Necessary and sufficient conditions for the minimum energy control of positive discrete-time linear systems with bounded inputs

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.2478/bpasts-2014-0010

• Języki publikacji: EN

Abstrakty

EN

The minimum energy control problem for the positive discrete-time linear systems with bounded inputs is formulated and solved. Necessary and 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.

Słowa kluczowe

EN

positive; discrete-time; minimum energy control; bounded inputs; procedure

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2014
• Tom: Vol. 62, nr 1
• Strony: 85--89
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Kaczorek T.

• 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] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. Circuits and Systems 58 (6), 1203-1210 (2011).
• [4] J. Klamka, Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht, 1991.
• [5] J. Klamka, “Minimum energy control of 2D systems in Hilbert spaces”, System Sciences 9 (1-2), 33-42 (1983).
• [6] J. Klamka, “Relative controllability and minimum energy control of linear systems with distributed delays in control”, IEEE Trans. Autom. Contr. 21 (4), 594-595 (1976).
• [7] J. Klamka, “Controllability and minimum energy control problem of fractional discrete-time systems”, in New Trends in Nanotechology and Fractional Calculus Applications, eds. D. Baleanu, Z.B. Guvenc, Tenreiro, and J.A. Machado, pp. 503-509, Springer-Verlag, New York, 2010.
• [8] T. Kaczorek and J. Klamka, “Minimum energy control of 2D linear systems with variable coefficients”, Int. J. Control 44 (3), 645-650 (1986).
• [9] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin, 2012.
• [10] T. Kaczorek, “Minimum energy control of fractional positive continuous-time linear systems”, Bull. Pol. Ac.: Tech. 61 (4), 803-807 (2013).
• [11] T. Kaczorek, Minimum energy control of descriptor positive discrete-time linear systems, Compel, (2014), (to be published).
• [12] T. Kaczorek, “Minimum energy control of positive fractional descriptor continuous-time linear systems”, IET Control Theory and Appl. doi: 10.1049/iet-cta.2013.0362 (2013).
• [13] T. Kaczorek, “Minimum energy control of positive continuoustime linear systems with bounded inputs”, Int. J. Appl. Math. and Comp. Sci. 23 (4), 725-730 (2013).
• [14] T. Kaczorek, “Minimum energy control of positive discretetime linear systems with bounded inputs”, Archive of Control Sciences 23 (2), 131-137 (2013).
• [15] T. Kaczorek, “An extension of Klamka’s method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs”, Bull. Pol. Ac.: Tech. 62 (2), (2014) (to be published).