Convexity of the Set of Fixed Points Generated by Some Control Systems
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-10-21
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
We deal with an application of the fixed point theorem for nonexpansive mappings to a class of control systems.
We study closed-loop and open-loop controllable dynamical systems governed by ordinary differential equations (ODEs) and establish convexity of the set of trajectories.
Solutions to the above ODEs are considered as fixed points of the associated system-operator.
If convexity of the set of trajectories is established, this can be used to estimate and approximate the reachable set of dynamical systems under consideration.
The estimations/approximations of the above type are important in various engineering applications as, for example, the verification of safety properties.
American Psychological Association (APA)
Azhmyakov, Vadim. 2009. Convexity of the Set of Fixed Points Generated by Some Control Systems. Journal of Applied Mathematics،Vol. 2009, no. 2009, pp.1-14.
https://search.emarefa.net/detail/BIM-460917
Modern Language Association (MLA)
Azhmyakov, Vadim. Convexity of the Set of Fixed Points Generated by Some Control Systems. Journal of Applied Mathematics No. 2009 (2009), pp.1-14.
https://search.emarefa.net/detail/BIM-460917
American Medical Association (AMA)
Azhmyakov, Vadim. Convexity of the Set of Fixed Points Generated by Some Control Systems. Journal of Applied Mathematics. 2009. Vol. 2009, no. 2009, pp.1-14.
https://search.emarefa.net/detail/BIM-460917
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-460917