Skip to main content
SpringerLink
Log in

Lazy Abstraction-Based Controller Synthesis

  • Conference paper
  • First Online:
Automated Technology for Verification and Analysis (ATVA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,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.

This research was sponsored in part by the DFG project 389792660-TRR 248 and by the ERC Grant Agreement 610150 (ERC Synergy Grant ImPACT). Kyle Hsu was funded by a DAAD-RISE scholarship.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    One can design an enumerative forward algorithm for controller synthesis, essentially as a backtracking search of an AND-OR tree [9], but dynamical perturbations greatly increase the width of the tree. Experimentally, this leads to poor performance in control examples.

  2. 2.

    This implicitly assumes that sampling times and grid sizes are such that no “holes” occur between consecutive cells visited by a trajectory. This can be formalized by assumptions on the growth rate of f in (1) which is beyond the scope of this paper.

  3. 3.

    We write with , as short for .

  4. 4.

    Available at http://mascot.mpi-sws.org/.

References

  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. 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. 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)

    Article  Google Scholar 

  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_16

    Chapter  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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. Cámara, J., Girard, A., Gössler, G.: Synthesis of switching controllers using approximately bisimilar multiscale abstractions. In: HSCC, pp. 191–200 (2011)

    Google Scholar 

  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_3

    Chapter  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. de Alfaro, L., Roy, P.: Solving games via three-valued abstraction refinement. Inf. Comput. 208(6), 666–676 (2010)

    Article  MathSciNet  Google Scholar 

  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. Fribourg, L., Kühne, U., Soulat, R.: Finite controlled invariants for sampled switched systems. Form. Methods Syst. Des. 45(3), 303–329 (2014)

    Article  Google Scholar 

  15. Girard, A.: Towards a multiresolution approach to linear control. TAC 51(8), 1261–1270 (2006)

    MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  17. Girard, A., Pola, G., Tabuada, P.: Approximately bisimilar symbolic models for incrementally stable switched systems. TAC 55(1), 116–126 (2010)

    MathSciNet  MATH  Google Scholar 

  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. Grüne, L.: An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation. Numer. Math. 75(3), 319–337 (1997)

    Article  MathSciNet  Google Scholar 

  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_69

    Chapter  Google Scholar 

  21. Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Lazy abstraction. ACM SIGPLAN Not. 37(1), 58–70 (2002)

    Article  Google Scholar 

  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_71

    Chapter  Google Scholar 

  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. Hsu, K., Majumdar, R., Mallik, K., Schmuck, A.-K.: Lazy abstraction-based controller synthesis. arXiv preprint arXiv:1804.02722 (2018)

  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. 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. 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. 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_76

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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_34

    Chapter  Google Scholar 

  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. Nilsson, P., et al.: Correct-by-construction adaptive cruise control: two approaches. IEEE Trans. Contr. Sys. Techn. 24(4), 1294–1307 (2016)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  34. Pola, G., Borri, A., Di Benedetto, M.D.: Integrated design of symbolic controllers for nonlinear systems. TAC 57(2), 534–539 (2012)

    MathSciNet  MATH  Google Scholar 

  35. Reissig, G., Weber, A., Rungger, M.: Feedback refinement relations for the synthesis of symbolic controllers. TAC 62(4), 1781–1796 (2017)

    MathSciNet  MATH  Google Scholar 

  36. Rungger, M., Stursberg, O.: On-the-fly model abstraction for controller synthesis. In: ACC, pp. 2645–2650. IEEE (2012)

    Google Scholar 

  37. Rungger, M., Zamani, M.: SCOTS: a tool for the synthesis of symbolic controllers. In: HSCC, pp. 99–104. ACM (2016)

    Google Scholar 

  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. Tabuada, P.: Verification and Control of Hybrid Systems: A Symbolic Approach. Springer, Heidelberg (2009). https://doi.org/10.1007/978-1-4419-0224-5

    Book  MATH  Google Scholar 

  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. 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 

Download references

Author information

Authors and Affiliations

  1. University of Toronto, Toronto, Canada

    Kyle Hsu

  2. MPI-SWS, Kaiserslautern, Germany

    Rupak Majumdar, Kaushik Mallik & Anne-Kathrin Schmuck

Authors
  1. Kyle Hsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rupak Majumdar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kaushik Mallik
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Anne-Kathrin Schmuck
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rupak Majumdar .

Editor information

Editors and Affiliations

  1. Institute of Information Science, Academia Sinica, Taipei, Taiwan

    Yu-Fang Chen

  2. DENSO AUTOMOTIVE Deutschland GmbH, Eching, Germany

    Chih-Hong Cheng

  3. Institute of Computer Science, TU München, Munich, Germany

    Javier Esparza

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Hsu, K., Majumdar, R., Mallik, K., Schmuck, AK. (2019). Lazy Abstraction-Based Controller Synthesis. In: Chen, YF., Cheng, CH., Esparza, J. (eds) Automated Technology for Verification and Analysis. ATVA 2019. Lecture Notes in Computer Science(), vol 11781. Springer, Cham. https://doi.org/10.1007/978-3-030-31784-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-31784-3_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-31783-6

  • Online ISBN: 978-3-030-31784-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation