Abstract
We present a method to solve fractional optimal control problems, where the dynamic control system depends on integer order and Caputo fractional derivatives. Our approach consists in approximating the initial fractional order problem with a new one that involves integer order derivatives only. The latter problem is then discretized, by application of finite differences, and solved numerically. We illustrate the effectiveness of the procedure with an example.
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Acknowledgments
This article was supported by Portuguese funds through the Center for Research and Development in Mathematics and Applications (CIDMA), and The Portuguese Foundation for Science and Technology (FCT), within project PEst-OE/MAT/UI4106/2014. Torres was also supported by the FCT project PTDC/EEI-AUT/1450/2012, co-financed by FEDER under POFC-QREN with COMPETE reference FCOMP-01-0124-FEDER-028894.
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Almeida, R., Torres, D.F.M. A discrete method to solve fractional optimal control problems. Nonlinear Dyn 80, 1811–1816 (2015). https://doi.org/10.1007/s11071-014-1378-1
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DOI: https://doi.org/10.1007/s11071-014-1378-1