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.
- 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 Scholar
Digital Library
- 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 Scholar
Cross Ref
- 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 Scholar
Digital Library
- 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 Scholar
Cross Ref
- 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 Scholar
Digital Library
- 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 Scholar
Cross Ref
- 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 Scholar
Cross Ref
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- P. Bouyer, T. Brihaye, and F. Chevalier. 2010. O-minimal hybrid reachability games. Logic. Methods Comput. Sci. 6 (2010). Google Scholar
Cross Ref
- 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 Scholar
Cross Ref
- 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 Scholar
Cross Ref
- 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 Scholar
Cross Ref
- 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 Scholar
Cross Ref
- 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 Scholar
Cross Ref
- 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 Scholar
Cross Ref
- 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 Scholar
Cross Ref
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
Cross Ref
- 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 Scholar
Digital Library
- 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 Scholar
Cross Ref
- 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 Scholar
Cross Ref
- M. L. Minsky. 1967. Computation: Finite and Infinite Machines. Prentice-Hall, Inc., Upper Saddle River, NJ.Google Scholar
Digital Library
- 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 Scholar
Digital Library
- A. Schrijver. 1986. Theory of Linear and Integer Programming. John Wiley and Sons.Google Scholar
Digital Library
- 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 Scholar
Cross Ref
- H. Le Verge. 1992. A Note on Chernikova’s Algorithm. Technical Report 635. IRISA, Rennes.Google Scholar
- 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 Scholar
Cross Ref
Index Terms
Automatic Synthesis of Switching Controllers for Linear Hybrid Systems: Reachability Control
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