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2014 | 24 | 4 | 735-743
Tytuł artykułu

Minimum energy control of fractional descriptor positive discrete-time linear systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Necessary and sufficient conditions for the positivity and reachability of fractional descriptor positive discrete-time linear systems are established. The minimum energy control problem for descriptor positive systems is formulated and solved. Sufficient conditions for the existence of a solution to the minimum energy control problem are given. A procedure for computation of optimal input sequences and a minimal value of the performance index is proposed and illustrated by a numerical example.
Rocznik
Tom
24
Numer
4
Strony
735-743
Opis fizyczny
Daty
wydano
2014
otrzymano
2013-11-21
poprawiono
2014-01-22
Twórcy
  • Faculty of Electrical Engineering, Białystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • 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.
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  • Dzieliński, A., Sierociuk, D. and Sarwas, G. (2009). Ultracapacitor parameters identification based on fractional order model, Proceedings of ECC'09, Budapest, Hungary, pp. 196-200.
  • Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.
  • Kaczorek, T. (1992). Linear Control Systems, Research Studies Press/J. Wiley, New York, NY.
  • Kaczorek, T. (2001). Positive 1D and 2D Systems, Springer-Verlag, London.
  • Kaczorek, T. (2008a). Fractional positive continuous-time systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2): 223-228, 10.2478/v10006-008-0020-0.
  • Kaczorek, T. (2008b). Practical stability of positive fractional discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 313-318.
  • Kaczorek, T. (2008c). Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, Journal Européen des Systèmes Automatisés 42(6-8): 769-787.
  • Kaczorek, T. (2009). Asymptotic stability of positive fractional 2D linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(3): 289-292.
  • Kaczorek, T. (2011a). Controllability and observability of linear electrical circuits, Electrical Review 87(9a): 248-254.
  • Kaczorek, T. (2011b). Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica 5(2): 42-51.
  • Kaczorek, T. (2011c). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(6): 1203-1210.
  • Kaczorek, T. (2011d). Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archives of Control Sciences 21(3): 287-298.
  • Kaczorek, T. (2012). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
  • Kaczorek, T. (2013a). Minimum energy control of fractional positive continuous-time linear systems, MMAR Conference, Międzyzdroje, Poland, pp. 622-626.
  • Kaczorek, T. (2013b). Minimum energy control of descriptor positive discrete-time linear systems, COMPEL 33(2): 1-14.
  • Kaczorek, T. and Klamka, J. (1986). Minimum energy control of 2D linear systems with variable coefficients, International Journal of Control 44(3): 645-650.
  • Klamka J., (1976). Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Transactions on Automatic Control 21(4): 594-595.
  • Klamka, J. (1983). Minimum energy control of 2D systems in Hilbert spaces, System Sciences 9(1-2): 33-42.
  • Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht.
  • Klamka, J. (2010). Controllability and minimum energy control problem of fractional discrete-time systems, in D. Baleanu, Z.B. Guvenc and J.A. Tenreiro Machado (Eds.), New Trends in Nanotechnology and Fractional Calculus, Springer-Verlag, New York, NY, pp. 503-509.
  • Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.
  • Ostalczyk, P. (2008). Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Technical University of Łódź Press, Łódź, (in Polish).
  • Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA.
  • Radwan, A.G., Soliman, A.M., Elwakil, A.S. and Sedeek, A. (2009). On the stability of linear systems with fractional-order elements, Chaos, Solitons and Fractals 40(5): 2317-2328.
  • Tenreiro Machado J.A., Ramiro Barbosa S., (2006). Functional dynamics in genetic algorithms, Workshop on Fractional Differentiation and Its Application, Porto, Portugal, Vol. 1, pp. 439-444.
  • Vinagre B.M., Monje C.A., Calderon A.J. (2002). Fractional order systems and fractional order control actions, IEEE CDC'02, Las Vegas, NV, USA, TW#2, Lecture 3.
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Bibliografia
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