Abstract
The problem is to develop concepts and theorems for equivalences of discrete-event systems and of hybrid systems.
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References
R. Alur and D.L. Dill. A theory of timed automata. Theoretical Computer Science, 126: 183–235, 1994.
J.C.M. Baeten and W.P. Weijland. Process algebra. Cambridge University Press, Cambridge, 1990.
V. Blondel and J. Tsitsiklis. Complexity of stability and controllability of elementary hybrid systems. To appear in Automatica. Report LIDS- P 2388, LIDS, Massachusetts Institute of Technology, Cambridge, MA, 1997.
L. Blum, F. Cucker, M. Shub, and S. Smale. Complexity and real computation. Springer, New York, 1997.
L. Blum, M. Shub, and S. Smale. On a theory of computation and complexity over the real numbers. Bull. Amer. Math. Soc., 21: 1–46, 1989.
N. Chomsky. Three models for the description of language. IRE Trans. Information Theory, 2: 113–124, 1956.
A. Church. Logic, arithmetic, and automata. In Proc. 1962 Internat. Congress of Math., pages 15–22, X, 1963. Mittag-Leffler Inst.
B. Dasgupta and E.D. Sontag. A polynomial-time algorithm for an equivalence problem which arises in hybrid system theory. In Proceedings of the Conference on Decision and Control, page to appear, New York, 1998. IEEE Press.
R. David and H. Alia. Petri nets and grafcet. Prentice Hall, New York, 1992.
S. Eilenberg. Automata, languages, and machines (Volumes A and B). Academic Press, New York, 1974, 1976.
T.A. Henzinger. Hybrid automata with finite bisimulations. In Z. Fiilop and F. Géseg, editors, ICALP95: Automata, languages, and programming, pages 324–335, Berlin, 1995. Springer-Verlag.
T.A. Henzinger, P.W. Kopke, A. Puri, and P. Varaiya. What’s decidable about hybrid automata. In X, editor, Proceedings of the 27th Annual Symposium on Theory of Computing, pages 373–382, X, 1995. ACM Press.
K. Krohn and J. Rhodes. Algebraic theory of machines. I. Prime decomposition theorem for finite semigroups and machines. Trans. Amer. Math. Soc., 116: 450–464, 1965.
R. Milner. Communication and concurrency. Prentice-Hall, Englewood Cliffs, NJ, 1989.
A. Overkamp. Supervisory control using failure semantics and partial specifications. IEEE Trans. Automatic Control, 42: 498–510, 1997.
P.J.G. Ramadge and W.M. Wonham. The control of discrete event systems. Proc. IEEE, 77: 81–98, 1989.
G. Rozenberg and A. Salomaa, editors. Handbook of formal languages, Volumes 1–3. Springer, Berlin, 1997.
M. Shayman and R. Kumar. Supervisory control of nondeterministic systems with driven events via prioritized synchronization and trajectory models. SIAM J. Control & Opt., 33: 469–497, 1995.
M. Sipser. Introduction to the theory of computation. PWS Publishing Company, Boston, 1997.
E.D. Sontag. On certain questions of rationality and decidability. J. Comp. Syst. Sci., 11: 375–381, 1975.
E.D. Sontag. Controllability is harder to decide than accessibility. SIAM J. Control & Opt., 26: 1106–1118, 1988.
E.D. Sontag. Mathematical control theory: Deterministic finite dimensional systems. Springer-Verlag, New York, 1990.
E.D. Sontag. From linear to nonlinear: Some complexity comparisons. In Proc. IEEE Conference on Decision and Control, pages 2916–2920, New York, 1995. IEEE Press.
L. Staiger. ω-languages. In G. Rozenberg and A. Salomaa, editors, Handbook of formal languages, pages 339–387. Springer, Berlin, 1997.
J.G. Thistle and W.M. Wonham. Control of infinite behavior of finite automata. SIAM J. Control & Opt., 32: 1075–1097, 1994.
W. Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of theoretical computer science, Volume B, pages 133–191. Elsevier Science Publishers B.V., Amsterdam, 1990.
J.N. Tsitsiklis. On the control of discrete-event systems. Math. Control Signals Systems, 2: 95–107, 1989.
J.H. van Schuppen. A sufficient condition for controllability of a class of hybrid systems. In T.A. Henzinger and S. Sastry, editors, Hybrid systems: Computation and control, number 1386 in Lecture Notes in Computer Science, pages 374–383, Berlin, 1998. Springer.
K.C. Wong and W.M. Wonham. Hierarchical control of discrete-event systems. J. Discrete Event Dynamics Systems, 6: 241–273, 1996.
Sheng Yu. Regular languages. In G. Rozenberg and A. Salomaa, editors, Handbook of formal languages, Volume 1, pages 41–110. Springer, Berlin, 1997.
H. Zhong and W.M. Wonham. On the consistency of hierarchical supervisors in discrete-event systems. IEEE Trans. Automatic Control, 35: 1125–1134, 1990.
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van Schuppen, J.H. (1999). Equivalences of discrete-event systems and of hybrid systems. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_47
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