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Fractional Optimal Control Within Caputo’s Derivative

[+] Author Affiliations
Raj Kumar Biswas, Siddhartha Sen

Indian Institute of Technology, Kharagpur, WB, India

Paper No. DETC2011-48045, pp. 353-360; 8 pages
doi:10.1115/DETC2011-48045
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5480-8
  • Copyright © 2011 by ASME

abstract

A general formulation and solution of fractional optimal control problems (FOCPs) in terms of Caputo fractional derivatives (CFDs) of arbitrary order have been considered in this paper. The performance index (PI) of a FOCP is considered as a function of both the state and control. The dynamic constraint is expressed by a fractional differential equation (FDE) of arbitrary order. A general pseudo-state-space representation of the FDE is presented and based on that, FOCP has been developed. A numerical technique based on Grünwald-Letnikov (G-L) approximation of the FDs is used for solving the resulting equations. Numerical example is presented to show the effectiveness of the formulation and solution scheme.

Copyright © 2011 by ASME
Topics: Optimal control

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