Approximately bisimilar symbolic models for incrementally stable switched systems

IEEE Transactions on Automatic Control

Volumn 55, Issue 1, 2010, Pages 116-126

  Girard, Antoine ^a   Pola, Giordano ^b   Tabuada, Paulo ^c  

^a UNIV GRENOBLE ALPES   (France)

^b UNIVERSITY OF L'AQUILA   (Italy)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Approximate bisimulation; Finite controllers; Switched systems

Indexed keywords

APPROXIMATE BISIMULATION; APRIORI; BOOST DC-DC CONVERTER; COMMON LYAPUNOV FUNCTIONS; DWELL TIME; ENGINEERING SYSTEMS; EVOLUTION OF TECHNOLOGY; INCREMENTAL STABILITY; MODELING PARADIGMS; MULTIPLE LYAPUNOV FUNCTION; PHYSICAL WORLD; STANDARD ASSUMPTIONS; SWITCHED SYSTEM; SYMBOLIC MODEL;

CONTROLLERS; DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS; MODELS; STABILIZATION; SWITCHING SYSTEMS;

SYSTEM STABILITY;

EID: 75449111394     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2034922     Document Type: Article

References (22)

1. D. Liberzon, Switching in Systems and Control. Boston, MA: Birkhauser, 2003.
2. P. Ramadge and W. Wonham, "Supervisory control of a class of discrete event systems," SIAM J. Control Optim., vol.25, no.1, pp. 206-230, 1987. (Pubitemid 17513624)
3. A. Arnold, A. Vincent, and I. Walukiewicz, "Games for synthesis of controllers with partial observation," Theor. Comput. Sci., vol.28, no.1, pp. 7-34, 2003.
4. A. Girard and G. Pappas, "Approximation metrics for discrete and continuous systems," IEEE Trans. Autom. Control, vol.52, no.5, pp. 782-798, May 2007.
5. R. Milner, Communication and Concurrency. Englewood Cliffs, NJ: Prentice Hall, 1989.
6. D. Park, "Concurrency and automata on infinite sequences," in Proc. GI-Conf. Theor. Comput. Sci., 1981, vol.LNCS, 104, pp. 167-183.
7. P. Tabuada, "Symbolic control of linear systems based on symbolic subsystems," IEEE Trans. Autom. Control, vol.51, no.6, pp. 1003-1013, Jun. 2006 (Pubitemid 43997249)
8. G. Pola, A. Girard, and P. Tabuada, "Approximately bisimilar symbolic models for nonlinear control systems," Automatica, vol.44, no.10, pp. 2508-2516, 2008.
9. A. Girard, G. Pola, and P. Tabuada, "Approximately bisimilar symbolic models for incrementally stable switched systems," in Hybrid Systems: Computation and Control, ser. LNCS. New York: Springer, 2008, vol.4981, pp. 201-214.
10. D. Angeli and E. Sontag, "Forward completeness, unboundedness observability, and their Lyapunov characterizations," Syst. Control Lett., vol.38, no.3, pp. 209-217, 1999.
11. D. Angeli, "A Lyapunov approach to incremental stability properties," IEEE Trans. Autom. Control, vol.47, no.3, pp. 410-421, Mar. 2002.
12. H. Khalil, Nonlinear Systems. Englewood Cliffs, NJ: Prentice Hall, 1996.
13. L. Praly and Y. Wang, "Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability," Math. Control Signals Syst., vol.9, pp. 1-33, 1996.
14. A. Girard and G. Pappas, "Approximate bisimulations for nonlinear dynamical systems," in Proc. IEEE Conf. Decision Control, 2005, pp. 684-689. (Pubitemid 46297046)
15. E. Aylward, P. Parrilo, and J.-J. Slotine, "Stability and robustness analysis of nonlinear systems via contraction metrics and sos programming," Automatica, vol.44, no.8, pp. 2163-2170, 2008.
16. M. Senesky, G. Eirea, and T. Koo, "Hybrid modelling and control of power electronics," in Hybrid Systems: Computation and Control, ser. LNCS. New York: Springer, 2003, vol.2623, pp. 450-465.
17. A. Beccuti, G. Papafotiou, and M. Morari, "Optimal control of the boost dc-dc converter," in Proc. IEEE Conf. Decision Control, 2005, pp. 4457-4462.
18. J. Buisson, P. Richard, and H. Cormerais, "On the stabilisation of switching electrical power converters," in Proc. Hybrid Syst.: Comput. Control, 2005, vol.LNCS, 3414, pp. 184-197.
19. A. Beccuti, G. Papafotiou, and M. Morari, "Explicit model predictive control of the boost dc-dc converter," in Proc. Anal. Design Hybrid Syst., 2006, pp. 315-320.
20. P. Tabuada, "An approximate simulation approach to symbolic control," IEEE Trans. Autom. Control, vol.53, no.6, pp. 1406-1418, Jun. 2008.
21. R. Alur, T. Henzinger, and G. Pappas, "Discrete abstractions of hybrid systems," Proc. IEEE, vol.88, pp. 971-984, 2000.
22. P. Tabuada, "Symbolic models for control systems," Acta Informatica, vol.43, no.7, pp. 477-500, 2008.