Fractional optimal control within caputo's derivative

Proceedings of the ASME Design Engineering Technical Conference

Volumn 3, Issue PARTS A AND B, 2011, Pages 353-360

  Biswas, Raj Kumar ^a   Sen, Siddhartha ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

Caputo fractional derivatives; Fractional order system; Optimal control; State space

Indexed keywords

ARBITRARY ORDER; CAPUTO FRACTIONAL DERIVATIVES; DYNAMIC CONSTRAINTS; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL-ORDER SYSTEMS; NUMERICAL EXAMPLE; NUMERICAL TECHNIQUES; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS; PERFORMANCE INDICES; STATE-SPACE;

DESIGN; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); OPTIMAL CONTROL SYSTEMS;

CONTROL;

EID: 84863591407     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC2011-48045     Document Type: Conference Paper

References (41)

1. Sage, A.P., and White, III, C.C., 1977, Optimum Systems Control, Prentice-Hall, Englewood Cliffs, New Jersey.
2. Oldham, K.B., and Spanier, J., 1974, The Fractional Calculus, Academic Press, New York.
3. Miller, K.S., and Ross, B., 1993, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York.
4. Samko, S.G., Kilbas, A.A., and Marichev, O.I., 1993, Fractional Integrals and Derivatives-Theory and Applications, Gordon and Breach, Longhorne, Pennsylvania.
5. Podlubny, I., 1999, Fractional Differential Equations, Academic Press, New York.
6. Magin, R.L., 2004, "Fractional Calculus in Bioengineering," Parts 1-3, Crit. Rev. Biomed. Eng., 32 (1), pp. 1-377.
7. Agrawal, O.P., Machado, J.A.T., and Sabatier, J., 2004, Nonlinear Dynamics, Special Issue: Fractional Derivatives and Their Applications, Kluwer Academic Publishers.
8. Caputo, M., 1969, Elasticita e Dissipacione, Zanichelli, Bologna.
9. Nonnenmacher, T.F., and Glöckle, W.G., 1991, "A Fractional Model for Mechanical Stress Relaxation," Philosophical Magazine Letters, 64(2), pp. 89-93.
10. Friedrich, C., 1991, "Relaxation and Retardation Functions of the Maxwell Model with Fractional Derivatives," Rehol. Acta, 30, pp. 151-158.
11. Zamani, M., Karimi-Ghartemani, M., and Sadati, N., 2007, "FOPID Controller Design for Robust Performance Using Particle Swarm Optimization," Journal of Fractional Calculus and Applied Analysis, 10 (2), pp. 169-188.
12. Agrawal, O.P., 2008, "Fractional Optimal Control of a Distributed System Using Eigenfunctions," Journal of Computational and Nonlinear Dynamics, 3(2), p. 021204.
13. Riewe, F., 1996, "Nonconservative Lagrangian and Hamiltonian Mechanics," Physical Review E, 53, pp. 1890-1899.
14. Riewe, F., 1997, "Mechanics with Fractional Derivatives," Physical Review E, 55, pp. 3582-3592.
15. Tarasov, V.E., and Zaslavsky, G.M., 2005, "Fractional Ginzburg-Landau Equation for Fractal Media," Physica A: Statistical Mechanics and its Applications, 354, pp. 249-261.
16. Kilmek, M., 2002, "Lagrangean and Hamiltonian Fractional Sequential Mechanics," Czechoslovak Journal of Physics, 52(11), pp. 1247-1253.
17. Kilmek, M., 2001, "Fractional Sequential Mechanics-Models with Symmetric Fractional Derivative," Czechoslovak Journal of Physics, 51(12), pp. 1348-1354.
18. Rabei, E.M., Ajlouni, A.-W., and Ghassib, H.B., 2006, "Quantization of Brownian Motion," International Journal of Theoretical Physics, 45(9), pp. 1613-1623.
19. Baleanu, D., and Avkar, T., 2004, "Lagrangians with Linear Velocities within Riemann-Liouville Fractional Derivatives," Nuovo Cimento Della Societa Italiana Di Fisica B - General Physics Relativity Astronomy and Mathematical Physics and Methods, 119, pp. 73-79.
