skip to main content
research-article

Automatic Synthesis of Switching Controllers for Linear Hybrid Systems: Reachability Control

Published:11 May 2017Publication History
Skip Abstract Section

Abstract

We consider the problem of computing the controllable region of a Linear Hybrid Automaton with controllable and uncontrollable transitions, w.r.t. a reachability objective. We provide an algorithm for the finite-horizon version of the problem, based on computing the set of states that must reach a given non-convex polyhedron while avoiding another one, subject to a polyhedral constraint on the slope of the trajectory. Experimental results are presented, based on an implementation of the proposed algorithm on top of the tool SpaceEx.

References

  1. R. Alur, T. A. Henzinger, and P.-H. Ho. 1996. Automatic symbolic verification of embedded systems. IEEE Trans. Softw. Eng. 22 (1996), 181--201. DOI:http://dx.doi.org/10.1109/32.489079 Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. E. Asarin, O. Bournez, T. Dang, O. Maler, and A. Pnueli. 2000. Effective synthesis of switching controllers for linear systems. Proc. IEEE 88, 7 (2000), 1011--1025. DOI:http://dx.doi.org/10.1109/5.871306 Google ScholarGoogle ScholarCross RefCross Ref
  3. R. Bagnara, P. M. Hill, and E. Zaffanella. 2008. The parma polyhedra library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Sci. Comput. Program. 72, 1--2 (2008), 3--21. DOI:http://dx.doi.org/10.1016/j.scico.2007.08.001 Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. A. Balluchi, L. Benvenuti, T. Villa, H. Wong-Toi, and A. Sangiovanni-Vincentelli. 2003. Controller synthesis for hybrid systems with a lower bound on event separation. Int. J. Control 76, 12 (2003), 1171--1200. DOI:http://dx.doi.org/10.1080/0020717031000123616 Google ScholarGoogle ScholarCross RefCross Ref
  5. M. Benerecetti and M. Faella. 2013. Tracking differentiable trajectories across polyhedra boundaries. In Proceedings of the 16th International Conference on Hybrid Systems Computation and Control (HSCC’13). ACM, 193--202. DOI:http://dx.doi.org/10.1145/2461328.2461360 Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. M. Benerecetti, M. Faella, and S. Minopoli. 2011a. Revisiting synthesis of switching controllers for linear hybrid systems. In Proceedings of the 50th IEEE Conference on Decision and Control. IEEE. Google ScholarGoogle ScholarCross RefCross Ref
  7. M. Benerecetti, M. Faella, and S. Minopoli. 2011b. Towards efficient exact synthesis for linear hybrid systems. In Proceedings of the 2nd International Symposium on Games, Automata, Logics, and Formal Verification (GandALF’11) (Electron. Proc. Theoret. Comput. Sci.), Vol. 54. DOI:http://dx.doi.org/10.4204/EPTCS.54.19 Google ScholarGoogle ScholarCross RefCross Ref
  8. M. Benerecetti, M. Faella, and S. Minopoli. 2012. Reachability games for linear hybrid systems. In Proceedings of the 15th International Conference of Hybrid Systems Computation and Control (HSCC’12). ACM, 65--74. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. M. Benerecetti, M. Faella, and S. Minopoli. 2013. Automatic synthesis of switching controllers for linear hybrid systems: Safety control. Theoret. Comput. Sci. 493 (2013), 116--138. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. P. Bouyer, T. Brihaye, and F. Chevalier. 2010. O-minimal hybrid reachability games. Logic. Methods Comput. Sci. 6 (2010). Google ScholarGoogle ScholarCross RefCross Ref
  11. N. V. Chernikova. 1968. Algorithm for discovering the set of all the solutions of a linear programming problem. U.S.S.R. Comput. Math. Math. Phys. 8, 6 (1968), 282--293. DOI:http://dx.doi.org/10.1016/0041-5553(68)90115-8 Google ScholarGoogle ScholarCross RefCross Ref
  12. L. de Alfaro, M. Faella, T. A. Henzinger, R. Majumdar, and M. Stoelinga. 2003. The element of surprise in timed games. In Proceedings of the 14th International Conference on Concurrency Theory (CONCUR’03) (Lect. Notes Comput. Sci.), Vol. 2761. Springer, 144--158. DOI:http://dx.doi.org/10.1007/978-3-540-45187-7_9 Google ScholarGoogle ScholarCross RefCross Ref
  13. L. de Alfaro, T. A. Henzinger, and R. Majumdar. 2001. Symbolic algorithms for infinite-state games. In Proceedings of the 12th International Conference on Concurrency Theory (CONCUR’01). (Lect. Notes Comput. Sci.). Springer. DOI:http://dx.doi.org/10.1007/3-540-44685-0_36 Google ScholarGoogle ScholarCross RefCross Ref
