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The selected problems of controllability of discrete-time switched linear systems with constrained switching rule

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Języki publikacji
EN
Abstrakty
EN
In this paper the controllability problem for discrete-time linear switched systems is considered. The main goal is to find a control signal that steers any initial state to a given final state independently of the switching signal. In the paper, it is assumed that there are some constraints posed on the switching signal. Moreover, we present a necessary and sufficient conditions of some kinds of controllability. Three types of controllability, namely: from zero initial state to any final state, from any initial state to zero final state and from any initial state to any final state are considered. Finally, three illustrative examples are shown.
Rocznik
Strony
657--666
Opis fizyczny
Bibliogr. 46 poz., rys., wykr.
Twórcy
autor
  • Silesian University of Technology, Institute of Automatic Control, 16 Akademicka St., 44-100 Gliwice, Poland
autor
  • Silesian University of Technology, Institute of Automatic Control, 16 Akademicka St., 44-100 Gliwice, Poland
autor
  • Silesian University of Technology, Institute of Automatic Control, 16 Akademicka St., 44-100 Gliwice, Poland
  • Silesian University of Technology, Institute of Automatic Control, 16 Akademicka St., 44-100 Gliwice, Poland
Bibliografia
  • [1] P.J. Antsaklis, J.A. Stiver, and M.D. Lemmon, “Hybrid system modeling and autonomous control systems”, Hybrid Systems, LNCS 736, 366–392 (1993).
  • [2] C.G. Cassandras and J. Lygeros, Stochastic Hybrid Systems, Taylor & Francis, London, 2006.
  • [3] M. Egerstedt and B. Mishra, Hybrid Systems: Computation and Control, Springer, Berlin, 2008.
  • [4] R. Goebel and R.G. Sanfelice, Hybrid Dynamical Systems: Modeling, Stability, and Robustness, Princeton University Press, Princeton, 2012.
  • [5] D. Liberzon, Switching in Systems and Control. Systems & Control: Foundations and Applications series, Birkhauser, Boston, 2003.
  • [6] R. Shorten, F. Wirth, O. Mason, K. Wulff, and Ch. King, “Stability criteria for switched and hybrid systems”, SIAM Review 49 (4), 545–592 (2007).
  • [7] Z. Sun and S.S. Ge, Switched Linear Systems–Control and Design, Springer, New York, 2004.
  • [8] Z. Sun and S.S. Ge, Stability Theory of Switched Dynamical Systems, Springer-Verlag, London, 2011.
  • [9] A. Back, J. Guckenheimer, and M. Myers, “A dynamical simulation facility for hybrid systems”, Hybrid Systems, LNCS 736, 255–267 (1993).
  • [10] T. Hagiwara and M. Araki, “Design of a stable feedback controller based on the multirate sampling of the plant output”, IEEE Trans. Automat. Contr. 33, 812–819 (1988).
  • [11] K.M. Passino, A.N. Michel, and P.J. Antsaklis, “Lyapunov stability of a class of discrete event systems”, IEEE Trans. Automat. Contr. 39, 269–279 (1994).
  • [12] P.P. Varaiya, “Smart cars on smart roads: problems of control”, IEEE Trans. Automat. Contr. 38, 195–207 (1993).
  • [13] J. Klamka, Controllability of Dynamical Systems, Kluwer, Dordrecht, 1991.
  • [14] S.S. Ge, Z. Sun, and T.H. Lee, “Reachability and controllability of switched linear discrete-time system”, IEEE Trans. Autom. Contr. 46 (9), 1437–1441 (2001).
  • [15] Y. Qiao and D. Cheng, “On partitioned controllability of switched linear systems”, Automatica 45 (1), 225–229 (2009).
  • [16] B. Sikora and J. Klamka, “On constrained stochastic controllability of dynamical systems with multiple delays in control”, Bull. Pol. Ac.: Tech. 60 (2), 301–305 (2012).
  • [17] J. Klamka, “Controllability of dynamical systems. A survey”, Bull. Pol. Ac.: Tech. 61 (2), 335–342 (2013).
  • [18] R. Zawiski, “On controllablity and measures of noncompactness”, AIP Conf. Proc. 1637 (1), 1241–1246 (2014).
  • [19] T. Kaczorek, “Minimum energy control of fractional positive continuous-time linear systems”, Bull. Pol. Ac.: Tech. 61 (4), 803–807 (2013).
  • [20] T. Kaczorek, “Minimum energy control of positive continuous-time linear systems with bounded inputs”, Int. J. Appl. Math. Comput. Sci. 23 (4), 725–730 (2013).
  • [21] T. Kaczorek, “An extension of Klamka’s method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs”, Bull. Pol. Ac.: Tech. 62 (2), 227–231 (2014).
