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Lazy Abstraction-Based Controller Synthesis

  • Kyle Hsu
  • Rupak MajumdarEmail author
  • Kaushik Mallik
  • Anne-Kathrin Schmuck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11781)

Abstract

Abstraction-based controller synthesis (ABCS) is a general procedure for automatic synthesis of controllers for continuous-time nonlinear dynamical systems against temporal specifications. ABCS works by first abstracting a time-sampled version of the continuous dynamics of the open-loop system by a symbolic finite state model.

References

  1. 1.
    Ames, A.D., et al.: First steps toward formal controller synthesis for bipedal robots. In: Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control, pp. 209–218. ACM (2015)Google Scholar
  2. 2.
    Gol, E.A., Lazar, M., Belta, C.: Language-guided controller synthesis for discrete-time linear systems. In: HSCC, pp. 95–104. ACM (2012)Google Scholar
  3. 3.
    Beyer, D., Henzinger, T.A., Jhala, R., Majumdar, R.: The software model checker blast. Int. J. Softw. Tools Technol. Transf. 9(5–6), 505–525 (2007)CrossRefGoogle Scholar
  4. 4.
    Beyer, D., Keremoglu, M.E.: CPAchecker: a tool for configurable software verification. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 184–190. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22110-1_16CrossRefGoogle Scholar
  5. 5.
    Borri, A., Dimarogonas, D.V., Johansson, K.H., Di Benedetto, M.D., Pola, G.: Decentralized symbolic control of interconnected systems with application to vehicle platooning. IFAC Proc. Vol. 46(27), 285–292 (2013)CrossRefGoogle Scholar
  6. 6.
    Bulancea, O.L., Nilsson, P., Ozay, N.: Nonuniform abstractions, refinement and controller synthesis with novel BDD encodings. arXiv preprint arXiv:1804.04280 (2018)
  7. 7.
    Cámara, J., Girard, A., Gössler, G.: Safety controller synthesis for switched systems using multi-scale symbolic models. In: CDC, pp. 520–525 (2011)Google Scholar
  8. 8.
    Cámara, J., Girard, A., Gössler, G.: Synthesis of switching controllers using approximately bisimilar multiscale abstractions. In: HSCC, pp. 191–200 (2011)Google Scholar
  9. 9.
    Cassez, F.: Efficient on-the-fly algorithms for partially observable timed games. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 5–24. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-75454-1_3CrossRefzbMATHGoogle Scholar
  10. 10.
    Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. J. ACM 50(5), 752–794 (2003)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Coogan, S., Arcak, M.: Efficient finite abstraction of mixed monotone systems. In: Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control, pp. 58–67. ACM (2015)Google Scholar
  12. 12.
    de Alfaro, L., Roy, P.: Solving games via three-valued abstraction refinement. Inf. Comput. 208(6), 666–676 (2010)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Fribourg, L., Kühne, U., Soulat, R.: Constructing attractors of nonlinear dynamical systems. In: OASIcs-OpenAccess Series in Informatics, vol. 31. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2013)Google Scholar
  14. 14.
    Fribourg, L., Kühne, U., Soulat, R.: Finite controlled invariants for sampled switched systems. Form. Methods Syst. Des. 45(3), 303–329 (2014)CrossRefGoogle Scholar
  15. 15.
    Girard, A.: Towards a multiresolution approach to linear control. TAC 51(8), 1261–1270 (2006)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Girard, A., Gössler, G., Mouelhi, S.: Safety controller synthesis for incrementally stable switched systems using multiscale symbolic models. TAC 61(6), 1537–1549 (2016)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Girard, A., Pola, G., Tabuada, P.: Approximately bisimilar symbolic models for incrementally stable switched systems. TAC 55(1), 116–126 (2010)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Gruber, F., Kim, E.S., Arcak, M.: Sparsity-aware finite abstraction. In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC), pp. 2366–2371. IEEE (2017)Google Scholar
  19. 19.
