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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

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

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Abstract

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.

Item Type:Article
Keyword:Control system; Quadratic integral constraint; Set of trajectories; Urysohn type integral equation
Faculty or Institute:Faculty of Science
Publisher:SpringerOpen
DOI Number:10.1186/s13660-015-0908-9
Altmetrics:http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1186/s13660-015-0908-9
ID Code:43163
Deposited By: Nabilah Mustapa
Deposited On:18 May 2016 11:19
Last Modified:18 May 2016 11:19

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