This paper discusses an interpretation of hybrid systems as executable models. A specification of a hybrid system for this purpose can be viewed as a program in a domain-specific programming language. We describe the semantics of HyVisual, which is such a domain-specific programming language. The semantic properties of such a language affect our ability to understand, execute, and analyze a model. We discuss several semantic issues that come in defining such a programming language, such as the interpretation of discontinuities in continuous-time signals, and the interpretation of discrete-event signals in hybrid systems, and the consequences of numerical ODE solver techniques. We describe the solution in HyVisual by giving its operational semantics.

## Type of Work

Article (10) Book (0) Theses (0) Multimedia (0)

## Peer Review

Peer-reviewed only (8)

## Supplemental Material

Video (0) Audio (0) Images (0) Zip (0) Other files (0)

## Publication Year

## Campus

UC Berkeley (4) UC Davis (0) UC Irvine (1) UCLA (0) UC Merced (0) UC Riverside (0) UC San Diego (0) UCSF (0) UC Santa Barbara (0) UC Santa Cruz (0) UC Office of the President (2) Lawrence Berkeley National Laboratory (7) UC Agriculture & Natural Resources (0)

## Department

Research Grants Program Office (RGPO) (2)

## Journal

## Discipline

## Reuse License

BY - Attribution required (1)

## Scholarly Works (10 results)

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.