Optimal control problem investigation for linear time-invariant systems of fractional order with lumped parameters described by equations with Riemann-Liouville derivative
type: Item
instance of: scholarly article
title: Optimal control problem investigation for linear time-invariant systems of fractional order with lumped parameters described by equations with Riemann-Liouville derivative
zbMATH Open document ID: 1347.49006
DOI: 10.1155/2016/4873083
author: V. A. Kubyshkin
author: S. S. Postnov
published in: Journal of Control Science and Engineering
publication date: 2016-10-20T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 49J30
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 6641353
zbMATH Keywords: linear time-invariant systems of fractional order
zbMATH Keywords: Riemann-Liouville derivative
Wikidata QID: Q59126054
describes a project that uses: quadgk
describes a project that uses: quadva
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/4873083
OpenAlex ID: W2403905583
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description: scientific article; zbMATH DE number 6641353