Optimal Control Problem Investigation for Linear Time-Invariant Systems of Fractional Order with Lumped Parameters Described by Equations with Riemann-Liouville Derivative
Joint Authors
Kubyshkin, V. A.
Postnov, S. S.
Source
Journal of Control Science and Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-05-26
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Electronic engineering
Information Technology and Computer Science
Abstract EN
This paper studies two optimal control problems for linear time-invariant systems of fractional order with lumped parameters whose dynamics is described by equations which contain Riemann-Liouville derivative.
The first problem is to find control with minimal norm and the second one is to find control with minimal control time at given restriction for control norm.
The problem setting with nonlocal initial conditions is considered which differs from other known settings for integer-order systems and fractional-order systems described in terms of equations with Caputo derivative.
Admissible controls are allowed to belong to the class of functions which are p -integrable on half segment.
The basic investigation approach is the moment method.
The correctness and solvability of moment problem are validated for considered problem setting for the system of arbitrary dimension.
It is shown that corresponding conditions are analogous to those derived for systems which are described in terms of equations with Caputo derivative.
For several particular cases of one- and two-dimensional systems the posed problems are solved explicitly.
The dependencies of basic values from derivative index and control time are analyzed.
The comparison is performed of obtained results with known results for analogous integer-order systems and fractional-order systems which are described by equations with Caputo derivative.
American Psychological Association (APA)
Kubyshkin, V. A.& Postnov, S. S.. 2016. Optimal Control Problem Investigation for Linear Time-Invariant Systems of Fractional Order with Lumped Parameters Described by Equations with Riemann-Liouville Derivative. Journal of Control Science and Engineering،Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1107897
Modern Language Association (MLA)
Kubyshkin, V. A.& Postnov, S. S.. Optimal Control Problem Investigation for Linear Time-Invariant Systems of Fractional Order with Lumped Parameters Described by Equations with Riemann-Liouville Derivative. Journal of Control Science and Engineering No. 2016 (2016), pp.1-12.
https://search.emarefa.net/detail/BIM-1107897
American Medical Association (AMA)
Kubyshkin, V. A.& Postnov, S. S.. Optimal Control Problem Investigation for Linear Time-Invariant Systems of Fractional Order with Lumped Parameters Described by Equations with Riemann-Liouville Derivative. Journal of Control Science and Engineering. 2016. Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1107897
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1107897