On the Robustness of Continuous Trajectories of the Nonlinear Control System Described by an Integral Equation

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2023, v.30 no.2, pp.191-201

https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.2.191

Nesir Huseyin (Department of Mathematics and Science Education, Sivas Cumhuriyet University)
Anar Huseyin (Department of Statistics and Computer Sciences, Sivas Cumhuriyet University)

Nesir Huseyin, & Anar Huseyin. (2023). ON THE ROBUSTNESS OF CONTINUOUS TRAJECTORIES OF THE NONLINEAR CONTROL SYSTEM DESCRIBED BY AN INTEGRAL EQUATION. 한국수학교육학회지시리즈B:순수및응용수학, 30(2), 191-201, https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.2.191

복사

Abstract

In this paper the control system described by Urysohn type integral equation is studied. It is assumed that control functions are integrally constrained. The trajectory of the system is defined as multivariable continuous function which satisfies the system's equation everywhere. It is shown that the set of trajectories is Lipschitz continuous with respect to the parameter which characterizes the bound of the control resource. An upper estimation for the diameter of the set of trajectories is obtained. The robustness of the trajectories with respect to the fast consumption of the remaining control resource is discussed. It is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the control resource.

keywords: Urysohn integral equation, nonlinear control system, integral constraint, robustness

바로가기메뉴

논문 상세

Vol.30 No.2

ON THE ROBUSTNESS OF CONTINUOUS TRAJECTORIES OF THE NONLINEAR CONTROL SYSTEM DESCRIBED BY AN INTEGRAL EQUATION

On the Robustness of Continuous Trajectories of the Nonlinear Control System Described by an Integral Equation

Abstract

한국수학교육학회지시리즈B:순수및응용수학