Computing differential invariants of hybrid systems as fixedpoints

André Platzer1, Edmund M. Clarke1
1Computer Science Department, Carnegie Mellon University, Pittsburgh, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Alur R, Pappas GJ (eds) (2004) Hybrid systems: computation and control, Proceedings of the 7th International Workshop, HSCC 2004, Philadelphia, PA, USA, March 25–27, 2004. LNCS, vol 2993. Springer, Berlin

Anai H, Weispfenning V (2001) Reach set computations using real quantifier elimination. In: Benedetto MDD, Sangiovanni-Vincentelli AL (eds) HSCC. LNCS, vol 2034. Springer, Berlin, pp 63–76. doi: 10.1007/3-540-45351-2_9

Asarin E, Dang T, Girard A (2003) Reachability analysis of nonlinear systems using conservative approximation. In: Maler O, Pnueli A (eds) HSCC. LNCS, vol 2623. Springer, Berlin, pp 20–35. doi: 10.1007/3-540-36580-X_5

Chutinan A, Krogh BH (2003) Computational techniques for hybrid system verification. IEEE Trans Autom Control 48(1):64–75. doi: 10.1109/TAC.2002.806655

Clarke EM (1979) Program invariants as fixedpoints. Computing 21(4):273–294. doi: 10.1007/BF02248730

Collins GE, Hong H (1991) Partial cylindrical algebraic decomposition for quantifier elimination. J Symb Comput 12(3):299–328. doi: 10.1016/S0747-7171(08)80152-6

Damm W, Hungar H, Olderog ER (2006) Verification of cooperating traffic agents. Int J Control 79(5):395–421

Damm W, Pinto G, Ratschan S (2005) Guaranteed termination in the verification of LTL properties of non-linear robust discrete time hybrid systems. In: Peled D, Tsay YK (eds) ATVA. LNCS, vol 3707. Springer, Berlin, pp 99–113. doi: 10.1007/11562948_10

Davoren JM, Nerode A (2000) Logics for hybrid systems. IEEE 88(7):985–1010. doi: 10.1109/5.871305

Donzé A, Maler O (2004) Systematic simulation using sensitivity analysis. In: Bemporad A et al. (eds) Hybrid systems: computation and control, Proceedings of the 10th international conference, HSCC 2007, Pisa, Italy. LNCS, vol 4416. Springer, Berlin, pp 174–189. doi: 10.1007/978-3-540-71493-4_16

Dowek G, Muñoz C, Carreño VA (2005) Provably safe coordinated strategy for distributed conflict resolution. In: Proceedings of the AIAA guidance navigation, and control conference and exhibit 2005, AIAA-2005-6047

Fränzle M (1999) Analysis of hybrid systems: an ounce of realism can save an infinity of states. In: Flum J, Rodríguez-Artalejo M (eds) CSL. LNCS, vol 1683. Springer, Berlin, pp 126–140

Frehse G (2005) PHAVer: Algorithmic verification of hybrid systems past HyTech. In: Morari M, Thiele L (eds) Hybrid systems: computation and control, Proceedings of the 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9–11, 2005. LNCS, vol 3414. Springer, Berlin, pp 258–273. doi: 10.1007/b106766

Gulwani S, Tiwari A (2008) Constraint-based approach for analysis of hybrid systems. In: Gupta A, Malik S (eds) Proceedings computer aided verification, CAV 2008, Princeton, NJ, USA. LNCS, vol 5123. Springer, Berlin, pp 190–203. doi: 10.1007/978-3-540-70545-1

Harel D, Kozen D, Tiuryn J (2000) Dynamic logic. MIT Press, Cambridge

Henzinger TA (1996) The theory of hybrid automata. In: LICS. IEEE Computer Society, Los Alamitos, pp 278–292

Henzinger TA, Ho PH, Wong-Toi H (1997) HyTech: a model checker for hybrid systems. In: Grumberg O (ed) CAV. LNCS, vol 1254. Springer, Berlin, pp 460–463

Hwang I, Kim J, Tomlin C (2007) Protocol-based conflict resolution for air traffic control. Air Traffic Control Q 15(1):1–34

