALYSIS, vol.20, no.4, pp.502-515, 2015 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 4
  • Publication Date: 2015
  • Doi Number: 10.3846/13926292.2015.1070766
  • Title of Journal : MATHEMATICAL MODELLING AND ANALYSIS
  • Page Numbers: pp.502-515

Abstract

Approximation of the sections of the set of trajectories of the control system described by a nonlinear Volterra integral equation is studied. The admissible control functions are chosen from the closed ball of the space L-p, p > 1, with radius mu and centered at the origin. The set of admissible control functions is replaced by the set of control functions, which includes a finite number of control functions and generates a finite number of trajectories. It is proved that the sections of the set of trajectories can be approximated by the sections of the set of trajectories, generated by a finite number of control functions.