Numerical analysis: 4th ed
Reliable solution of special event location problems for ODEs
ACM Transactions on Mathematical Software (TOMS)
State event location in differential-algebraic models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
An Overview of Hybrid Simulation Phenomena and Their Support by Simulation Packages
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Accurate Event Detection for Simulating Hybrid Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
On the stability of zeno equilibria
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Operational semantics of hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Impulse differential inclusions driven by discrete measures
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
A core language for executable models of cyber physical systems: work in progress report
ACM SIGBED Review - Work-in-Progress (WiP) Session of the 2nd International Conference on Cyber Physical Systems
On the stability of zeno equilibria
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
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In this paper we propose a technique to extend the simulation 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 practical to exactly simulate a Zeno hybrid system. Therefore, we propose a method for constructing approximations of Zeno models by leveraging the completed hybrid system model. Using these approximation, we can simulate a Zeno hybrid system model beyond its Zeno point and reveal the complete dynamics of the system being modeled.