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April  2014, 10(2): 363-381. doi: 10.3934/jimo.2014.10.363

Fractional order optimal control problems with free terminal time

Shakoor Pooseh 1, , Ricardo Almeida 1, and  Delfim F. M. Torres 1,

1. 

CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal, Portugal, Portugal

Received  December 2012 Revised  July 2013 Published  October 2013

We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal-time triplet to be optimal are obtained. Situations with constraints present at the end time are also considered. Under appropriate assumptions, it is shown that the obtained necessary optimality conditions become sufficient. Numerical methods to solve the problems are presented, and some computational simulations are discussed in detail.
Keywords: free-time problem, fractional calculus, fractional optimal control, numerical approximations., Optimization and control.
Mathematics Subject Classification: Primary: 26A33, 33F05; Secondary: 49K1.
Citation: Shakoor Pooseh, Ricardo Almeida, Delfim F. M. Torres. Fractional order optimal control problems with free terminal time. Journal of Industrial & Management Optimization, 2014, 10 (2) : 363-381. doi: 10.3934/jimo.2014.10.363
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show all references

References:
[1]

Nonlinear Dynam., 38 (2004), 323-337. doi: 10.1007/s11071-004-3764-6.  Google Scholar

[2]

J. Phys. A, 40 (2007), 6287-6303. doi: 10.1088/1751-8113/40/24/003.  Google Scholar

[3]

J. Vib. Control, 14 (2008), 1291-1299. doi: 10.1177/1077546307087451.  Google Scholar

[4]

J. Vib. Control, 16 (2010), 1967-1976. doi: 10.1177/1077546309353361.  Google Scholar

[5]

Mech. Res. Comm., 35 (2008), 429-438. doi: 10.1016/j.mechrescom.2008.05.003.  Google Scholar

[6]

in Spectral and Evolution Problems, Vol. 10 (Sevastopol, 1999), Natl. Taurida Univ. "V. Vernadsky," Simferopol', 2000, 147-155.  Google Scholar

[7]

McGraw-Hill, Inc., Singapore, 1992. Google Scholar

[8]

Int. Math. Forum, 3 (2008), 479-493.  Google Scholar

[9]

Nonlinear Dynam., 53 (2008), 215-222. doi: 10.1007/s11071-007-9309-z.  Google Scholar

[10]

Struct. Multidiscip. Optim., 38 (2009), 571-581. doi: 10.1007/s00158-008-0307-7.  Google Scholar

[11]

North-Holland Mathematics Studies, 204, Elsevier Science B. V., Amsterdam, 2006.  Google Scholar

[12]

Prentice-Hall Inc., Englewood Cliffs, NJ, 1970. Google Scholar

[13]

Pac. J. Optim., 7 (2011), 63-81.  Google Scholar

[14]

Automatica J. IFAC, 48 (2012), 2116-2129. doi: 10.1016/j.automatica.2012.06.055.  Google Scholar

[15]

J. Ind. Manag. Optim., 8 (2012), 19-40. doi: 10.3934/jimo.2012.8.19.  Google Scholar

[16]

Imperial College Press, London, 2012.  Google Scholar

[17]

A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1993.  Google Scholar

[18]

Carpathian J. Math., 26 (2010), 210-221.  Google Scholar

[19]

Signal Process., 91 (2011), 379-385. doi: 10.1016/j.sigpro.2010.07.016.  Google Scholar

[20]

Numer. Funct. Anal. Optim., 33 (2012), 301-319. doi: 10.1080/01630563.2011.647197.  Google Scholar

[21]

Comput. Math. Appl., 64 (2012), 3090-3100. doi: 10.1016/j.camwa.2012.01.068.  Google Scholar

[22]

Asian J. Control, 15 (2013), 698-712. doi: 10.1002/asjc.617.  Google Scholar

[23]

Comput. Math. Appl., 59 (2010), 1644-1655. doi: 10.1016/j.camwa.2009.08.006.  Google Scholar

[24]

Int. J. Differ. Equ., 2010 (2010), Art. ID 461048, 16 pp. doi: 10.1155/2010/461048.  Google Scholar

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