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Minimum energy control of 2D positive continuous-discrete linear systems

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Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The minimum energy control problem for the 2D positive continuous-discrete linear systems is formulated and solved. Necessary and sufficient conditions for the reachability at the point of the systems are given. Sufficient conditions for the existence of solution to the problem are established. It is shown that if the system is reachable then there exists an optimal input that steers the state from zero boundary conditions to given final state and minimizing the performance index for only one step (q = 1). A procedure for solving of the problem is proposed and illustrated by a numerical example.
Rocznik
Strony
165--168
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
  • Faculty of Electrical Engineering, Bialystok University of Technology, ul. Wiejska 45D, 15-351 Bialystok, Poland
Bibliografia
  • 1. Bistritz Y. (2003), A stability test for continuous-discrete bivariate polynomials, Proc. Int. Symp. on Circuits and Systems, Vol. 3, 682-685.
  • 2. Busłowicz M. (2010), Robust stability of the new general 2D model of a class of continuous-discrete linear systems, Bull. Pol. Acad. Sci. Techn., Vol. 57, No. 4, 561-565.
  • 3. Busłowicz M. (2010), Stability and robust stability conditions for a general model of scalar continuous-discrete linear systems, Measurement Automation and Monitoring, Vol. 56, No. 2, 133-135.
  • 4. Dymkov M., Gaishun I., Rogers E., Gałkowski K. and Owens D.H. (2004), Control theory for a class of 2D continuous-discrete linear systems, Int. J. Control, Vol. 77, No. 9, 847-860. 5. Farina L. and Rinaldi S. (2000), Positive Linear Systems; Theory and Applications, J. Wiley, New York.
  • 6. Gałkowski K., Rogers E., Paszke W. and Owens D.H. (2003), Linear repetitive process control theory applied to a physical example, Int. J. Appl. Math. Comput. Sci., Vol. 13, No. 1, 87-99.
  • 7. Kaczorek T. (1998), Reachability and minimum energy control of positive 2D continuous-discrete systems, Bull. Pol. Acad. Sci. Tech., Vol. 46, No. 1, 85-93.
  • 8. Kaczorek T. (2001), Positive 1D and 2D systems, Springer Verlag, London.
  • 9. Kaczorek T. (2007), Positive 2D hybrid linear systems, Bull. Pol. Acad. Sci. Tech., Vol. 55, No. 4, 351-358.
  • 10. Kaczorek T. (2008a), Positive fractional 2D hybrid linear systems, Bull. Pol. Acad. Tech., Vol. 56, No. 3, 273-277.
  • 11. Kaczorek T. (2008b), Realization problem for positive 2D hybrid systems, COMPEL, Vol. 27, No. 3, 613-623.
  • 12. Kaczorek T. (2011a), New stability tests of positive standard and fractional linear systems, Circuit and Systems, Vol. 2, No. 4, 261-268.
  • 13. Kaczorek T. (2011b), Stability of continuous-discrete linear systems described by general model, Bull. Pol. Acad. Sci. Tech., Vol. 59, No. 2, 189-193.
  • 14. Kaczorek T. (2012), Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
  • 15. Kaczorek T. (2013), Minimum energy control of fractional positive continuous-time linear systems, Proc. of Conf. MMAR, Międzyzdroje, Poland.
  • 16. Kaczorek T. (2013), Minimum energy control of positive fractional descriptor continous time linear systems, IET Control Theory and Applications, Vol. 8 No. 4, 219-225.
  • 17. Kaczorek T. (2014), Minimum energy control of descriptor positive discrete-time linear systems, Compel, Vol. 33, No.3, 1-14.
  • 18. Kaczorek T., Klamka J. (1986), Minimum energy control of 2D linear systems with variable coefficients, Int. J. of Control, Vol. 44, No. 3, 645-650.
  • 19. Kaczorek T., Marchenko V. and Sajewski Ł. (2008), Solvability of 2D hybrid linear systems - comparison of three different methods, Acta Mechanica et Automatica, Vol. 2, No. 2, 59-66.
  • 20. Klamka J. (1976), Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Trans. Autom. Contr., Vol. 21, No. 4, 594-595.
  • 21. Klamka J. (1983), Minimum energy control of 2D systems in Hilbert spaces, System Sciences, Vol. 9, No. 1-2, 33-42.
  • 22. Klamka J. (1991), Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht.
  • 23. Klamka J. (2010), Controllability and minimum energy control problem of fractional discrete-time systems, Chapter in New Trends in Nanotechnology and Fractional Calculus, Eds. Baleanu D., Guvenc Z.B., Tenreiro Machado J.A., Springer-Verlag, New York, 503-509.
  • 24. Narendra K.S. and Shorten R. (2010), Hurwitz stability of Metzler matrices, IEEE Trans. Autom. Contr., Vol. 55, No. 6, 1484-1487.
  • 25. Sajewski Ł. (2009), Solution of 2D singular hybrid linear systems, Kybernetes, Vol. 38, No. 7/8, 1079-1092.
  • 26. Xiao Y. (2001), Stability test for 2-D continuous-discrete systems, Proc. 40th IEEE Conf. on Decision and Control, Vol. 4, 3649-3654.
  • 27. Xiao Y. (2003), Stability, controllability and observability of 2-D continuous-discrete systems, Proc. Int. Symp. on Circuits and Systems, Vol. 4, 468-471.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b8e38016-ce45-4e8c-8f3c-69a237c3c7b2
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