The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems

JVC/Journal of Vibration and Control

Volumn 17, Issue 13, 2011, Pages 2059-2065

  Yousefi, S A ^a   Lotfi, A ^a   Dehghan, M ^b  

^a SHAHID BEHESHTI UNIVERSITY   (Iran)

^b AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Collocation method; fractional optimal control problems (FOCPs); Legendre multiwavelet technique; optimal control

Indexed keywords

ALGEBRAIC SYSTEM; APPROXIMATE SOLUTION; COLLOCATION METHOD; EXACT SOLUTION; LEGENDRE; MULTIWAVELET; NUMERICAL RESULTS; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS;

ALGEBRA; CONTROL; OPTIMIZATION;

NUMERICAL METHODS;

EID: 80155171902     PISSN: 10775463     EISSN: 17412986     Source Type: Journal    
DOI: 10.1177/1077546311399950     Document Type: Article

References (31)

1. Agrawal OP. A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dynamics. 2004 ; 38: 323-337 (Pubitemid 40400624) (Pubitemid 40400624)
2. Agrawal OP, Baleanu D. Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems. Journal of Vibration and Control. 2007 ; 13: 1269-1281 (Pubitemid 47482812) (Pubitemid 47482812)
3. Baleanu D. About fractional quantization and fractional variational principles. Communications in Non-linear Science and Numerical Simulation. 2009a ; 14: 2520-2523
4. Baleanu D. Fractional variational principles in action. Physica Scripta. 2009b ; 136: 014006-014006
5. Beylkin G, Coifman R, Rokhlinn V. Fast wavelet transforms and numerical algorithms. Communications in Pure and Applied Mathematics. 1991 ; 44: 141-183
6. Chawla S, Lenhart S. Application of optimal control theory to bioremediation. Journal of Computational and Applied Mathematics. 2000 ; 114: 81-102 (Pubitemid 30132494) (Pubitemid 30132494)
7. Chui CK Wavelets: A Mathematical Tool for Signal Analysis. Philadelphia, PA: SIAM ; 1997 :
8. Defterli O. A numerical scheme for two dimensional optimal-control problems with memory effect. Computers and Mathematics with Applications. 2010 ; 59: 1630-1636
9. Dehghan M, Manafian Herris J and Saadatmandi A (2010) Application of semi-analytic methods for the Fitzhugh-Nagumo equation which models the transmission of nerve impulses. Mathematical Methods in the Applied Sciences 33: 1384-1398.
10. Dehghan M, Manafian J, Saadatmandi A. Solving non-linear fractional partial differential equations using the homotopy analysis method. Numerical Methods for Partial Differential Equations. 2010a ; 26: 448-479
11. Dehghan M, Manafian J, Saadatmandi A. The solution of the linear fractional partial differential equations using the homotopy analysis method. Zeitschrift für Naturforschung. 2010b ; 65a: 935-945
12. Dehghan M, Shakeri F. Solution of an integro-differential equation arising in oscillating magnetic fields using He's homotopy perturbation method. Progress In Electromagnetics Research, PIER. 2008 ; 78: 361-376
13. Dehghan M, Shakeri F. Solution of parabolic integro-differential equations arising in heat conduction in materials with memory via He's variational iteration technique. International Journal for Numerical Methods in Biomedical Engineering. 2010 ; 26: 705-715
14. Dehghan M, Salehi R. A seminumeric approach for solution of the eikonal partial differential equation and its applications. Numerical Methods for Partial Differential Equations. 2010 ; 26: 702-722
15. Dehghan M, Shakourifar M and Hamidi A (2009) The solution of linear and nonlinear systems of Volterra functional equations using Adomian-Pade technique. Chaos Solitons and Fractals 39: 2509-2521.
16. El-Borai Mahmoud M, El-Said El-Nadi K, El-Akabawy Eman G. On the Fractional optimal control. International Journal of Applied Mathematics and Mechanics. 2008 ; 4: 13-18
17. Gu JS, Jiang WS. The Haar wavelets operational matrix of integration. International Journal of Systems Science. 1996 ; 27: 623-628
18. Jafari Samimi A, Yousefi SA, Tehranchian AM. An application of optimal control theory in economics: optimal fiscal and monetary policies in Iran. Applied Mathematics and Computation. 2006 ; 172: 198-209 (Pubitemid 43132837) (Pubitemid 43132837)
19. Kilbas AA, Srivastava HM, Trujillo JJ Theory and Application of Fractional Differential Equations. Amsterdam: Elsevier ; 2006 :
20. Ming Q, Hwang C, Shih YP. The computation of wavelet-Galerkin approximation on a bounded interval. International Journal of Numerical Methods in Engineering. 1996 ; 39: 2921-2944 (Pubitemid 126648055) (Pubitemid 126648055)
21. Momani S, Noor MA. Numerical methods for fourth-order fractional integro-differential equations. Applied Mathematics and Computation. 2006 ; 182: 754-760 (Pubitemid 44716325) (Pubitemid 44716325)
22. Rabei EM, Nawafleh KI, Hijjawi RS, Muslih SI, Baleanu D. The Hamilton formalism with fractional derivatives. Journal of Mathematical Analysis and Applications. 2007 ; 327: 891-897 (Pubitemid 44742791) (Pubitemid 44742791)
23. Saadatmandi A, Dehghan M. The numerical solution of problems in calculus of variation using Chebyshev finite difference method. Physics Letters A. 2008 ; 372: 4037-4040
24. Saadatmandi A, Dehghan M. A new operational matrix for solving fractional-order differential equations. Computers and Mathematics with Applications. 2010 ; 59: 1326-1336
25. Saadatmandi A, Dehghan M. A Legendre collocation method for fractional integro-differential equations. Journal of Vibration and Control. 2011 ;:
26. Samko SG, Kilbas AA, Marichev OI Fractional Integrals and Derivatives Theory and Applications. New York: Gordon and Breach ; 1993 :
27. Sethi S, Thompson G Optimal Control Theory: Applications to Management Science and Economics. Dordrecht: Kluwer ; 2000 :
28. Tatari M, Dehghan M. Solution of problems in calculus of variations via He's variational iteration method. Physics Letters A. 2007 ; 362: 401-406
29. Tricaud C, Chen Y. An approximate method for numerically solving fractional order optimal control problems of general form. Computers and Mathematics with Applications. 2010 ; 59: 1644-1655
30. Wu JL. A wavelet operational method for solving fractional partial differential equations numerically. Applied Mathematics and Computation. 2009 ; 214: 31-40
31. Yousefi SA. Legendre multiwavelet Galerkin method for solving the hyperbolic telegraph equation. Numerical Methods for Partial Differential Equations. 2010 ; 26: 535-543