Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions
In this paper the control system is considered described by a Urysohn type integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector. The functions from the space L2([t0,θ];Rm) satisfying a quadratic integral constraint are chosen as admis...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/43163/ http://psasir.upm.edu.my/id/eprint/43163/1/43163.pdf |
| _version_ | 1848850154792157184 |
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| author | Alias, Idham Arif Huseyin, Nesir Huseyin, Anar |
| author_facet | Alias, Idham Arif Huseyin, Nesir Huseyin, Anar |
| author_sort | Alias, Idham Arif |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper the control system is considered described by a Urysohn type integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector. The functions from the space L2([t0,θ];Rm) satisfying a quadratic integral constraint are chosen as admissible control functions. The set of trajectories generated by all admissible control functions is studied. The boundedness, closedness, precompactness, and hence the compactness of the set of trajectories in the space of continuous functions is proved. |
| first_indexed | 2025-11-15T10:01:47Z |
| format | Article |
| id | upm-43163 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:01:47Z |
| publishDate | 2016 |
| publisher | SpringerOpen |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-431632016-05-18T03:19:01Z http://psasir.upm.edu.my/id/eprint/43163/ Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions Alias, Idham Arif Huseyin, Nesir Huseyin, Anar In this paper the control system is considered described by a Urysohn type integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector. The functions from the space L2([t0,θ];Rm) satisfying a quadratic integral constraint are chosen as admissible control functions. The set of trajectories generated by all admissible control functions is studied. The boundedness, closedness, precompactness, and hence the compactness of the set of trajectories in the space of continuous functions is proved. SpringerOpen 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/43163/1/43163.pdf Alias, Idham Arif and Huseyin, Nesir and Huseyin, Anar (2016) Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions. Journal of Inequalities and Applications, 2016 (1). art. no. 36. pp. 1-14. ISSN 1025-5834; ESSN: 1029-242X http://link.springer.com/article/10.1186%2Fs13660-015-0908-9 10.1186/s13660-015-0908-9 |
| spellingShingle | Alias, Idham Arif Huseyin, Nesir Huseyin, Anar Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions |
| title | Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions |
| title_full | Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions |
| title_fullStr | Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions |
| title_full_unstemmed | Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions |
| title_short | Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions |
| title_sort | compactness of the set of trajectories of the control system described by a urysohn type integral equation with quadratic integral constraints on the control functions |
| url | http://psasir.upm.edu.my/id/eprint/43163/ http://psasir.upm.edu.my/id/eprint/43163/ http://psasir.upm.edu.my/id/eprint/43163/ http://psasir.upm.edu.my/id/eprint/43163/1/43163.pdf |