The approximation of reachable sets of control systems with integral constraint on controls

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Guseinov K. G., Ozer O., Akyar E., Ushakov V. N.

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, vol.14, no.1-2, pp.57-73, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1-2
  • Publication Date: 2007
  • Doi Number: 10.1007/s00030-006-4036-6
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.57-73
  • Keywords: control system, reachable set, integral constraint, ATTAINABLE SETS, MINIMUM ENERGY, DYNAMICS, TIME
  • Anadolu University Affiliated: No


In this paper an approximation method for the construction of reachable sets of control systems with integral constraints on the control is considered. It is assumed that the control system is non-linear with respect to the phase state vector and is linear with respect to the control vector. The admissible control functions are chosen from the ball centered at the origin with radius mu(0) in L-p, p > 1. The reachable set is replaced by the set which consists of finite number of points. The estimated accuracy of the Hausdorff distance between the reachable set and the set which is approximately constructed is obtained.