Abstract
We consider hybrid systems as networks consisting of continuous input-output systems and discrete input-output automata. Some of the outputs may be connected to some of the inputs; the others server as the inputs and outputs of the hybrid system. We define a class of regular flows for such systems and make some remarks about them.
This research was supported in part by NASA grant NAG2-513 and NSF grant DMS 910-1089.
This research is supported in part by NSF grant DMS 910-1089.
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References
Z. Bartosiewicz, “Ordinary differential equations on real affine varieties,” Bulletin of the Polish Academy of Sciences: Mathematics, Volume 35, pp. 13–18, 1987.
Z. Bartosiewicz, “Minimal Polynomial Realizations,” Mathematics of Control, Signals, and Systems, Volume 1, pp. 227–237, 1988.
J. Glimm and A. Jaffe, Quantum Physics: A Functional Integral Point of View, Springer-Verlag, New York, 1981.
R. L. Grossman, “Path planning, persistent stores, and hybrid systems,” submitted for publication.
R. L. Grossman and R. G. Larson, “The realization of input-output maps using bialgebras, Forum Math., Volume 4, pp. 109–121, 1992.
R. L. Grossman and R. G. Larson, “Viewing hybrid systems as products of control systems and automata,” Proceedings of the 31st IEEE Conference on Decision and Control, IEEE Press, 1992.
R. L. Grossman and R. G. Larson, “A bialgebra approach to hybrid systems, submitted for publication.
R. L. Grossman and R. G. Larson, “Hybrid systems as free products of bialgebras, in preparation.
R. L. Grossman and D. E. Radford, “Bialgebra deformations of certain universal enveloping algebras,” Communications in Pure and Applied Algebra, to appear.
W. Kohn, “Declarative control theory,” AIAA GN & D Journal, February, 1989.
W. Kohn and A. Nerode, “Models for hybrid sysems: Automata, topologies and stability,” submitted for publication.
M. E. Sweedler, Hopf algebras, W. A. Benjamin, New York, 1969.
E. D. Sontag, Polynomial Response Maps, Lecture Notes in Control and Information Sciences, Volume 13, Springer-Verlag, New York, 1979.
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© 1993 Springer-Verlag Berlin Heidelberg
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Grossman, R.L., Larson, R.G. (1993). Some remarks about flows in hybrid systems. In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds) Hybrid Systems. HS HS 1992 1991. Lecture Notes in Computer Science, vol 736. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57318-6_36
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DOI: https://doi.org/10.1007/3-540-57318-6_36
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