20. Muslih, S.I., and Baleanu, D., 2005, "Hamiltonian Formulation of Systems with Linear Velocities within Riemann-Liouville Fractional Derivatives," Journal of Mathematical Analysis and Applications, 304, pp. 599-606.
21. Muslih, S.I., and Baleanu, D., 2005, "Formulation of Hamiltonian Equations for Fractional Variational Problems," Czechoslovak Journal of Physics, 55, pp. 633-642.
22. Baleanu, D., 2009, "Fractional Variational Principles in Action," Physica Scripta, T136, p. 014006.
23. Baleanu, D., 2008, "Fractional Constrained Systems and Caputo Derivatives," Journal of Computational and Nonlinear Dynamics, 3(2), p. 021102.
24. Agrawal, O.P., 2002, "Formulation of Euler-Lagrange Equations for Fractional Variational Problems," Mathematical Analysis and Applications, 272, pp. 368-379.
25. Agrawal, O.P., 2004, "A General Formulation and Solution Scheme for Fractional Optimal Control Problems," Nonlinear Dynamics, 38, pp. 323-337.
26. Agrawal, O.P., 2007, "A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems," Journal of Vibration and Control, 13, pp. 1269-1281.
27. Baleanu, D., Defterli, O., and Agrawal, O.P., 2009, "A Central Difference Numerical Scheme for Fractional Optimal Control Problems," Journal of Vibration and Control, 15, pp. 583-597.
28. Biswas, R.K., and Sen, S., 2009, "Numerical Method for Solving Fractional Optimal Control Problems," ASME Paper No. DETC2009-87008, Proceedings of IDETC/CIE 2009, ASME, California.
29. Biswas, R.K., and Sen, S., 2011, "Fractional Optimal Control Problems with Specified Final Time," Journal of Computational and Nonlinear Dynamics, 6(2), p. 021009.
30. Tricaud, C., and Chen, Y.Q., 2010, "An Approximate Method for Numerically Solving Fractional Order Optimal Control Problems of General Form," Computers and Mathematics with Applications, 59, pp. 1644-1655.
31. Biswas, R.K., and Sen, S., 2010, "Fractional Optimal Control Problems: A Pseudo-State-Space Approach," Journal of Vibration and Control (in press), doi: 10.1177/1077546310373618.
32. Özdemir, N., Karadeniz, D., and İskender, B.B., 2009, "Fractional Optimal Control Problem of a Distributed System in Cylindrical Coordinates," Physics Letters A, 373(2), pp. 221-226.
33. Özdemir, N., Agrawal, O.P., Karadeniz, D., and İskender, B.B., 2009, "Fractional Optimal Control Problem of an Axis-Symmetric Diffusion-Wave Propagation," Physica Scripta, T136, p. 014024.
34. Tricaud, C., and Chen, Y.Q., 2010, "Time-Optimal Control of Systems with Fractional Dynamics," International Journal of Differential Equations, 2010, p. 461048.
35. Bagley, R.L., and Calico, R.A., 1991, "Fractional Order State Equations for the Control of Viscoelastic Structures," Journal of Guidance, Control, and Dynamics, 14(2), pp. 304-311.
36. Padovan, J., and Sawicki, J.T., 1997, "Diophantine Type Fractional Derivative Representation of Structural Dynamics," Computational Mechanics, 19(5), pp. 335-340.
37. Raynaud, H.-F., and Zerganoh, A., 2000, "State Space Representation for Fractional Order Controllers," Automatica, 36(7), pp. 1017-1021.
38. Lixia, Y., and Agrawal, O.P., 2002, "A Numerical Scheme for Dynamic Systems Containing Fractional Derivatives," Journal of Vibration and Acoustics, 124, pp. 321-324.
39. Djamah, T., Mansouri, R., Djennoune, S., and Bettayeb, M., 2008, "Optimal Low Order Model Identification of Fractional Dynamic Systems," Applied Mathematics and Computation, 206, pp. 543-554.
40. Kuroda, M., 2008, "Formulation of A State Equation Including Fractional Order State Vectors," Journal of Computational and Nonlinear Dynamics, 3(2), p. 21202.
41. Hartely, T.T., and Lorenzo, C.F., 2002, "Dynamics and Control of Initialized Fractional Order Systems," Nonlinear Dynamics, 29, pp. 201-233.