Existence of optimal solutions to lagrange problem for a fractional nonlinear control system with riemann-liouville derivative

Dariusz Idczak; Rafał Kamocki

doi:10.3934/mcrf.2017016

Article Contents

2017, Volume 7, Issue 3: 449-464. Doi: 10.3934/mcrf.2017016

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Existence of optimal solutions to lagrange problem for a fractional nonlinear control system with riemann-liouville derivative

Dariusz Idczak and
Rafał Kamocki^,

Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

* Corresponding author: Rafał Kamocki
* Corresponding author: Rafał Kamocki

Received: February 2016

Revised: November 2016

Published: October 2017

The project was financed with funds of National Science Centre, granted on the basis of decision DEC-2011/01/B/ST7/03426.

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Abstract

In the paper, a nonlinear control system containing the Riemann-Liouville derivative of order $α∈(0, 1)$ with a nonlinear integral performance index is studied. We discuss the existence of optimal solutions to such problem under some convexity assumption. Our study relies on the implicit function theorem for multivalued mappings.

Keywords:

Riemann-Liouville integrals and derivatives,
fractional control systems,
existence of optimal solutions.

Mathematics Subject Classification: Primary: 26A33; Secondary: 49J15.

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References

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