  14. G. Frehse, C. Le Guernic, A. Donzé, S. Cotton, R. Ray, O. Lebeltel, R. Ripado, A. Girard, T. Dang, and O. Maler. 2011. SpaceEx: Scalable verification of hybrid systems. In Proceedings of the 23rd Conference on Computer Aided Verification (CAV’11). 379--395. Google ScholarGoogle ScholarCross RefCross Ref
  15. L. C. G. J. M. Habets, P. J. Collins, and J. H. van Schuppen. 2006. Reachability and control synthesis for piecewise-affine hybrid systems on simplices. IEEE Trans. on Automatic Control 51, 6 (2006), 938--948. DOI:http://dx.doi.org/10.1109/TAC.2006.876952 Google ScholarGoogle ScholarCross RefCross Ref
  16. T. A. Henzinger. 1996. The theory of hybrid automata. In Proceedings of the 11th IEEE Symposium on Logic in Computer Science. 278--292. DOI:http://dx.doi.org/0.1109/LICS.1996.561342Google ScholarGoogle ScholarCross RefCross Ref
  17. T. A. Henzinger, B. Horowitz, and R. Majumdar. 1999. Rectangular hybrid games. In Proceedings of the 10th International Conference on Concurrency Theory (CONCUR’99) (Lect. Notes Comput. Sci.), Vol. 1664. Springer, 320--335. DOI:http://dx.doi.org/10.1007/3-540-48320-9_23 Google ScholarGoogle ScholarCross RefCross Ref
  18. T. A. Henzinger, P. W. Kopke, A. Puri, and P. Varaiya. 1995. What’s decidable about hybrid automata? In Proceedings of the 27th Annual ACM Symposium on Theory of Computing (STOC’95). ACM, 373--382. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. T. A. Henzinger, P. W. Kopke, A. Puri, and P. Varaiya. 1998. What’s decidable about hybrid automata? J. Comput. Syst. Sci. 57, 1 (1998), 94--124. DOI:http://dx.doi.org/10.1006/jcss.1998.1581 Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Z. Lin and M. E. Broucke. 2006. Resolving control to facet problems for affine hypersurface systems on simplices. In 45th IEEE Conference on Decision and Control. 2625--2630. DOI:http://dx.doi.org/10.1109/CDC.2006.377067 Google ScholarGoogle ScholarCross RefCross Ref
  21. J. Lygeros, C. Tomlin, and S. Sastry. 1999. Controllers for reachability specifications for hybrid systems. Automatica 35, 3 (1999), 349--370. DOI:http://dx.doi.org/10.1016/S0005-1098(98)00193-9 Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. O. Maler. 2002. Control from computer science. Ann. Rev. Control 26, 2 (2002), 175--187. DOI:http://dx.doi.org/10.1016/S1367-5788(02)00030-5 Google ScholarGoogle ScholarCross RefCross Ref
  23. O. Maler, A. Pnueli, and J. Sifakis. 1995. On the synthesis of discrete controllers for timed systems. In Proceedings of the 12th Annual Symposium on Theoretical Aspects of Computer Science (Lect. Notes Comput. Sci.), Vol. 900. Springer. DOI:http://dx.doi.org/10.1007/3-540-59042-0_76 Google ScholarGoogle ScholarCross RefCross Ref
  24. M. L. Minsky. 1967. Computation: Finite and Infinite Machines. Prentice-Hall, Inc., Upper Saddle River, NJ.Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. P. J. Ramadge and W. M. Wonham. 1987. Supervisory control of a class of discrete-event processes. SIAM J. Contr. Optim. 25 (1987), 206--230. DOI:http://dx.doi.org/10.1137/0325013 Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. A. Schrijver. 1986. Theory of Linear and Integer Programming. John Wiley and Sons.Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. C. J. Tomlin, J. Lygeros, and S. Shankar Sastry. 2000. A game theoretic approach to controller design for hybrid systems. Proc. IEEE 88, 7 (2000), 949--970. Google ScholarGoogle ScholarCross RefCross Ref
  28. H. Le Verge. 1992. A Note on Chernikova’s Algorithm. Technical Report 635. IRISA, Rennes.Google ScholarGoogle Scholar
  29. H. Wong-Toi. 1997. The synthesis of controllers for linear hybrid automata. In Proceedings of the 36th IEEE Conference on Decision and Control. IEEE. 4607--4612. DOI:http://dx.doi.org/10.1109/CDC.1997.649708 Google ScholarGoogle ScholarCross RefCross Ref

Index Terms

  1. Automatic Synthesis of Switching Controllers for Linear Hybrid Systems: Reachability Control

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader
      About Cookies On This Site

      We use cookies to ensure that we give you the best experience on our website.

      Learn more

      Got it!