  • [22] T. Kaczorek, “Minimum energy control of fractional positive continuous-time linear systems with bounded inputs”, Int. J. Appl. Math. Comput. Sci. 24 (2), 335–340 (2014).
  • [23] T. Kaczorek, “Necessary and sufficient conditions for the minimum energy control of positive discrete-time linear systems with bounded inputs”, Bull. Pol. Ac.: Tech. 62 (1), 85–89 (2014).
  • [24] E.J. Davison and E.C. Kunze, “Controllability of integro-differential systems in banach space”, SIAM J. Control Optim. 8 (1), 489–497 (1970).
  • [25] J. Klamka, “Approximate controllability of second order dynamical systems”, Appl. Math. Comput. Sci. 2 (1), 135–146 (1992).
  • [26] D.N. Chalishajar, R.K. George, and A.K. Nandakunaran, “Exact controllability of the nonlinear third-order dispersion equation”, J. Math. Anal. Appl. 332, 1028–1044 (2007).
  • [27] D.N. Chalishajar, R.K. George, and A.K. Nandakumaran, “Trajectory controllability of nonlinear integro-differential system”, J. Franklin Inst. 347 (7), 1065–1075 (2010).
  • [28] V.D. Blondel and J.N. Tsitsiklis, “Complexity of stability and controllability of elementary hybrid systems”, Automatica 35 (3), 479–489 (1999).
  • [29] Z. Sun, S.S. Ge, and T.H. Lee, “Controllability and reachability criteria for switched linear system”, Automatica 38 (5), 775–786 (2002).
  • [30] G. Xie and L. Wang, “Reachability realization and stabilizability of switched linear discrete-time systems”, J. Math. Anal. Appl. 280, 209–220 (2003).
  • [31] M.I. Krastanov and V.M. Veliov, “On the controllability of switching linear systems”, Automatica 41, 663–668 (2005).
  • [32] Z. Ji, H. Lin, and T.H. Lee, “A new perspective on criteria and algorithms for reachability of discrete-time switched linear systems”, Automatica 45, 1584–1587 (2009).
  • [33] J. Klamka and M. Niezabitowski, “Controllability of switched linear dynamical systems”, IEEE 18th Int. Conf. on Methods and Models in Automation and Robotics 1, 464–467 (2013).
  • [34] J. Klamka, A. Czornik, and M. Niezabitowski, “Stability and controllability of switched systems”, Bull. Pol. Ac.: Tech. 61 (3), 547–555 (2013).
  • [35] J. Klamka and M. Niezabitowski, “Controllability of Switched Infinite-dimensional Linear Dynamical Systems”, IEEE 19th Int. Conf. on Methods and Models in Automation and Robotics 1, 171–175 (2014).
  • [36] A. Czornik and A. Swierniak, “On controllability with respect to the expectation of discrete time jump linear systems”, J. Franklin Inst. 338, 443–453 (2001).
  • [37] A. Czornik and A. Swierniak, “Controllability of discrete time jump linear systems”, Dynam. Cont. Dis. Ser. B 12 (2), 165–191 (2005).
  • [38] V.B. Zhivetin, Advanced Calculus: Lectures, Pensoft Publishers, Sofia, 2007.
  • [39] A. Babiarz, A. Czornik, J. Klamka, M. Niezabitowski, and R. Zawiski, “The mathematical model of the human arm as a switched linear system”, IEEE 19th Int. Conf. on Methods and Models in Automation and Robotics 1, 508–513 (2014).
  • [40] A. Babiarz, R. Bieda, K. Jaskot, and J. Klamka, “The dynamics of the human arm with an observer for the capture of body motion parameters”, Bull. Pol. Ac.: Tech. 61 (4), 955–971 (2014).
  • [41] D. Lee, M. Glueck, A. Khan, E. Fiume, and K. Jackson, “A survey of modeling and simulation of skeletal muscle”, ACM Transactions on Graphics 28 (4), 1–13 (2010).
  • [42] T. Neumann, K. Varanasi, N. Hasler, M. Wacker, M. Magnor, and C. Theobalt, “Capture and statistical modeling of arm-muscle deformations”, Computer Graphics Forum 32, 285–294 (2013).
  • [43] W. Li, “Optimal control for biological movement system”, PhD Thesis, University of California, Berkeley, 2006.
  • [44] P.R. Pagilla and Y. Zhu, “Adaptive control of mechanical systems with time-varying parameters and disturbances”, J. Dyn. Syst. Meas. Control 126 (3), 520–530 (2004).
  • [45] R. Burkan and I. Uzmay, “A model of parameter adaptive law with time varying function for robot control”, Appl. Math. Model. 29 (4), 361–371 (2005).
  • [46] A. Babiarz, “On mathematical modelling of the human arm using switched linear system”, AIP Conf. Proc. 1637 (1), 47–54 (2014).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a66dd2e4-7c4a-4b61-9fdb-c287e2601797
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