Minimum energy control of positive continuous-time linear systems with bounded inputs

Tadeusz Kaczorek

doi:10.2478/amcs-2013-0054

.blurhash-client-img { display: none !important; }

Minimum energy control of positive continuous-time linear systems with bounded inputs

International Journal of Applied Mathematics and Computer Science

Volume 23 (2013): Issue 4 (December 2013)

By: Tadeusz Kaczorek

Open Access

|Dec 2013

Abstract

The minimum energy control problem for 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.

References

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.
Search in Google Scholar
Dzieliński A., Sierociuk D. and Sarwas G. (2009). Ultracapacitor parameters identification based on fractional order model, Proceedings of ECC’09, Budapest, Hungary.10.23919/ECC.2009.7074403
Search in Google Scholar
Dzieliński A. and Sierociuk D. (2008a). Stability of discrete fractional order state-space systems, Journal of Vibrations and Control 14(9/10): 1543-1556.10.1177/1077546307087431
Search in Google Scholar
Farina L. and Rinaldi S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.10.1002/9781118033029
Search in Google Scholar
Kaczorek T. (1992). Linear Control Systems, Research Studies Press/J.Wiley, New York, NY.
Search in Google Scholar
Kaczorek T. (2001). Positive 1D and 2D Systems, Springer-Verlag, London.10.1007/978-1-4471-0221-2
Search in Google Scholar
Kaczorek T. (2008a). Fractional positive continuous-time systems and their reachability, International Journal of Applied Mathematics Computer Science 18(2): 223-228, DOI: 10.2478/v10006-008-0020-0.10.2478/v10006-008-0020-0
Search in Google Scholar
Kaczorek T. (2008b) Practical stability of positive fractional discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 313-317.10.2478/v10175-010-0143-y
Search in Google Scholar
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): 769-787.10.3166/jesa.42.769-787
Search in Google Scholar
Kaczorek T. (2009). Asymptotic stability of positive fractional 2D linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(3): 289-292.10.2478/v10175-010-0131-2
Search in Google Scholar
Kaczorek T. (2011a) Controllability and observability of linear electrical circuits, Electrical Review 87(9a): 248-254.
Search in Google Scholar
Kaczorek T. (2011b). Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica 5(2): 42-51.
Search in Google Scholar
Kaczorek T. (2011c). Positive linear systems consisting of n subsystems with different fractional orders, Transactions of IEEE: Circuits and Systems 58(6): 1203-1210.10.1109/TCSI.2010.2096111
Search in Google Scholar
Kaczorek T. (2011d) Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archive of Control Sciences 21(3): 287-298.10.2478/v10170-010-0044-1
Search in Google Scholar
Kaczorek T. (2012). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.10.1007/978-3-642-20502-6
Search in Google Scholar
Kaczorek T. (2013a) Minimum energy control of fractional positive continuous-time linear systems, Proceedings of the 18th International Conference on Methods and Models in Automation and Robotics, Mi˛edzyzdroje, Poland, NN 514638940.10.1109/MMAR.2013.6669982
Search in Google Scholar
Kaczorek T. (2013b). Minimum Energy Control of Descriptor Positive Discrete-time Linear Systems, Compel, (in press).10.1109/MMAR.2013.6669982
Search in Google Scholar
Kaczorek T. and Klamka J. (1986). Minimum energy control of 2D linear systems with variable coefficients, International Journal of Control 44(3): 645-650.10.1080/00207178608933623
Search in Google Scholar
Klamka J. (1991) Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht.
Search in Google Scholar
Klamka J. (1983). Minimum energy control of 2D systems in Hilbert spaces, System Sciences 9(1-2): 33-42.
Search in Google Scholar
Klamka J. (1976). Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Transactions on Automatic Control 21(4): 594-595.10.1109/TAC.1976.1101280
Search in Google Scholar
Klamka J. (2010). Controllability and minimum energy control problem of fractional discrete-time systems, in D.10.1109/ACIIDS.2009.53
Search in Google Scholar
Baleanu, Z.B. Guvenc and J.A. Tenreiro Machado (Eds.), New Trends in Nanotechology and Fractional Calculus, Springer-Verlag, New York, NY, pp. 503-509.
Search in Google Scholar
Klamka J. (1993). Controllability of dynamical systems-a survey, Archives of Control Sciences 2(3-4): 281-307.
Search in Google Scholar
Klamka J. (1977). Minimum energy control of discrete systems with delays in control, International Journal of Control 26(5): 737-744.10.1080/00207177708922289
Search in Google Scholar