|
Vol: 50(64) No: 1 / March 2005 On the Control Problem in a Hybrid Systems Class Virginia Ecaterina Oltean Faculty of Control and Computers, "Politehnica" University of Bucharest, Spl.Independentei 313, 77206 Bucharest, Romania, e-mail: ecaterina_oltean@yahoo.com Keywords: discrete event system, hybrid system, supervisory control, switching control law. Abstract Hybrid systems result from the integration of time-driven dynamics with event-driven dynamics. In a class of hybrid supervision systems (HSS), a continuous plant is controlled, through an interface, by a logical discrete event system (DES). Based upon a state space partition, the plant coupled to the interface is abstracted to a DES-plant automaton and the DES controller can be synthesized by adapting results from the Supervisory Control Theory of Ramadge and Wonham. Starting from a HSS model firstly proposed by the ISIS Group, the paper introduces an algorithm for the design of the DES controller. The formal model description is systematically reconsidered and the control problem is comparatively formulated both at the continuous-time and discrete event levels. Some challenges related to the extraction of the DES-plant model are overviewed. References [1] C. G. Cassandras and S. Lafortune, “Discrete event systems: the state of the art and new directionsâ€, Applied and Computational Control, Signals and Circuits, vol.1, pp. 83-148, 1999. [2] P. J. Ramadge and W.M. Wonham, “The control of discrete event systemsâ€, Proc. of the IEEE, vol. 77(1), pp. 81-98, 1989. [3] R. Alur, C. Courcoubetis, N. Halbwachs, T. A. Henzinger, P. H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine, “The algorithmic analysis of hybrid systemsâ€, Theoretical Comp. Science, Elsevier, vol. 138, pp. 3-34, 1995. [4] V. I. Utkin, “Variable structure systems with sliding modesâ€, IEEE Trans. on AC, vol. 22(2), pp. 212-222, 1977. [5] A. Nerode and W. Kohn, “Models for hybrid systems: automata, topologies, controllability, observabilityâ€, in Hybrid Systems, vol. 736 of LNCS, pp. 317-356, 1995. [6] P. J. Antsaklis and A. Nerode, “Hybrid control systems: an introductory discussion to the special issueâ€, IEEE Trans. on AC, vol. 43(4), pp. 457-460, 1998. [7] B. H. Krogh and L. Chutinan, “Hybrid systems: modeling and supervisory controlâ€, in Advances in control: highlights of ECC’99, Springer Verlag (Ed. Frank P.M.), pp. 227-246, 1999. [8] J. A. Stiver and P. J. Antsaklis, “State space partitioning for a class of hybrid control systemsâ€, Proc. of the American Control Conference, San Francisco, CA, USA, vol. F, pp. 2303-2304, 1993. [9] J. A. Stiver, P. J. Antsaklis, and M. D. Lemmon, “A logical DES approach to the design of hybrid control systemsâ€, Technical Report of the ISIS Group at the University of Notre Dame, ISIS-94-011, 1994. [10] J. A. Stiver, X. D. Koutsoukos, and P.J. Antsaklis, “An invariant based approach to the design of hybrid control systemsâ€, Technical Report of the ISIS Group at the University of Notre Dame, ISIS-222-001, 2000. [11] R. Kumar, Modelling and Control of Logical Discrete Event Systems, Kluwer Academic Publishers, Norwell, USA, 1995. [12] V. E. Oltean, “The observability concept in a class of hybrid control systemsâ€, Rev. Roum. Sci. Techn.-Électr.-Énerg., vol. 44(3), pp. 363-367, 1999. [13] V. E. Oltean, “Hybrid control systems - basic problems and trendsâ€, Rev. Roum. Sci. Techn.-Électr.-Énerg., vol. 46(2), pp. 225-238, 2001. [14] V. E. Oltean, Th. Borangiu, and M. Manu, “The supervision of hybrid control systems - a layered architectureâ€, in Computer Aided Systems Theory, vol. 1798 of LNCS, pp. 573-587, 2000. |