An Efficient Approximation Technique for Solving a Class of Fractional Optimal Control Problems

An Efficient Approximation Technique for Solving a Class of Fractional Optimal Control Problems In this paper, we discuss a class of fractional optimal control problems, where the system dynamical constraint comprises a combination of classical and fractional derivatives. The necessary optimality conditions are derived and shown that the conditions are sufficient under certain assumptions. Additionally, we design a well-organized algorithm to obtain the numerical solution of the proposed problem by exercising Laguerre polynomials. The key motive associated with the present approach is to convert the concerned fractional optimal control problem to an equivalent standard quadratic programming problem with linear equality constraints. Given examples illustrate the computational technique of the method together with its efficiency and accuracy. Graphical representations are provided to analyze the performance of the state and control variables for distinct prescribed fractions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Optimization Theory and Applications Springer Journals

An Efficient Approximation Technique for Solving a Class of Fractional Optimal Control Problems

Loading next page...
 
/lp/springer_journal/an-efficient-approximation-technique-for-solving-a-class-of-fractional-ezE05dWp9C
Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory
ISSN
0022-3239
eISSN
1573-2878
D.O.I.
10.1007/s10957-017-1143-y
Publisher site
See Article on Publisher Site

Abstract

In this paper, we discuss a class of fractional optimal control problems, where the system dynamical constraint comprises a combination of classical and fractional derivatives. The necessary optimality conditions are derived and shown that the conditions are sufficient under certain assumptions. Additionally, we design a well-organized algorithm to obtain the numerical solution of the proposed problem by exercising Laguerre polynomials. The key motive associated with the present approach is to convert the concerned fractional optimal control problem to an equivalent standard quadratic programming problem with linear equality constraints. Given examples illustrate the computational technique of the method together with its efficiency and accuracy. Graphical representations are provided to analyze the performance of the state and control variables for distinct prescribed fractions.

Journal

Journal of Optimization Theory and ApplicationsSpringer Journals

Published: Jul 20, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off