Minimum energy control of fractional positive continuous-time linear systems with bounded inputs
Tadeusz Kaczorek
International Journal of Applied Mathematics and Computer Science, Tome 24 (2014), p. 335-340 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:271904
@article{bwmeta1.element.bwnjournal-article-amcv24i2p335bwm,
     author = {Tadeusz Kaczorek},
     title = {Minimum energy control of fractional positive continuous-time linear systems with bounded inputs},
     journal = {International Journal of Applied Mathematics and Computer Science},
     volume = {24},
     year = {2014},
     pages = {335-340},
     zbl = {1293.49042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv24i2p335bwm}
}
Tadeusz Kaczorek. Minimum energy control of fractional positive continuous-time linear systems with bounded inputs. International Journal of Applied Mathematics and Computer Science, Tome 24 (2014) pp. 335-340. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv24i2p335bwm/

[000] 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.

[001] Dzieliński, A., Sierociuk, D. and Sarwas, G. (2009). Ultracapacitor parameters identification based on fractional order model, Proceedings of ECC'09, Budapest, Hungary. | Zbl 1268.34091

[002] Dzieliński, A. and Sierociuk, D. (2008). Stability of discrete fractional order state-space systems, Journal of Vibrations and Control 14(9/10): 1543-1556. | Zbl 1229.93143

[003] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY. | Zbl 0988.93002

[004] Kaczorek, T. (1992). Linear Control Systems, Research Studies Press and J. Wiley, New York, NY. | Zbl 0784.93002

[005] Kaczorek, T. (2001). Positive 1D and 2D Systems, Springer-Verlag, London. | Zbl 1005.68175

[006] 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. | Zbl 1235.34019

[007] 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.

[008] 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.

[009] Kaczorek, T. (2009). Asymptotic stability of positive fractional 2D linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(3): 289-292.

[010] Kaczorek, T. (2011a). Controllability and observability of linear electrical circuits, Electrical Review 87(9a): 248-254.

[011] Kaczorek, T. (2011b). Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica 5(2): 42-51.

[012] Kaczorek, T. (2011c). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions Circuits and Systems 58(6): 1203-1210.

[013] 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. | Zbl 1264.93096

[014] Kaczorek, T. (2012). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin. | Zbl 1221.93002

[015] Kaczorek, T. (2013a). Minimum energy control of fractional positive continuous-time linear systems, MMAR 2013, Międzyzdroje, Poland. | Zbl 1285.49002

[016] Kaczorek, T. (2013c). Minimum energy control of positive discrete-time linear systems with bounded inputs, Archives of Control Sciences 23(2): 205-211. | Zbl 1291.93183

[017] 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. | Zbl 1285.49002

[018] Kaczorek, T. (2014a). Minimum energy control of descriptor positive discrete-time linear systems, COMPEL 33(3) | Zbl 1309.93093

[019] 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).

[020] Kaczorek, T. and Klamka, J. (1986). Minimum energy control of 2D linear systems with variable coefficients, International Journal of Control 44(3): 645-650. | Zbl 0637.93044

[021] Klamka, J. (1976a). Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Transactions on Automatic Control 21(4): 594-595. | Zbl 0332.93013

[022] Klamka, J. (1976b). Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Transactions on Automatic Control 21(4): 594-595. | Zbl 0332.93013

[023] Klamka, J. (1977). Minimum energy control of discrete systems with delays in control, International Journal of Control 26(5): 737-744. | Zbl 0412.49022

[024] Klamka, J. (1983). Minimum energy control of 2D systems in Hilbert spaces, System Sciences 9(1-2): 33-42. | Zbl 0574.93009

[025] Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht. | Zbl 0732.93008

[026] 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 Nanotechology and Fractional Calculus, Springer-Verlag, New York, NY, pp. 503-509. | Zbl 1222.93030

[027] Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY. | Zbl 0292.26011

[028] Ostalczyk, P. (2008). Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Technical University of Łódź Press, Łódź, (in Polish).

[029] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA. | Zbl 0924.34008

[030] 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. | Zbl 1198.93151

[031] Solteiro Pires, E.J., Tenreiro Machado, J.A. and Moura Oliveira, P.B. (2006). Fractional dynamics in genetic algorithms, Workshop on Fractional Differentiation and Its Application, Porto, Portugal, Vol. 2, pp. 414-419.

[032] Vinagre, B.M. (2002). Fractional order systems and fractional order control actions, IEEE CDC'02, Las Vegas, USA, NV, TW#2, Lecture 3.