Compactness of the set of trajectories of the controllable system described by an affine integral equation

Huseyin N., Huseyin A.

APPLIED MATHEMATICS AND COMPUTATION, cilt.219, sa.16, ss.8416-8424, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 219 Sayı: 16
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.amc.2013.03.005
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.8416-8424
  • Sivas Cumhuriyet Üniversitesi Adresli: Hayır

Özet

In this paper the control system with integral constraint on the controls is studied. It is assumed that the behavior of the system is described by an affine Volterra integral equation which is nonlinear with respect to the state vector and is linear with respect to the control vector. The closed ball of the space L-p (p > 1) with radius mu(0) and centered at the origin, is chosen as the set of admissible control functions. It is proved that the set of trajectories is abounded, closed, precompact and hence compact subset of the space of continuous functions. (C) 2013 Elsevier Inc. All rights reserved.