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

• Autorzy: Tadeusz Kaczorek
• 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.

Słowa kluczowe

EN

fractional system; descriptor system; positive system; minimum energy control

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2014
• Tom: 24
• Numer: 4
• Strony: 735-743

Daty

wydano

2014

otrzymano

2013-11-21

poprawiono

2014-01-22

Twórcy

autor

Tadeusz Kaczorek

• 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.
• Dzieliński, A. and Sierociuk, D. (2008). Stability of discrete fractional order state-space systems, Journal of Vibrations and Control 14(9/10): 1543-1556.
• 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.

Identyfikatory

DOI

10.2478/amcs-2014-0054