Lanotte R, Tini S (2005) Taylor approximation for hybrid systems. In: Morari M, Thiele L (eds) Hybrid systems: computation and control, Proceedings of the 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9–11, 2005. LNCS, vol 3414. Springer, Berlin, pp 402–416. doi: 10.1007/b106766

Mansfield EL (1991) Differential Gröbner bases. PhD thesis, University of Sydney

Massink M, Francesco ND (2001) Modelling free flight with collision avoidance. In: Andler SF, Offutt J (eds) ICECCS. IEEE Computer Society, Los Alamitos, pp 270–280. doi: 10.1109/ICECCS.2001.930186

Parrilo PA (2003) Semidefinite programming relaxations for semialgebraic problems. Math Program 96(2):293–320. doi: 10.1007/s10107-003-0387-5

Piazza C, Antoniotti M, Mysore V, Policriti A, Winkler F, Mishra B (2005) Algorithmic algebraic model checking, I: challenges from systems biology. In: Etessami K, Rajamani SK (eds) CAV. LNCS, vol 3576. Springer, Berlin, pp 5–19. doi: 10.1007/11513988_3

Platzer A (2008) Differential-algebraic dynamic logic for differential-algebraic programs. J Log Comput. doi: 10.1093/logcom/exn070

Platzer A (2008) Differential dynamic logic for hybrid systems. J Autom Reas 41(2):143–189. doi: 10.1007/s10817-008-9103-8

Platzer A, Clarke EM (2007) The image computation problem in hybrid systems model checking. In: Bemporad A et al. (eds) Hybrid systems: computation and control, Proceedings of the 10th international conference, HSCC 2007, Pisa, Italy. LNCS, vol 4416. Springer, Berlin, pp 473–486. doi: 10.1007/978-3-540-71493-4_37

Platzer A, Clarke EM (2008) Computing differential invariants of hybrid systems as fixedpoints. In: Gupta A, Malik S (eds) Proceedings computer aided verification, CAV 2008, Princeton, NJ, USA. LNCS, vol 5123. Springer, Berlin, pp 176–189. doi: 10.1007/978-3-540-70545-1_17

Platzer A, Clarke EM (2008) Computing differential invariants of hybrid systems as fixedpoints. Tech Rep CMU-CS-08-103, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA

Platzer A, Quesel JD (2008) KeYmaera: A hybrid theorem prover for hybrid systems. In: Armando A, Baumgartner P, Dowek G (eds) IJCAR. LNCS, vol 5195. Springer, Berlin, pp 171–178. doi: 10.1007/978-3-540-71070-7_15

Platzer A, Quesel JD (2008) Logical verification and systematic parametric analysis in train control. In: Egerstedt M, Mishra B (eds) HSCC. LNCS, vol 4981. Springer, Berlin, pp 646–649. doi: 10.1007/978-3-540-78929-1_55

Prajna S, Jadbabaie A (2004) Safety verification of hybrid systems using barrier certificates. In: Alur R, Pappas GJ (eds) Hybrid systems: computation and control, Proceedings of the 7th international workshop, HSCC 2004, Philadelphia, PA, USA, March 25–27, 2004. LNCS, vol 2993. Springer, Berlin, pp 477–492. doi: 10.1007/b96398

Prajna S, Jadbabaie A, Pappas GJ (2007) A framework for worst-case and stochastic safety verification using barrier certificates. IEEE Trans Autom Control 52(8):1415–1429. doi: 10.1109/TAC.2007.902736

Rodríguez-Carbonell E, Tiwari A (2005) Generating polynomial invariants for hybrid systems. In: Morari M, Thiele L (eds) Hybrid systems: computation and control, Proceedings of the 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9–11, 2005. LNCS, vol 3414. Springer, Berlin, pp 590–605. doi: 10.1007/b106766

Sankaranarayanan S, Sipma H, Manna Z (2004) Constructing invariants for hybrid systems. In: Alur R, Pappas GJ (eds) Hybrid systems: computation and control, Proceedings of the 7th international workshop, HSCC 2004, Philadelphia, PA, USA, March 25–27, 2004. LNCS, vol 2993. Springer, Berlin, pp 539–554. doi: 10.1007/b96398

Tomlin C, Pappas GJ, Sastry S (1998) Conflict resolution for air traffic management: a study in multi-agent hybrid systems. IEEE Trans Autom Control 43(4):509–521. doi: 10.1109/9.664154