## Abstract

This site is maintained by the Virtual Action Group on Hybrid Dynamic Systems. It intends to provide a convenient entry point into the world of combined continuous/discrete modeling and analysis. It compiles researchers who are active in the field, research projects that are underway, links to a number of selected papers and software, and it provides news about conferences, workshops, special issues, and the like. Any suggestions or comments to improve this site are more than welcome. For contributions please contact Xue Liu.

The virtual action group is part of the IEEE Control Systems Society Technical Committee on Computer Aided Control System Design. For additional information refer to the IEEE Technical Committee on Hybrid Dynamical Systems.

## Introduction

System models can be applied to efficiently design, analyze, and control physical processes. At times the detailed continuous physical behavior is the focus of study and other times discrete behaviors such as communication and synchronization is of main of interest. Continuous models have a unified description formalism in the form of differential equations, possibly supplemented by a set of algebraic constraints. Discrete modeling formalisms are more diverse but often can be captured by a state representation.

Physical processes are controlled by sophisticated control algorithms implemented in software on digital computers. Such embedded control systems combine continuous physical behavior with discrete control algorithms and are called hybrid systems. To achieve ever more rigorous safety and optimization constraints, and to handle the increasing complexity, an integrated hybrid systems formalism is required to model discrete and continuous aspects, as well as their interaction.

Another source of hybrid system behavior results from abstraction in continuous physical system models. Typically, a physical system operates on a hierarchy of temporal and spatial scales and at a given level, the more detailed behavior is not of interest to the modeler. Therefore, the behavior can be abstracted into a discontinuous change, resulting in hybrid system models as well.

When the continuous dimension of a hybrid system is time, system behavior has a direction of flow and covers the entire temporal interval of interest without gaps. This forms an important class of hybrid systems wich are called hybrid dynamic systems.

## Goals

System models can be applied to efficiently design, analyze, and control physical processes. At times the detailed continuous physical behavior is the focus of study and other times discrete behaviors such as communication and synchronization is of main of interest. Continuous models have a unified description formalism in the form of differential equations, possibly supplemented by a set of algebraic constraints. Discrete modeling formalisms are more diverse but often can be captured by a state representation.

Physical processes are controlled by sophisticated control algorithms implemented in software on digital computers. Such embedded control systems combine continuous physical behavior with discrete control algorithms and are called hybrid systems. To achieve ever more rigorous safety and optimization constraints, and to handle the increasing complexity, an integrated hybrid systems formalism is required to model discrete and continuous aspects, as well as their interaction. Another source of hybrid system behavior results from abstraction in continuous physical system models. Typically, a physical system operates on a hierarchy of temporal and spatial scales and at a given level, the more detailed behavior is not of interest to the modeler. Therefore, the behavior can be abstracted into a discontinuous change, resulting in hybrid system models as well.

When the continuous dimension of a hybrid system is time, system behavior has a direction of flow and covers the entire temporal interval of interest without gaps. This forms an important class of hybrid systems wich are called hybrid dynamic systems.