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Journal of Industrial and Management Optimization (JIMO)
 

Fractional order optimal control problems with free terminal time

Pages: 363 - 381, Volume 10, Issue 2, April 2014      doi:10.3934/jimo.2014.10.363

 
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Shakoor Pooseh - CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal (email)
Ricardo Almeida - CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal (email)
Delfim F. M. Torres - CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal (email)

Abstract: 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:  Optimization and control, fractional calculus, fractional optimal control, free-time problem, numerical approximations.
Mathematics Subject Classification:  Primary: 26A33, 33F05; Secondary: 49K15.

Received: December 2012;      Revised: July 2013;      Available Online: October 2013.

 References