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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 850789, 5 pages
Research Article

Approximate Equivalence of the Hybrid Automata with Taylor Theory

1Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu 610041, China
2Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Guangxi 530006, China
3Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China

Received 26 January 2014; Revised 7 April 2014; Accepted 22 April 2014; Published 11 May 2014

Academic Editor: Guiming Luo

Copyright © 2014 Anping He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Hybrid automaton is a formal model for precisely describing a hybrid system in which the computational processes interact with the physical ones. The reachability analysis of the polynomial hybrid automaton is decidable, which makes the Taylor approximation of a hybrid automaton applicable and valuable. In this paper, we studied the simulation relation among the hybrid automaton and its Taylor approximation, as well as the approximate equivalence relation. We also proved that the Taylor approximation simulates its original hybrid automaton, and similar hybrid automata could be compared quantitatively, for example, the approximate equivalence we proposed in the paper.