On transfinite hybrid automata

Authors:
Katsunori Nakamura;Akira Fusaoka
Affiliations:
Department of Computer Science, Ritsumeikan University, Nojihigashi, Kusatsu-city, SIGA, Japan;Department of Computer Science, Ritsumeikan University, Nojihigashi, Kusatsu-city, SIGA, Japan
Venue:
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Year:
2005

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Abstract

In this paper, we propose a new method to deal with hybrid systems based on the concept of the nonstandard analysis and the Büchi's transfinite automata. An essential point of the method is a generalization of hybrid automata with hyperfinite iteration of an infinitesimal transition in * ℝ. This nonstandard model of hybrid automata allows discrete but hyperfinite state transition, so that we can describe and reason about the interaction of the continuous and discrete dynamics in the algebraic framework. In this enlarged perspective of the hybrid automata, we discuss about the asymptotic orbit of the dynamics that is peculiar to the hybrid systems such as Zeno.