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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 4
  • Publication Date: 2015
  • Doi Number: 10.3846/13926292.2015.1070766
  • Journal Name: Mathematical Modelling and Analysis
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.502-515
  • Keywords: nonlinear Volterra integral equation, control system, integral constraint, set of trajectories, approximation method, ATTAINABLE SETS, CONSTRAINT
  • Anadolu University Affiliated: Yes

Abstract

© 2015, © Vilnius Gediminas Technical University, 2015.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 Lp, p > 1, with radius µ 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.