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ISSN : 1226-0657

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Vol.30 No.2
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On the Robustness of Continuous Trajectories of the Nonlinear Control System Described by an Integral Equation

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Anar Huseyin
Nesir, H. , & Anar, H. (2023). On the Robustness of Continuous Trajectories of the Nonlinear Control System Described by an Integral Equation. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 30(2), 191-201, https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.2.191
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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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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