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Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

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Volume 61, Issue 3 (Sep 2013)


Fixed final time and free final state optimal control problem for fractional dynamic systems – linear quadratic discrete-time case

A. Dzieliński
  • Electrical Engineering Institute of Control and Industrial Electronics, Warsaw University of Technology, 75 Koszykowa St., 00-662 Warszawa, Poland
/ P.M. Czyronis
  • Corresponding author
  • Bumar Elektronika S.A., 30 Poligonowa St., 04-451 Warszawa, Poland
  • Email:
Published Online: 2013-10-15 | DOI: https://doi.org/10.2478/bpasts-2013-0072


The optimization problem for fractional discrete-time systems with a quadratic performance index has been formulated and solved. The case of fixed final time and a free final state has been considered. A method for numerical computation of optimization problems has been presented. The presented method is a generalization of the well-known method for discrete-time systems of integer order. The efficiency of the method has been demonstrated on numerical examples and illustrated by graphs. Graphs also show the differences between the fractional and classical (standard) systems theory. Results for other cases of the fractional system order (coefficient ) and not illustrated with numerical examples have been obtained through a computer algorithm written for this purpose.

Keywords : fractional order systems; discrete-time systems; optimal control; linear quadratic performance index

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About the article

Published Online: 2013-10-15

Published in Print: 2013-09-01

Citation Information: Bulletin of the Polish Academy of Sciences: Technical Sciences, ISSN (Print) 0239-7528, DOI: https://doi.org/10.2478/bpasts-2013-0072. Export Citation

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