PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Minimum energy control of fractional positive continuous-time linear systems

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The minimum energy control problem for the fractional positive continuous-time linear systems is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.
Twórcy
autor
  • Faculty of Electrical Engineering, Bialystok University of Technology, 45D Wiejska St., 15-351 Bialystok, Poland
Bibliografia
  • [1] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
  • [2] T. Kaczorek, Positive 1D and 2D systems, Springer Verlag, London, 2001.
  • [3] K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
  • [4] P. Ostalczyk, Epitome of the Fractional Calculus: Theory and its Applications in Automatics, Lodz University of Technology Publishing House, Łodź, 2008, (in Polish).
  • [5] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [6] T. Kaczorek, “Fractional positive continuous-time systems and their reachability”, Int. J. Appl. Math. Comput. Sci. 18 (2), 223-228 (2008).
  • [7] T. Kaczorek, “Positivity and reachability of fractional electrical circuits”, Acta Mechanica et Automatica 3, 42-51 (2011).
  • [8] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. Circuits and Systems 58, 1203-1210 (2011).
  • [9] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin, 2012.
  • [10] M. Busłowicz, “Stability of linear continuous time fractional order systems with delays of the retarded type”, Bull. Pol. Ac.: Tech. 56 (4), 319-324 (2008).
  • [11] A. Dzieliński. and D. Sierociuk, “Stability of discrete fractional order state-space systems”, Journal of Vibrations and Control, 14, 9/10, 1543-1556 (2008).
  • [12] T. Kaczorek, “Asymptotic stability of positive fractional 2D linear systems”, Bull. Pol. Ac.: Tech. 57 (3), 287-292 (2009).
  • [13] T. Kaczorek, “Practical stability of positive fractional discretetime linear systems”, Bull. Pol. Ac.: Tech. 56 (4), 313-318 (2008).
  • [14] A. Dzieliński, D. Sierociuk, and G. Sarwas, “Ultracapacitor parameters identification based on fractional order model”, Proc. ECC’09 1, CD-ROM (2009).
  • [15] A.G. Radwan, A.M. Soliman, A.S. Elwakil, and A. Sedeek, “On the stability of linear systems with fractional-order elements”, Chaos, Solitones and Fractals 40, 2317-2328 (2009).
  • [16] T. Machado J.A. Ramiro, and S. Barbosa, “Functional dynamics in genetic algorithms”, Workshop on Fractional Differenation and Its Application 1, 439-444 (2006).
  • [17] B.M. Vinagre, C.A. Monje, and A.J. Calderon, “Fractional order systems and fractional order control actions”, IEEE CDC’02 Fractional Calculus Applications in Automatic Control and Robotics 3, CD-ROM (2002).
  • [18] J. Klamka, Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht, 1991.
  • [19] J. Klamka, “Minimum energy control of 2D systems in Hilbert spaces”, System Sciences 9, 33-42 (1983).
  • [20] J. Klamka, “Relative controllability and minimum energy control of linear systems with distributed delays in control”, IEEE Trans. Autom. Contr. 21, 594-595 (1976).
  • [21] T. Kaczorek and J. Klamka, “Minimum energy control of 2D linear systems with variable coefficients”, Int. J. Control 44, 645-650 (1986).
  • [22] J. Klamka, “Controllability and minimum energy control problem of fractional discrete-time systems”, in New Trends in Nanotechology and Fractional Calculus, eds. D. Baleanu, Z.B.Guvenc, J.A. Tenreiro Machado, pp. 503-509, Springer-Verlag, New York, 2010.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9d91a8e3-4705-4f95-b854-0d0f7ebd12b9
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.