Geodesic
Approximation of sections of the set of trajectories for a control system with bounded control resources
Trudy Instituta matematiki i mehaniki, Tome 23 (2017) no. 1, pp. 116-127 Cet article a éte moissonné depuis la source Math-Net.Ru

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A. Huseyin, N. Huseyin, Kh. Guseinov. Approximation of sections of the set of trajectories for a control system with bounded control resources. The approximation of the set of trajectories is studied for a control system described by the Urysohn integral equation. It is assumed that the system has limited control resources. The closed ball of the space $L_p$, $p>1$, with radius $r$ centered at the origin is chosen as the set of admissible control functions. The set of admissible control functions is replaced step by step by a set that consists of a finite number of control functions and generates a finite number of trajectories. It is proved that sections of the set of trajectories can be approximated by sections of a set consisting of a finite number of trajectories.
Keywords: Urysohn integral equation, control system, integral constraint, set of trajectories, approximation. 
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A. Huseyin; N. Huseyin; Kh. G. Guseinov. Approximation of sections of the set of trajectories for a control system with bounded control resources. Trudy Instituta matematiki i mehaniki, Tome 23 (2017) no. 1, pp. 116-127. http://geodesic.mathdoc.fr/item/TIMM_2017_23_1_a12/

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