Optimality conditions and a solution scheme for fractional optimal control problems

Structural and Multidisciplinary Optimization

Volumn 38, Issue 6, 2009, Pages 571-581

  Jelicic, Zoran D ^a   Petrovacki, Nebojsa ^b  

^a UNIVERSITY OF NOVI SAD   (Serbia)

^b 3255 Weat Stetson Avenue   (United States)

Author keywords

Expansion formula for fractional derivative; Fractional order systems; Optimal control

Indexed keywords

EXPANSION FORMULA; EXPANSION FORMULA FOR FRACTIONAL DERIVATIVE; FRACTIONAL DERIVATIVES; FRACTIONAL ORDER; FRACTIONAL ORDER SYSTEMS; INTEGER ORDER; NEW SOLUTIONS; OPTIMAL CONTROL; OPTIMAL CONTROL PROBLEM; OPTIMALITY; OPTIMALITY CONDITIONS;

DERIVATIVES; DIFFERENTIAL EQUATIONS; OPTIMIZATION;

OPTIMAL CONTROL SYSTEMS;

EID: 67649553786     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-008-0307-7     Document Type: Article

References (19)

1. OP Agrawal 2002 Formulation of Euler-Lagrange equations for fractional variational problems J Math Anal Appl 272 368 379
2. OP Agrawal 2004 A general formulation and solution for fractional optimal control problems Nonlinear Dyn 38 323 337 (Pubitemid 40400624)
3. OP Agrawal 2006 Fractional variational calculus and the transversality conditions J Phys A Math Gen 39 10375 10384 (Pubitemid 44183559)
4. OP Agrawal 2008 A genaral finite element formulatiuon for fractional variational problems J Math Anal Appl 337 1 12
5. TM Atanackovic B Stankovic 2004 An expansion formula for fractional derivatives and its applications Fractional Calculus and Applied Analysis 7 3 365 378
6. TM Atanackovic B Stankovic 2007 On a class of differential equations with left and right fractional derivatives ZAMM, Z Angew Math Mech 87 537 546
7. TM Atanackovic B Stankovic 2007 On a differential equation with left and right fractional derivatives Fractional Calculus Applied Analysis 10 138 150
8. Atanackovic TM, Konjik S, Pilipovic S (2008) Variational problems with fractional derivatives: Euler-Lagrange equations. J Phys A Math Theor 41. doi: 10.1088/1751-8113/41/9/095201
9. D Baleanu T Akvar 2004 Lagragians with linear velocities within Riemann-Liouville fractional derivatives Nuovo Cimento B 119 73 79 (Pubitemid 39057448)
10. Jelicic ZD, Petrovacki ND (2007) Fractional derivative model of EDFA with ASE. In: SIAM conference on control and its applications, San Francisco June 2007
11. Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, North-Holland Mathematics Studies 204
12. Petrovacki N, Jelicic ZD (2006) Optimal transient response of erbium-doped fiber amplifiers. In: IEEE international conference on numerical simulation of semiconductor optoelectronic devices. NUSOD '06, Singapore, Sept 2006
13. EM Rabei KI Nawafleh RS Hijjawi SI Muslih D Baleanu 2007 The Hamilton formalism with fractional derivatives J Math Anal Appl 327 891 897 (Pubitemid 44742791)
14. S Sh Rekhviashvili 2004 The lagrange formalism with fractional derivatives in problems of mechanics Tech Phys Lett 30 33 37
15. P Ruge C Trinks 2004 Consistent modelling of infinite beams by fractional dynamics Nonlinear Dyn 38 267 284 (Pubitemid 40400620)
16. Samko SG, Kilbas AA, Marichev OI (1993) Fractional integrals and derivatives. Gordon and Breach Science Publishers
17. Vujanovic BD, Atanackovic TM (2004) An introduction to modern variational principles of mechanics. Birkhäuser, Boston
18. Yuan L, Agrawal OP (1998) A numerical scheme for dynamic systems containing fractional derivatives. In: Proceedings of DETC'98 1998 ASME design engineering technical conferences, Atlanta Georgia September 13-16
19. L Yuan OP Agrawal 2002 A numerical scheme for dynamic systems containing fractional derivatives J Vib Acoust 124 321 324 (Pubitemid 35202698)