# American Institute of Mathematical Sciences

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

## Fractional order optimal control problems with free terminal time

 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.
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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