On the Properties of the Set of Trajectories of the Control System Described by Urysohn Type Integral Equation

Year 2023, , 1772 - 1781, 24.10.2023

Nesir Hüseyin

https://doi.org/10.29130/dubited.1186317

Abstract

In this study, the properties of the set of trajectories of the control system described by Urysohn type integral equation are studied. It is assumed that the control functions satisfy integral constraint. It is proved that the set of trajectories is Lipschitz continuous with respect to the parameter which characterizes the bound of control resource. An upper estimation for the diameter of the set of trajectories is given. Robustness of the system’s trajectory with respect to the remaining control resource is discussed.

Keywords

Nonlinear integral equation, Control system, Integral constraint, Set of trajectories, Robustness

Urysohn Tür İntegral Denklem ile Verilen Kontrol Sistemin Yörüngeler Kümesinin Özellikleri Üzerine

Abstract

Bu çalışmada Urysohn tür integral denklem ile verilen control systemin yörüngeler kümesinin özellikleri incelenmektedir. Kontrol fonksiyonların integral kısıtı sağladığı varsayılmaktadır. Yörüngeler kümesinin control kaynağın sınırını belirleyen parametreye göre Lipschitz sürekli olduğu kanıtlanmıştır. Yörüngeler kümesinin çapı için bir üst değerlendirme verilmiştir. Sistemin yörüngesinin, kalan control kaynağına göre robastlığı tartışılmaktadır.

Keywords

Doğrusal olmayan integral denklem, Kontrol sistem, İntegral kısıtlama, Yörüngeler kümesi, Robastlık

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