Communicating Embedded Systems: Software and Design

Chapter 7

Tools for the Analysis of Hybrid Models ¹

7.1. Introduction

Complex control systems that interact with an external physical environment generally consist of heterogenous components such as software, analog or digital hardware, sensors, and actuators. Mathematical models of such systems and of the external environment are necessary during the design phase: these models make it possible to explore the behavior resulting from the interaction between the controller and the environment, either analytically or by simulation.

Hybrid systems are the result of the composition of the two most commonly used models of dynamical systems: continuous dynamical systems defined by differential equations, and discrete event systems defined by automata, Petri nets, etc. Continuous models are particularly well suited to the “physical” sciences, whereas discrete models are natural abstractions for software or digital hardware. Research on hybrid systems deals with models that combine discrete and continuous dynamics, and, in the last two decades, has attempted to extend analysis methods specific to each type of dynamics in order to study the dynamics of the complete system.

A promising approach, reachability analysis, combines ideas borrowed from algorithmic verification of discrete systems (model-checking) and from numerical simulation of continuous systems. This approach, which uses graph exploration techniques, numerical analysis and computational geometry, makes it possible to compute ...