Control system defined by some integral operator

Opuscula Mathematica

Marek Majewski¹ 

[1] Department of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland;

关键词: Volterra equation;    implicit function theorem;    sensitivity;   

DOI  :  http://dx.doi.org/10.7494/OpMath.2017.37.2.313

来源: DOAJ

【 摘 要 】

In the paper we consider a nonlinear control system governed by the Volterra integral operator. Using a version of the global implicit function theorem we prove that the control system under consideration is well-posed and robust, i.e. for any admissible control \(u\) there exists a uniquely defined trajectory \(x_{u}\) which continuously depends on control \(u\) and the operator \(u\mapsto x_{u}\) is continuously differentiable. The novelty of this paper is, among others, the application of the Bielecki norm in the space of solutions which allows us to weaken standard assumptions.

【 授权许可】

Unknown