Approximation of the set of trajectories of a control system described by the Urysohn integral equation


Huseyin N. , Huseyin A. , Guseinov K. G.

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, vol.21, no.2, pp.59-72, 2015 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 2
  • Publication Date: 2015
  • Title of Journal : TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN
  • Page Numbers: pp.59-72

Abstract

The approximation of the set of trajectories of a control system described by the Urysohn integral equation is considered. The closed ball of the space L-p([a,b]; R-m) (p > 1) of radius r centered at the origin is chosen as the set of admissible controls. This set is replaced by a set of control functions, which consists of a finite number of controls and generates a finite number of trajectories. An accuracy estimate is obtained for the Hausdorff distance between the set of trajectories and the set consisting of a finite number of trajectories.