APPROXIMATION OF THE SET OF INTEGRABLE TRAJECTORIES OF THE CONTROL SYSTEM WITH L2 NORM CONSTRAINTS ON CONTROL FUNCTIONS

被引：0

作者：

Huseyin, Nesir ^{[1
]}

Huseyin, Anar ^{[2
]}

Guseinov, Khalik g. ^{[3
]}

机构：

[1] Sivas Cumhuriyet Univ, Dept Math & Sci Educ, TR-58140 Sivas, Turkiye

[2] Sivas Cumhuriyet Univ, Dept Stat & Comp Sci, TR-58140 Sivas, Turkiye

[3] Karabakh Univ, Sch Engn, AZ-2600 Khankendi, Azerbaijan

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2024年 / 13卷 / 04期

关键词：

Control system; integral constraint; Urysohn integral equation; integrable trajectory; set of trajectories; approximation; REACHABLE SET; EQUATIONS;

D O I：

10.3934/eect.2024023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper an approximation of the set of multivariable and L-2 integrable trajectories of the control system described by Urysohn type integral equation is considered. It is assumed that the system is affine with respect to the control vector. The admissible control functions are chosen from the closed ball of the space L-2, centered at the origin with radius rho. The set of admissible control functions is replaced, step by step, by the set of controls consisting of a finite number of piecewise-constant control functions. It is proved that under appropriate choosing of the discretization parameters, the set of trajectories generated by a finite number of piecewise-constant control functions is an internal approximation of the set of trajectories.

引用

页码：1212 / 1228

页数：17

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