A hamiltonian formulation and a direct numerical scheme for fractional optimal control problems

JVC/Journal of Vibration and Control

Volumn 13, Issue 9-10, 2007, Pages 1269-1281

  Agrawal, Om P ^a   Baleanu, Dumitru ^b  

^a Southern Illinois University Carbondale   (United States)

^b CANKAYA UNIVERSITY   (Turkey)

Author keywords

Fractional calculus; Fractional Euler Lagrange equations; Fractional optimal control; Riemann Liouville fractional derivatives

Indexed keywords

ALGEBRA; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; DYNAMICS; ERROR ANALYSIS; EULER EQUATIONS; LAGRANGE MULTIPLIERS; OPTIMAL CONTROL SYSTEMS;

FRACTIONAL CALCULUS; FRACTIONAL EULER LAGRANGE EQUATIONS; FRACTIONAL OPTIMAL CONTROLS; RIEMANN LIOUVILLE FRACTIONAL DERIVATIVES;

HAMILTONIANS;

EID: 34748901185     PISSN: 10775463     EISSN: 17412986     Source Type: Journal    
DOI: 10.1177/1077546307077467     Document Type: Article

References (23)

1. Agrawal, O.P., 1989, " General formulation for the numerical solution of optimal control problems " International Journal of Control 50 (2). 627 - 638.
2. Agrawal, O.P., 2001, " A new Lagrangian and a new Lagrange equation of motion for fractionally damped systems, " Journal of Applied Mechanics 68, 339-341. (Also in Proceedings of the ASME-IMECE 1999, Nashville, TN, November 14-19, 1999 ).
3. Agrawal, O.P., 2002, " Formulation of Euler-Lagrange equations for fractional variational problems, " Journal of Mathematical Analysis and Applications 272, 368 - 379.
4. Agrawal, O.P., 2004, " A general formulation and solution scheme for fractional optimal control problems " Nonlinear Dynamics 38, 323 - 337.
5. Agrawal, O.P., 2005, " A general scheme for stochastic analysis of fractional optimal control problems, " in Fractional Differentiation and Its Applications, A. L. Mahaute, J. A. T. Machado, J. C. Trigeassou, and J. Sabatier (eds), Books on Demand, Germany, pp. 615 - 624.
6. Baleanu, D., 2004, " About metafluid dynamics, " Czechoslovak Journal of Physics 54, 1165 - 1170.
7. Baleanu, D., 2006, " Fractional Hamiltonian analysis of irregular systems, " Signal Processing 86 (10). 2632 - 2636.
8. Baleanu, D. and Avkar, T., 2004, " Lagrangians with linear velocities within Riemann-Liouville fractional derivatives, " Nuovo Cimento B 119, 73 - 79.
9. Baleanu, D. and Muslih, S.I., 2005, " Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives " Physica Scripta 72, 119 - 123.
10. Bryson Jr, A.E. and Ho. Y.C., 1975, Applied Optimal Control: Optimization, Estimation, and Control, Blaisdell Publishing Company, Waltham, MA.
11. Dreisigmeyer, D.W. and Young, P.M., 2003, " Nonconservative Lagrangian mechanics: A generalized function approach, " Journal of Physics A: Mathematical and General 36, 8297 - 8310.
12. Dreisigmeyer, D.W. and Young, P.M., 2004, " Extending Bauer's corollary to fractional derivatives, " Journal of Physics A: Mathematical and General 37, 117 - 121.
13. Gregory, J. and Lin, C., 1992, Constrained Optimization in the Calculus of Variations and Optimal Control Theory, Van Nostrand-Reinhold, New York.
14. Hestenes, M.R., 1966, Calculus of Variations and Optimal Control Theory, Wiley, New York.
15. Klimek, M., 2001, " Fractional sequential mechanics model with symmetric fractional derivatives " Czechoslovak Journal of Physics 51, 1348 - 1354.
16. Klimek, M., 2002, " Stationary conservation laws for fractional differential equations with variable coefficients, " Journal of Physics A: Mathematical and General 35, 6675 - 6693.
17. Muslih, S.I. and Baleanu, D., 2005 a, " Hamiltonian formulation of systems with linear velocities within Riemann- Liouville fractional derivative, " Journal of Mathematical Analysis and Applications 304, 599 - 606.
18. Muslih, S.I. and Baleanu, D., 2005 b, " Formulation of Hamiltonian equations for fractional variational problems " Czechoslovak Journal of Physics 55, 633 - 642.
19. Muslih, S.I., Baleanu, D., and Rabei, E., 2006 " Hamiltonian formulation of classical fields within Riemann- Liouville fractional derivatives " Physica Scripta 73, 436 - 438.
20. Podlubny, I., 1999, Fractional Differential Equations, Academic Press, New York.
21. Riewe, F., 1996, " Nonconservative Lagrangian and Hamiltonian mechanics, " Physical Review E,53 (2). 1890 - 1899.
22. Riewe, R., 1997, " Mechanics with fractional derivatives " Physical Review E55 (3). 3582 - 3592.
23. Tarasov, V.E. and Zaslavsky, G.M., 2005, " Fractional Ginzburg-Landau equation for fractal media " Physica A - Statistical Mechanics and Its Applications 354, 249 - 261.