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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


Citation

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

Abstract / Synopsis

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.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
DOI Number: https://doi.org/10.1186/s13660-015-0908-9
Publisher: SpringerOpen
Keywords: Control system; Quadratic integral constraint; Set of trajectories; Urysohn type integral equation
Depositing User: Nabilah Mustapa
Date Deposited: 18 May 2016 03:19
Last Modified: 18 May 2016 03:19
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1186/s13660-015-0908-9
URI: http://psasir.upm.edu.my/id/eprint/43163
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