    Grüne, L.: An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation. Numer. Math. 75(3), 319–337 (1997)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Henzinger, T.A., Jhala, R., Majumdar, R.: Counterexample-guided control. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 886–902. Springer, Heidelberg (2003).  https://doi.org/10.1007/3-540-45061-0_69CrossRefGoogle Scholar
  21. 21.
    Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Lazy abstraction. ACM SIGPLAN Not. 37(1), 58–70 (2002)CrossRefGoogle Scholar
  22. 22.
    Herbreteau, F., Srivathsan, B., Walukiewicz, I.: Lazy abstractions for timed automata. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 990–1005. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-39799-8_71CrossRefGoogle Scholar
  23. 23.
    Hsu, K., Majumdar, R., Mallik, K., Schmuck, A.-K.: Lazy abstraction-based control for safety specifications. In: 2018 IEEE Conference on Decision and Control (CDC), pp. 4902–4907. IEEE (2018)Google Scholar
  24. 24.
    Hsu, K., Majumdar, R., Mallik, K., Schmuck, A.-K.: Lazy abstraction-based controller synthesis. arXiv preprint arXiv:1804.02722 (2018)
  25. 25.
    Hsu, K., Majumdar, R., Mallik, K., Schmuck, A.-K.: Multi-layered abstraction-based controller synthesis for continuous-time systems. In: HSCC, pp. 120–129. ACM (2018)Google Scholar
  26. 26.
    Khaled, M., Zamani, M.: pFaces: an acceleration ecosystem for symbolic control. In: Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control, pp. 252–257. ACM (2019)Google Scholar
  27. 27.
    Li, Y., Liu, J.: ROCS: a robustly complete control synthesis tool for nonlinear dynamical systems. In: HSCC, pp. 130–135. ACM (2018)Google Scholar
  28. 28.
    Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 229–242. Springer, Heidelberg (1995).  https://doi.org/10.1007/3-540-59042-0_76CrossRefGoogle Scholar
  29. 29.
    Mallik, K., Schmuck, A.-K., Soudjani, S., Majumdar, R.: Compositional synthesis of finite-state abstractions. IEEE Trans. Autom. Control 64(6), 2629–2636 (2018)MathSciNetCrossRefGoogle Scholar
  30. 30.
    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).  https://doi.org/10.1007/978-3-540-71493-4_34CrossRefGoogle Scholar
  31. 31.
    Mouelhi, S., Girard, A., Gössler, G.: CoSyMA: a tool for controller synthesis using multi-scale abstractions. In: HSCC, pp. 83–88. ACM (2013)Google Scholar
  32. 32.
    Nilsson, P., et al.: Correct-by-construction adaptive cruise control: two approaches. IEEE Trans. Contr. Sys. Techn. 24(4), 1294–1307 (2016)CrossRefGoogle Scholar
  33. 33.
    Nilsson, P., Ozay, N., Liu, J.: Augmented finite transition systems as abstractions for control synthesis. Discret. Event Dyn. Syst. 27(2), 301–340 (2017)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Pola, G., Borri, A., Di Benedetto, M.D.: Integrated design of symbolic controllers for nonlinear systems. TAC 57(2), 534–539 (2012)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Reissig, G., Weber, A., Rungger, M.: Feedback refinement relations for the synthesis of symbolic controllers. TAC 62(4), 1781–1796 (2017)MathSciNetzbMATHGoogle Scholar
  36. 36.
    Rungger, M., Stursberg, O.: On-the-fly model abstraction for controller synthesis. In: ACC, pp. 2645–2650. IEEE (2012)Google Scholar
  37. 37.
    Rungger, M., Zamani, M.: SCOTS: a tool for the synthesis of symbolic controllers. In: HSCC, pp. 99–104. ACM (2016)Google Scholar
  38. 38.
    Saoud, A., Girard, A., Fribourg, L.: Contract based design of symbolic controllers for vehicle platooning. In: HSCC, pp. 277–278. ACM (2018)Google Scholar
  39. 39.
    Tabuada, P.: Verification and Control of Hybrid Systems: A Symbolic Approach. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-1-4419-0224-5CrossRefzbMATHGoogle Scholar
  40. 40.
    Vizel, Y., Grumberg, O., Shoham, S.: Lazy abstraction and sat-based reachability in hardware model checking. In: FMCAD, pp. 173–181. IEEE (2012)Google Scholar
  41. 41.
    Hussien, O., Tabuada, P.: Lazy controller synthesis using three-valued abstractions for safety and reachability specifications. In: CDC 2018, pp. 3567–3572 (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kyle Hsu
    • 1
  • Rupak Majumdar
    • 2
    Email author
  • Kaushik Mallik
    • 2
  • Anne-Kathrin Schmuck
    • 2
  1. 1.University of TorontoTorontoCanada
  2. 2.MPI-SWSKaiserslauternGermany

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