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.
@article{bwmeta1.element.bwnjournal-article-amcv23z4p725bwm, author = {Tadeusz Kaczorek}, title = {Minimum energy control of positive continuous-time linear systems with bounded inputs}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {23}, year = {2013}, pages = {725-730}, zbl = {1285.49002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv23z4p725bwm} }
Tadeusz Kaczorek. Minimum energy control of positive continuous-time linear systems with bounded inputs. International Journal of Applied Mathematics and Computer Science, Tome 23 (2013) pp. 725-730. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv23z4p725bwm/
[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. (2008a). 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/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 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 Systèmes 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, Transactions of IEEE: 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, Proceedings of the 18th International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, NN 514638940. | Zbl 1285.49002
[016] Kaczorek T. (2013b). Minimum Energy Control of Descriptor Positive Discrete-time Linear Systems, Compel, (in press). | Zbl 1291.93183
[017] 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
[018] Klamka J. (1991) Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht. | Zbl 0732.93008
[019] Klamka J. (1983). Minimum energy control of 2D systems in Hilbert spaces, System Sciences 9(1-2): 33-42. | Zbl 0574.93009
[020] 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. | Zbl 0332.93013
[021] 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 Nanotechology and Fractional Calculus, Springer-Verlag, New York, NY, pp. 503-509. | Zbl 1222.93030
[022] Klamka J. (1993). Controllability of dynamical systems-a survey, Archives of Control Sciences 2(3-4): 281-307. | Zbl 0818.93002
[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