Summary: Beyond Zeno: Get on with it!
Haiyang Zheng, Edward A. Lee, and Aaron D. Ames
Center for Hybrid and Embedded Software Systems (CHESS)
Department of Electrical Engineering and Computer Sciences
University of California, Berkeley, 94720, U.S.A.
Abstract. In this paper we propose a technique to extend the sim-
ulation of a Zeno hybrid system beyond its Zeno time point. A Zeno
hybrid system model is a hybrid system with an execution that takes
an infinite number of discrete transitions during a finite time interval.
We argue that the presence of Zeno behavior indicates that the hybrid
system model is incomplete by considering some classical Zeno models
that incompletely describe the dynamics of the system being modeled.
This motivates the systematic development of a method for completing
hybrid system models through the introduction of new post-Zeno states,
where the completed hybrid system transitions to these post-Zeno states
at the Zeno time point. In practice, simulating a Zeno hybrid system
is challenging in that simulation effectively halts near the Zeno time
point. Moreover, due to unavoidable numerical errors, it is not practi-