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Minimum energy control of fractional positive continuous-time linear systems with bounded inputs

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EN
Abstrakty
EN
A minimum energy control problem for fractional positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.
Twórcy
autor
  • Faculty of Electrical Engineering, Białystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • [1] Busłowicz, M. (2008). Stability of linear continuous time fractional order systems with delays of the retarded type, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 319–324.
  • [2] Dzieliński, A., Sierociuk, D. and Sarwas, G. (2009). Ultracapacitor parameters identification based on fractional order model, Proceedings of ECC’09, Budapest, Hungary.
  • [3] Dzieliński, A. and Sierociuk, D. (2008). Stability of discrete fractional order state-space systems, Journal of Vibrations and Control 14(9/10): 1543–1556.
  • [4] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.
  • [5] Kaczorek, T. (1992). Linear Control Systems, Research Studies Press and J. Wiley, New York, NY.
  • [6] Kaczorek, T. (2001). Positive 1D and 2D Systems, Springer-Verlag, London.
  • [7] Kaczorek, T. (2008a). Fractional positive continuous-time systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2): 223–228, DOI: 10.2478/v10006-008-0020-0.
  • [8] Kaczorek, T. (2008b). Practical stability of positive fractional discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 313–317.
  • [9] Kaczorek, T. (2008c). Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, Journal Européen des Systémes Automatisés 42(6–8): 769–787.
  • [10] Kaczorek, T. (2009). Asymptotic stability of positive fractional 2D linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(3): 289–292.
  • [11] Kaczorek, T. (2011a). Controllability and observability of linear electrical circuits, Electrical Review 87(9a): 248–254.
  • [12] Kaczorek, T. (2011b). Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica 5(2): 42–51.
  • [13] Kaczorek, T. (2011c). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions Circuits and Systems 58(6): 1203–1210.
  • [14] Kaczorek, T. (2011d). Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archive of Control Sciences 21(3): 287–298.
  • [15] Kaczorek, T. (2012). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
  • [16] Kaczorek, T. (2013a). Minimum energy control of fractional positive continuous-time linear systems, MMAR 2013, Międzyzdroje, Poland.
  • [17] Kaczorek, T. (2013c). Minimum energy control of positive discrete-time linear systems with bounded inputs, Archives of Control Sciences 23(2): 205–211.
  • [18] Kaczorek, T. (2013d). Minimum energy control of positive continuous-time linear systems with bounded inputs, International Journal of Applied Mathematics and Computer Science 23(4): 725–730, DOI: 10.2478/amcs-2013-0054.
  • [19] Kaczorek, T. (2014a). Minimum energy control of descriptor positive discrete-time linear systems, COMPEL 33(3).
  • [20] Kaczorek, T. (2014b). An extension of Klamka’s method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs, Bulletin of the Polish Academy of Sciences: Technical Sciences 62(2), (in press).
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-37dac280-5289-4292-8d36-4eaeb3440fb0
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