Abstract
The notion of dynamical consistency [3] is extended to hybrid systems so as to define the set of dynamically consistent hybrid partition machines associated with a continuous system S. After the presentation of some basic results on the algebraic structure of discrete partition machines, dynamical consistency is defined for hybrid systems, and the lattice HIBC(S) of hybrid in-block controllable partition machines is investigated. A sufficient condition for the existence of a non-trivial HIBC(S) is presented.
Work supported by NSERC grant A1329 and project B5 of NSERC-NCE-IRIS program.
Also affiliated with the Canadian Institute for Advanced Research.
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References
R. Brockett. Language driven hybrid systems. In Proceedings of the 33rd IEEE Conference on Decision and Control, pages 4210–4214, Lake Buena Vista, FL, 1994.
P. E. Caines and R. Ortega. The semi-lattice of piecewise constant controls for non-linear systems: A possible foundation for fuzzy control. To be presented at NOLCOS 95, Tahoe, CA, June 1995.
P.E. Caines and Y-J. Wei. The hierarchical lattices of a finite machine. To appear in System and Control Letters, 1995.
M. Glaum. Smooth partitions, transversality and graphs. Master's thesis, Department of Mathematics, The University of British Columbia, Vancouver, Canada, 1993.
R. Hermann and A. J. Krener. Nonlinear controllability and observability. IEEE Trans. on Automatic Control, AC-22(5):728–740, October 1977.
W. Kohn, J. James, and A. Nerode. A hybrid systems approach to integration of medical models. In Proceedings of the 33nd IEEE Conference on Decision and Control, pages 4247–4252, Lake Buena Vista, FL, 1994.
W. Kohn, A. Nerode, J. Remmel, and X. Ge. Multiple agent hybrid control: Carrier manifolds and chattering approximations to optimal control. In Proceedings of the 33nd IEEE Conference on Decision and Control, pages 4221–4227, Lake Buena Vista, FL, 1994.
E. J. McShane and T. A. Botts. Real Analysis. D. Van Nostrand Campany, Inc, Princeton, New Jersey.
A. Nerode and W. Kohn. Models for hybrid systems: Automata, topologies, stability. Technical report, Cornell University, Ithaca, NY, 1992.
J. A. Stiver and P.J. Antsaklis. On the controllability of hybrid control systems. In Proceedings of the 32nd IEEE Conference on Decision and Control, pages 294–299, San Antonio, Texas, 1993.
J. A. Stiver, P.J. Antsaklis, and M.D. Lemmon. Digital control from a hybrid perspective. In Proceedings of the 33rd IEEE Conference on Decision and Control, pages 4241–4246, Lake Buena Vista, FL, 1994.
Y-J Wei. Logic Control: Markovian Fragments, Hierarchy and Hybrid Systems. PhD thesis, Department of Electrical Engineering, McGill University, Montreal, Canada, 1995. in preparation.
Y-J. Wei and P.E. Caines. Lattice structure and hierarchical cocolog for finite machines. In Proceedings of the 33rd IEEE Conference in Decision and Control, pages 3125–3130, Lake Buena Vista,FL, December 1994.
W.M. Wonham. Towards an abstract internal model principle. IEEE Trans. on Systems, Man, and Cyberneics, SMC-6(11):735–739, November 1976.
J. Zabczyk. Mathematical Control Theory: An Introduction. Birkhäuser, Boston, USA, 1992.
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Caines, P.E., Wei, YJ. (1995). On dynamically consistent hybrid systems. In: Antsaklis, P., Kohn, W., Nerode, A., Sastry, S. (eds) Hybrid Systems II. HS 1994. Lecture Notes in Computer Science, vol 999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60472-3_5
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DOI: https://doi.org/10.1007/3-540-60472-3_5
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