Distributed Synthesis of State-Dependent Switching Control

  • Adrien Le Coënt
  • Laurent Fribourg
  • Nicolas MarkeyEmail author
  • Florian De Vuyst
  • Ludovic Chamoin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9899)


We present a correct-by-design method of state-dependent control synthesis for linear discrete-time switching systems. Given an objective region R of the state space, the method builds a capture set S and a control which steers any element of S into R. The method works by iterated backward reachability from R. More precisely, S is given as a parametric extension of R, and the maximum value of the parameter is solved by linear programming. The method can also be used to synthesize a stability control which maintains indefinitely within R all the states starting at R. We explain how the synthesis method can be performed in a distributed manner. The method has been implemented and successfully applied to the synthesis of a distributed control of a concrete floor heating system with 11 rooms and \(2^{11}=2048\) switching modes.


Heat Transfer Coefficient Control Synthesis Symbolic State Parametric Extension Control Pattern 
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  1. 1.
    Alur, R., Henzinger, T.A.: Reactive modules. Formal Methods Syst. Des. 15(1), 7–48 (1999)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Asarin, E., Bournez, O., Dang, T., Maler, O., Pnueli, A.: Effective synthesis of switching controllers for linear systems. Proc. IEEE 88(7), 1011–1025 (2000)CrossRefGoogle Scholar
  3. 3.
    Fribourg, L., Kühne, U., Markey, N.: Game-based synthesis of distributed controllers for sampled switched systems. In: SynCoP 2015, OASIcs 44, pp. 48–62 (2015)Google Scholar
  4. 4.
    Fribourg, L., Kühne, U., Soulat, R.: Finite controlled invariants for sampled switched systems. Formal Methods Syst. Des. 45(3), 303–329 (2014)CrossRefzbMATHGoogle Scholar
  5. 5.
    Gillula, J.H., Hoffmann, G.M., Huang, H., Vitus, M.P., Tomlin, C.: Applications of hybrid reachability analysis to robotic aerial vehicles. Int. J. Rob. Res. 30(3), 335–354 (2011)CrossRefGoogle Scholar
  6. 6.
    Girard, A.: Low-complexity switching controllers for safety using symbolic models. In: ADHS 2012, pp. 82–87 (2012)Google Scholar
  7. 7.
    Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, Berlin (2001)CrossRefzbMATHGoogle Scholar
  8. 8.
    Kühne, U., Soulat, R.: Minimator 1.0 (2015).
  9. 9.
    Larsen, K.G., Mikučionis, M., Muñiz, M., Srba, J., Taankvist, J.H.: Online and compositional learning of controllers with application to floor heating. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 244–259. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49674-9_14 CrossRefGoogle Scholar
  10. 10.
    Le Coënt, A., Fribourg, L., Markey, N., De Vuyst, F., Chamoin, L.: Distributed synthesis of state-dependent switching control. Technical report, March 2016.
  11. 11.
    Le Coent, A., Alexandre Dit Sandretto, J., Chapoutot, A., Fribourg, L.: Control of nonlinear switched systems based on validated simulation. In: SNR 2016. IEEE (2016)Google Scholar
  12. 12.
    Liberzon, D.: Switching in Systems and Control. Springer, Berlin (2012)zbMATHGoogle Scholar
  13. 13.
    Meyer, P.-J., Girard, A., Witrant, E.: Safety control with performance guarantees of cooperative systems using compositional abstractions. In: ADHS 2015, pp. 317–322 (2015)Google Scholar
  14. 14.
    Mitchell, I.M.: Comparing forward and backward reachability as tools for safety analysis. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 428–443. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Adrien Le Coënt
    • 1
  • Laurent Fribourg
    • 2
  • Nicolas Markey
    • 2
    Email author
  • Florian De Vuyst
    • 1
  • Ludovic Chamoin
    • 3
  1. 1.CMLA, ENS Cachan, CNRS, Université Paris-SaclayCachan CedexFrance
  2. 2.LSV, ENS Cachan, CNRS, Université Paris-SaclayCachan CedexFrance
  3. 3.LMT, ENS Cachan, CNRS, Université Paris-SaclayCachan CedexFrance

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