Skip to main content

Safety Guarantees for Hybrid Systems

  • Living reference work entry
  • First Online:
Encyclopedia of Systems and Control

Abstract

Hybrid systems describe processes that typically need to satisfy a set of strict physical, computation, and communication constraints. Mission-critical and time-critical cyber-physical systems are a prime example where these constraints play a key role in analysis, controller synthesis, and implementation. On top of classical notions such as stability, safety plays a major role in the control design of hybrid systems. There is a long history of methods related to the safety analysis and safety enforcement for dynamical systems, with the ones concerning linear systems being more mature than the others. Due to the importance and complexity of the underlying problem, several different techniques have been developed for hybrid systems. This entry summarizes the most important approaches and tools, together with references for further reading.

R.J. and N.A. are supported by the CHIST-ERA 2018 project DRUID-NET “Edge Computing Resource Allocation for Dynamic Networks”

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Bibliography

  • Ahmadi AA, Majumdar A (2014) DSOS and SDSOS optimization: LP and SOCP-based alternatives to sum of squares optimization. In: 2014 48th annual conference on information sciences and systems (CISS). IEEE, pp 1–5

    Google Scholar 

  • Alur R (2011) Formal verification of hybrid systems. In: 2011 proceedings of the ninth ACM international conference on embedded software (EMSOFT). IEEE, pp 273–278

    Google Scholar 

  • Alur R, Dill DL (1994) A theory of timed automata. Theor Comput Sci 126(2):183–235

    Article  MathSciNet  Google Scholar 

  • Alur R, Henzinger TA, Lafferriere G, Pappas GJ (2000) Discrete abstractions of hybrid systems. Proc IEEE 88(7):971–984

    Article  Google Scholar 

  • Athanasopoulos N, Jungers RM (2018) Combinatorial methods for invariance and safety of hybrid systems. Automatica 98:130–140

    Article  MathSciNet  Google Scholar 

  • Aubin JP, Bayen AM, Saint-Pierre P (2011) Viability theory: new directions. Springer, Heidelber/Dordrecht/London/New York

    Book  Google Scholar 

  • Belta C, Yordanov B, Gol EA (2017) Formal methods for discrete-time dynamical systems. In: Studies in systems, decision and control. Springer, Heidelberg

    Book  Google Scholar 

  • Blanchini F, Miani S (2008) Set-theoretic methods in control. Birkhäuser, Boston

    Book  Google Scholar 

  • Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Calafiore GC, Campi MC (2006) The scenario approach to robust control design. IEEE Trans Autom Control 51:742–753

    Article  MathSciNet  Google Scholar 

  • Coogan S, Arcak M (2012) Guard synthesis for safety of hybrid systems using sum of squares programming. In: 2012 IEEE 51st annual conference on decision and control (CDC). IEEE, pp 6138–6143

    Google Scholar 

  • De Santis E, Di Benedetto MD, Berardi L (2004) Computation of maximal safe sets for switching systems. IEEE Trans Autom Control 49(2):184–195

    Article  MathSciNet  Google Scholar 

  • Doyen L, Frehse G, Pappas GJ, Platzer A (2018) Verification of hybrid systems. In: Handbook of model checking. Springer, Cham, pp 1047–1110

    Chapter  Google Scholar 

  • Fukuda K (2004) Frequently asked questions in polyhedral computation. Technical report, Swiss Federal Institute of Technology

    Google Scholar 

  • Girard A (2005) Reachability of uncertain linear systems using zonotopes. In: Proceedings of the international workshop on hybrid systems: computation and control, pp 291–305

    Chapter  Google Scholar 

  • Goebel R, Sanfelice RG, Teel AR (2012) Hybrid dynamical systems: modeling stability, and robustness. Princeton University Press, Princeton

    Book  Google Scholar 

  • Haghverdi E, Tabuada P, Pappas GJ (2005) Bisimulation relations for dynamical, control, and hybrid systems. Theor Comput Sci 342(2–3):229–261

    Article  MathSciNet  Google Scholar 

  • Heemels WP, De Schutter B, Bemporad A (2001) Equivalence of hybrid dynamical models. Automatica 37:1085–1091

    Article  Google Scholar 

  • Henrion D, Korda M (2014) Convex computation of the region of attraction of polynomial control systems. IEEE Trans Autom Control 59(2):297–312

    Article  MathSciNet  Google Scholar 

  • Julius AA, Pappas GJ (2008) Probabilistic testing for stochastic hybrid systems. In: 2008 47th IEEE conference on decision and control. IEEE, pp 4030–4035

    Google Scholar 

  • Jungers R (2009) The joint spectral radius: theory and applications, vol 385. Springer Science & Business Media, Berlin

    Book  Google Scholar 

  • Katoen JP (2016) The probabilistic model checking landscape. In: Proceedings of the 31st annual ACM/IEEE symposium on logic in computer science. ACM, pp 31–45

    Google Scholar 

  • Kenanian J, Balkan A, Jungers RM, Tabuada P (2019) Data driven stability analysis of black-box switched linear systems. Automatica, 109, p. 108533

    Article  MathSciNet  Google Scholar 

  • Legat B, Tabuada P, Jungers RM (2018) Computing controlled invariant sets for hybrid systems with applications to model-predictive control. arxiv preprint: https://arxivorg/abs/180204522

    Google Scholar 

  • Maghenem M, Sanfelice RG (2019) Characterizations of safety in hybrid inclusions via barrier functions. In: 22nd ACM international workshop on hybrid systems: computation and control, pp 109–118

    Google Scholar 

  • Parrilo PA (2000) Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Ph.D. thesis, California Institute of Technology

    Google Scholar 

  • Philippe M, Athanasopoulos N, Angeli D, Jungers RM (2019) On path-complete lyapunov functions: geometry and comparison. IEEE Trans Autom Control 64:1947–1957

    Article  MathSciNet  Google Scholar 

  • Pnueli A (1977) The temporal logic of programs. In: 18th annual symposium on foundations of computer science (sfcs 1977). IEEE, pp 46–57

    Google Scholar 

  • Prajna S, Jadbabaie A (2004) Safety verification of hybrid systems using barrier certificates. In: International workshop on hybrid systems: computation and control. Springer, Berlin, pp 477–492

    Chapter  Google Scholar 

  • Sloth C, Pappas GJ, Wisniewski R (2012) Compositional safety analysis using barrier certificates. In: International workshop on hybrid systems: computation and control, pp 15–24

    Google Scholar 

  • Tomlin CJ, Mitchell I, Bayen AM, Oishi M (2003) Computational techniques for the verification of hybrid systems. Proc IEEE 91(7):986–1001

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Raphael M. Jungers .

Editor information

Editors and Affiliations

Section Editor information

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer-Verlag London Ltd., part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Jungers, R.M., Athanasopoulos, N. (2020). Safety Guarantees for Hybrid Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_100049-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_100049-1

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics