Geodesic
Approximation of the set of trajectories of a control system described by the Urysohn integral equation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 59-72

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The approximation of the set of trajectories of a control system described by the Urysohn integral equation is considered. The closed ball of the space $L_p([a,b];\mathbb{R}^m)$ $(p>1)$ of radius $r$ centered at the origin is chosen as the set of admissible controls. This set is replaced by a set of control functions, which consists of a finite number of controls and generates a finite number of trajectories. An accuracy estimate is obtained for the Hausdorff distance between the set of trajectories and the set consisting of a finite number of trajectories.
Keywords: Urysohn integral equation, control system, integral constraint, set of trajectories, approximation. 
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     title = {Approximation of the set of trajectories of a control system described by the {Urysohn} integral equation},
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N. Huseyin; A. Huseyin; Kh. G. Guseinov. Approximation of the set of trajectories of a control system described by the Urysohn integral equation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 59-72. http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a5/