Control system defined by some integral operator
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...
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AGH Univeristy of Science and Technology Press
2017-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol37/2/art/opuscula_math_3713.pdf |
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doaj-be2709f2f2dc4835a94f329e50ee1df52020-11-25T00:20:18ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742017-01-01372313325http://dx.doi.org/10.7494/OpMath.2017.37.2.3133713Control system defined by some integral operatorMarek Majewski0Department of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, PolandIn 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.http://www.opuscula.agh.edu.pl/vol37/2/art/opuscula_math_3713.pdfVolterra equationimplicit function theoremsensitivity |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Marek Majewski |
| spellingShingle |
Marek Majewski Control system defined by some integral operator Opuscula Mathematica Volterra equation implicit function theorem sensitivity |
| author_facet |
Marek Majewski |
| author_sort |
Marek Majewski |
| title |
Control system defined by some integral operator |
| title_short |
Control system defined by some integral operator |
| title_full |
Control system defined by some integral operator |
| title_fullStr |
Control system defined by some integral operator |
| title_full_unstemmed |
Control system defined by some integral operator |
| title_sort |
control system defined by some integral operator |
| publisher |
AGH Univeristy of Science and Technology Press |
| series |
Opuscula Mathematica |
| issn |
1232-9274 |
| publishDate |
2017-01-01 |
| description |
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. |
| topic |
Volterra equation implicit function theorem sensitivity |
| url |
http://www.opuscula.agh.edu.pl/vol37/2/art/opuscula_math_3713.pdf |
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AT marekmajewski controlsystemdefinedbysomeintegraloperator |
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1725368705419837440 |