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New Trends in Nanotechnology and Fractional Calculus Applications pp 503–509Cite as

Controllability and Minimum Energy Control Problem of Fractional Discrete-Time Systems

Abstract

In the paper minimum energy control problem of infinite-dimensional fractional-discrete time linear systems is addressed. Necessary and sufficient conditions for the exact controllability of the system are established. Sufficient conditions for the solvability of the minimum energy control of the infinite-dimensional fractional discrete-time systems are given. A procedure for computation of the optimal sequence of inputs minimizing the quadratic performance index is proposed.

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References

  1. Klamka J (1991) Controllability of dynamical systems. Kluwer, Dordrecht

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  2. Kaczorek T (2002) Positive 1D and 2D systems. Springer, London

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  3. Kaczorek T (2007) Rechability and controllability to zero of cone fractional linear systems. Arch Control Sci. 17(3):357–367

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  4. Klamka J (2002) Positive controllability of positive systems. In Proceedings of American Control Conference, ACC-2002. Anchorage, CD-ROM

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Acknowledgements

This work was supported by the Ministry of Science and High Education of Poland under grant NN 514 415834.

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Authors and Affiliations

  1. Institute of Control Engineering, Silesian Technical University Akademicka 16, 44–100, Gliwice, Poland

    Jerzy Klamka

Authors
  1. Jerzy Klamka
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Correspondence to Jerzy Klamka .

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Editors and Affiliations

  1. Fac. Engineering & Architecture, Cankaya University, Ogretmenler Cad. 14, Ankara, 06530, Turkey

    Dumitru Baleanu

  2. Fac. Engineering & Architecture, Cankaya University, Ogretmenler Cad. 14, Ankara, 06530, Turkey

    Ziya B. Guvenc

  3. Polytechnic Institute of Porto, Institute of Engineering of the, Rua Dr. Antonio Bernardino de Almeida, Porto, 4200-072, Portugal

    J. A. Tenreiro Machado

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Klamka, J. (2010). Controllability and Minimum Energy Control Problem of Fractional Discrete-Time Systems. In: Baleanu, D., Guvenc, Z., Machado, J. (eds) New Trends in Nanotechnology and Fractional Calculus Applications. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3293-5_45

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  • DOI: https://doi.org/10.1007/978-90-481-3293-5_45

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  • Online ISBN: 978-90-481-3293-5

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