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Abstract and Applied Analysis
Volume 2008, Article ID 295817, 14 pages
Research Article

On the Continuity Properties of the Attainable Sets of Nonlinear Control Systems with Integral Constraint on Controls

Department of Mathematics, Anadolu University, Eskisehir 26470, Turkey

Received 11 June 2007; Revised 30 August 2007; Accepted 6 November 2007

Academic Editor: Agacik Zafer

Copyright © 2008 Khalik G. Guseinov and Ali S. Nazlipinar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The attainable sets of the nonlinear control systems with integral constraint on the control functions are considered. It is assumed that the behavior of control system is described by differential equation which is nonlinear with respect to phase-state vector and control vector. The admissible control functions are chosen from the closed ball centered at the origin with radius πœ‡0 in 𝐿𝑝([𝑑0,πœƒ];β„π‘š)(π‘βˆˆ(1,+∞)). Precompactness of the solutions set is specified, and dependence of the attainable sets on the initial conditions and on the parameters of the control system is studied.