Details

Autor(en) / Beteiligte

• Huseyin, Nesir
• Huseyin, Anar
• Guseinov, Khalik G.
• Gout, Christian
• Lyche, Tom
• Boissonnat, Jean-Daniel
• Gibaru, Olivier
• Schumaker, Larry L
• Mazure, Marie-Laurence
• Cohen, Albert
• Schumaker, Larry L.

Titel

On the Set of Trajectories of the Control Systems with Limited Control Resources

Ist Teil von

• Curves and Surfaces, 2015, Vol.9213, p.280-288

Ort / Verlag

Switzerland: Springer International Publishing AG

Erscheinungsjahr

2015

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_p$$\end{document}(p>1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(p>1)$$\end{document} with radius μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} and for each fixed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} is continuous with respect to p. The upper evaluation for the diameter of the set of trajectories is given.