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

Trudy Inst. Mat. i Mekh. UrO RAN, 2022 Volume 28, Number 3, Pages 274–284 (Mi timm1942)

This article is cited in 1 paper

On the properties of the set of trajectories of nonlinear control systems with integral constraints on the control functions

N. Huseyina, A. Huseyina, Kh. G. Guseinovb

a Sivas Cumhuriyet University
b Eskisehir Technical University

Abstract: The control systems described by nonlinear differential equations and integral constraints on the control functions are studied. Admissible control functions are chosen from a closed ball of the space $L_p,$ $p\in (1,\infty]$, with radius $r$ and centered at the origin. It is proved that the set of trajectories of the system is continuous at $p=\infty$ with respect to the Hausdorff pseudometric. It is shown that every trajectory is robust with respect to the fast and full consumption of the remaining control resource which implies that to achieve the desired result, it is advisable to spend the available control resource in small portions. This allows to prove that every trajectory can be approximated by the trajectory, generated by full consumption of the control resource.

Keywords: nonlinear control system; set of trajectories; integral constraint; geometric constraint; Hausdorff continuity; robustness.

MSC: 93C10, 93B03, 93B35

Received: 10.05.2022
Revised: 09.06.2022
Accepted: 13.06.2022

Language: English

DOI: 10.21538/0134-4889-2022-28-3-274-284



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