A constrained dynamic optimization problem of a fractional order system with fixed final time has been considered here. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems. The dynamic constraint is described by a fractional differential equation of order less than 1, and the fractional derivative is defined in terms of Riemann–Liouville. The performance index includes the terminal cost function in addition to the integral cost function. A general transversility condition in addition to the optimal conditions has been obtained using the Hamiltonian approach. Both the specified and unspecified final state cases have been considered. A numerical technique using the Grünwald–Letnikov definition is used to solve the resulting equations obtained from the formulation. Numerical examples are provided to show the effectiveness of the formulation and solution scheme. It has been observed that the numerical solutions approach the analytical solutions as the order of the fractional derivatives approach 1.
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April 2011
Research Papers
Fractional Optimal Control Problems With Specified Final Time Available to Purchase
Raj Kumar Biswas,
Raj Kumar Biswas
Department of Electrical Engineering,
e-mail: [email protected]
Indian Institute of Technology
, Kharagpur 721302, India
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Siddhartha Sen
Siddhartha Sen
Department of Electrical Engineering,
Indian Institute of Technology
, Kharagpur 721302, India
Search for other works by this author on:
Raj Kumar Biswas
Department of Electrical Engineering,
Indian Institute of Technology
, Kharagpur 721302, Indiae-mail: [email protected]
Siddhartha Sen
Department of Electrical Engineering,
Indian Institute of Technology
, Kharagpur 721302, IndiaJ. Comput. Nonlinear Dynam. Apr 2011, 6(2): 021009 (6 pages)
Published Online: October 28, 2010
Article history
Received:
December 17, 2009
Revised:
July 29, 2010
Online:
October 28, 2010
Published:
October 28, 2010
Citation
Biswas, R. K., and Sen, S. (October 28, 2010). "Fractional Optimal Control Problems With Specified Final Time." ASME. J. Comput. Nonlinear Dynam. April 2011; 6(2): 021009. https://doi.org/10.1115/1.4002508
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