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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2015 Volume 21, Number 2, Pages 59–72 (Mi timm1171)

This article is cited in 5 papers

Approximation of the set of trajectories of a control system described by the Urysohn integral equation

N. Huseyin, A. Huseyin, Kh. G. Guseinova

a Anadolu University

Abstract: 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.

UDC: 517.977

Received: 10.12.2014



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