Approximation of sections of the set of trajectories for a control system with bounded control resources

Huseyin A., Huseyin N., Guseinov K.

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, vol.23, no.1, pp.116-127, 2017 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.21538/0134-4889-2017-23-1-116-127
  • Journal Name: TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.116-127
  • Keywords: Urysohn integral equation, control system, integral constraint, set of trajectories, approximation
  • Anadolu University Affiliated: Yes

Abstract

The approximation of the set of trajectories is studied for a control system described by the Urysohn integral equation. It is assumed that the system has limited control resources. The closed ball of the space L-p, p > 1, with radius r centered at the origin is chosen as the set of admissible control functions. The set of admissible control functions is replaced step by step by a set that consists of a finite number of control functions and generates a finite number of trajectories. It is proved that sections of the set of trajectories can be approximated by sections of a set consisting of a finite number of trajectories.