On the set of trajectories of the control systems with limited control resources

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

8th International Conference on Curves and Surfaces, 2014, Paris, France, 12 - 18 June 2014, vol.9213, pp.280-288 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 9213
  • Doi Number: 10.1007/978-3-319-22804-4_21
  • City: Paris
  • Country: France
  • Page Numbers: pp.280-288
  • Keywords: Integral equation, Control system, Integral constraint, Set of trajectories, INTEGRAL-EQUATION
  • Anadolu University Affiliated: Yes

Abstract

© Springer International Publishing Switzerland 2015.The set of trajectories of the control system with limited control resources is studied. It is assumed that the behavior of the system is described by a Volterra type integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector. The closed ball of the space Lp (p > 1) with radius μ and centered at the origin, is chosen as the set of admissible control functions. It is proved that for each fixed p the set of trajectories is Lipschitz continuous with respect to μ and for each fixed μ is continuous with respect to p. The upper evaluation for the diameter of the set of trajectories is given.