Convexity of the Set of Fixed Points Generated by Some Control Systems
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 ab...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2009/291849 |
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| _version_ | 1832567397420105728 |
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| author | Vadim Azhmyakov |
| author_facet | Vadim Azhmyakov |
| author_sort | Vadim Azhmyakov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b44b018ccea84f259bd5027210692ac7 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b44b018ccea84f259bd5027210692ac72025-02-03T01:01:39ZengWileyJournal of Applied Mathematics1110-757X1687-00422009-01-01200910.1155/2009/291849291849Convexity of the Set of Fixed Points Generated by Some Control SystemsVadim Azhmyakov0Departamento de Control Automatico, Cinvestav, A.P. 14-740, Avenida Instituto Politecnico Nacional 2508, 07360 Mexico DF, MexicoWe 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.http://dx.doi.org/10.1155/2009/291849 |
| spellingShingle | Vadim Azhmyakov Convexity of the Set of Fixed Points Generated by Some Control Systems Journal of Applied Mathematics |
| title | Convexity of the Set of Fixed Points Generated by Some Control Systems |
| title_full | Convexity of the Set of Fixed Points Generated by Some Control Systems |
| title_fullStr | Convexity of the Set of Fixed Points Generated by Some Control Systems |
| title_full_unstemmed | Convexity of the Set of Fixed Points Generated by Some Control Systems |
| title_short | Convexity of the Set of Fixed Points Generated by Some Control Systems |
| title_sort | convexity of the set of fixed points generated by some control systems |
| url | http://dx.doi.org/10.1155/2009/291849 |
| work_keys_str_mv | AT vadimazhmyakov convexityofthesetoffixedpointsgeneratedbysomecontrolsystems |