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An Introduction to Hybrid Automata

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Handbook of Networked and Embedded Control Systems

Part of the book series: Control Engineering ((CONTRENGIN))

Hybrid systems are digital real-time systems embedded in analog environments. A paradigmatic example of a hybrid system is a digital embedded control program for an analog plant environment, like a furnace or an airplane: the controller state moves discretely between control modes, and in each control mode, the plant state evolves continuously according to physical laws. Those systems combine discrete and continuous dynamics. Those aspects have been studied in computer science and in control theory. Computer scientists have introduced hybrid automata [28], a formal model that combines discrete control graphs, usually called finite state automata, with continuously evolving variables. A hybrid automaton exhibits two kinds of state changes: discrete jump transitions occur instantaneously, and continuous flow transitions occur when time elapses.

This chapter is organized as follows. First, we introduce the syntax and semantics of hybrid automata, and show how complex hybrid systems can be modeled compositionally as products of hybrid automata. Then, we define safety properties of hybrid automata and show how to model them using monitors. We show that the verification of those properties reduces naturally to reachability problems, that is, to decide if there exists a trajectory of the hybrid system that reaches a given set of states. As hybrid automata can be very complex mathematical objects, restricted subclasses for which we have automatic analysis methods have been introduced. In this introduction, we focus on rectangular hybrid automata and show how they can be used to overapproximate the behavior of more complex hybrid automata. We close the chapter by referencing the literature to allow the reader into go deeper into this flourishing research subject.

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Author information

Authors and Affiliations

  1. Computer Science Department, University of Brussels, Belgium

    Jean-François Raskin

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  1. Jean-François Raskin
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Editors and Affiliations

  1. Department of Applied Informatics, University of Macedonia, Thessaloniki, 54006, Greece

    Dimitrios Hristu-Varsakelis

  2. Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, 20742, USA

    William S. Levine

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© 2005 Birkhäuser Boston

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Raskin, JF. (2005). An Introduction to Hybrid Automata. In: Hristu-Varsakelis, D., Levine, W.S. (eds) Handbook of Networked and Embedded Control Systems. Control Engineering. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4404-0_21

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  • DOI: https://doi.org/10.1007/0-8176-4404-0_21

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3239-7

  • Online ISBN: 978-0-8176-4404-8

  • eBook Packages: EngineeringEngineering (R0)

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