Real-Time Systems

, Volume 53, Issue 3, pp 327–353 | Cite as

Timed-automata abstraction of switched dynamical systems using control invariants

  • Patricia Bouyer
  • Nicolas Markey
  • Nicolas Perrin
  • Philipp Schlehuber-Caissier
Article

Abstract

The development of formal methods for control design is an important challenge with potential applications in a wide range of safety-critical cyber-physical systems. Focusing on switched dynamical systems, we propose a new abstraction, based on time-varying regions of invariance (control funnels), that models behaviors of systems as timed automata. The main advantage of this method is that it allows for the automated verification and reactive controller synthesis without discretizing the evolution of the state of the system. Efficient and analytic constructions are possible in the case of linear dynamics whereas bounding funnels with conjectured properties based on numerical simulations can be used for general nonlinear dynamics. We demonstrate the potential of our approach with three examples.

Keywords

Switched dynamical systems Timed automata Cyber-physical systems 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Patricia Bouyer
    • 1
  • Nicolas Markey
    • 1
  • Nicolas Perrin
    • 2
    • 3
  • Philipp Schlehuber-Caissier
    • 2
  1. 1.LSV – CNRS & ENS CachanUniversité Paris-SaclayCachanFrance
  2. 2.Sorbonne Universités, UPMC Univ Paris 06, UMR 7222, ISIRParisFrance
  3. 3.CNRS, UMR 7222, ISIRParisFrance

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