Abstractions for hybrid systems

Formal Methods in System Design

Volumn 32, Issue 1, 2008, Pages 57-83

  Tiwari, Ashish ^a  

^a SRI INTERNATIONAL   (United States)

Author keywords

Hybrid systems; Predicate abstraction; Qualitative simulation

Indexed keywords

AUTOMATA THEORY; CASE BASED REASONING; COMPUTER SIMULATION;

FINITE STATE DISCRETE ABSTRACTIONS; HYBRID SYSTEMS; PREDICATE ABSTRACTION; QUALITATIVE SIMULATION;

SYSTEMS ANALYSIS;

EID: 37849026123     PISSN: 09259856     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10703-007-0044-3     Document Type: Conference Paper

References (54)

1. Alur R, Courcoubetis C, Halbwachs N, Henzinger TA, Ho P-H, Nicollin X, Olivero A, Sifakis J, Yovine S (1995) The algorithmic analysis of hybrid systems. Theor Comput Sci 138(3):3-34
2. Alur R, Courcoubetis C, Henzinger TA, Ho P-H Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In: Grossman et al [17], pp 209-229
3. Alur R, Dang T, Ivancic F Counter-example guided predicate abstraction of hybrid systems. In: Garavel and Hatcliff [13], pp 208-223
4. Alur R, Dang T, Ivancic F Progress on reachability analysis of hybrid systems using predicate abstraction. In: Maler and Pnueli [31]
5. Alur R, Henzinger T, Lafferriere G, Pappas GJ (2000) Discrete abstractions of hybrid systems. Proc IEEE 88(2):971-984
6. Alur R, Pappas GJ (eds) (2004) Hybrid systems: computation and control, 7th international workshop, HSCC 2004, Philadelphia, PA, March 25-27, 2004, Proceedings. Lecture notes in computer science, vol 2993. Springer, Berlin
7. Ball T, Podelski A, Rajamani SK (2001) Boolean and Cartesian abstraction for model checking C programs. In: Proc of the 7th intl conf on tools and algorithms for the construction and analysis of systems, TACAS 2001. Lecture notes in computer science. Springer, Berlin, pp 268-283
8. Chutinan A, Krogh BH (1999) Verification of polyhedral-invariant hybrid automata using polygonal flow pipe approximations. In: Vaandrager FW, van Schuppen JH (eds) HSCC. Lecture notes in computer science, vol 1569. Springer, Berlin, pp 76-90
9. Chutinan A, Krogh BH (2001) Verification of infinite-state dynamic systems using approximate quotient transition systems. IEEE Trans Autom Control 46(9):1401-1410
10. Clarke EM, Fehnker A, Han Z, Krogh BH, Stursberg O, Theobald M Verification of hybrid systems based on counterexample-guided abstraction refinement. In: Garavel and Hatcliff [13], pp 192-207
11. Collins GE (1975) Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition. In: Proc 2nd GI conf automata theory and formal languages. Lecture notes in computer science, vol 33. Springer, Berlin, pp 134-183
12. Dang T, Maler O (1998) Reachability analysis via face lifting. In: Henzinger TA, Sastry S (eds) HSCC. Lecture notes in computer science, vol 1386. Springer, Berlin, pp 96-109
13. Garavel H, Hatcliff J (eds) (2003) In: 9th intl conf on tools and algorithms for the construction and analysis of systems, TACAS 2003. Lecture notes in computer science, vol 2619. Springer, Berlin
14. Ghosh R, Tomlin CJ (2001) Lateral inhibition through delta-notch signaling: a piecewise affine hybrid model. In: Hybrid systems: computation and control, HSCC 2001. LNCS, vol 2034. Springer, Berlin, pp 232-246
15. Godbole D, Lygeros J (1994) Longitudinal control of the lead car of a platoon. IEEE Trans Veh Technol 43(4):1125-1135
16. Graf S, Saïdi H (1997) Construction of abstract state graphs with PVS. In: Grumberg O (ed) Proc 9th conference on computer-aided verification (CAV'97). Lecture notes in computer science, vol 1254. Springer, Berlin, pp 72-83
17. Grossman RL, Nerode A, Ravn AP, Rischel H (eds) (1993) In: Hybrid systems. Lecture notes in computer science, vol 736. Springer, Berlin
18. Grumberg O, Long DE (1994) Model checking and modular verification. ACM Trans Program Lang Syst 16(3):843-871
19. Henzinger MR, Henzinger TA, Kopke PW (1995) Computing simulations on finite and infinite graphs. In: Proc 36th annual IEEE symp on foundations of computer science FOCS, pp 453-462
20. Henzinger TA (1995) Hybrid automata with finite bisimulations. In: Proc 22nd intl colloquium on automata, languages, and programming, ICALP 1995. Lecture notes in computer science, vol 944. Springer, Berlin, pp 324-335
21. Henzinger TA, Ho P-H (1995) Algorithmic analysis of nonlinear hybrid systems. In: Wolper P (ed) Computer aided verification, Proc of the 7th intl conf, CAV '95. Lecture notes in computer science, vol 939. Springer, Berlin, pp 225-238
22. Henzinger TA, Ho P-H (1995) A note on abstract interpretation strategies for hybrid automata. In: Antsaklis P, Kohn W, Nerode A (eds) Hybrid systems II. Lecture notes in computer science, vol 999. Springer, Berlin, pp 252-264
23. Henzinger TA, Ho P-H, Wong-Toi H (1998) Algorithmic analysis of nonlinear hybrid systems. IEEE Trans Autom Control 43:540-554
24. Henzinger TA, Kopke PW, Puri A, Varaiya P (1998) What's decidable about hybrid automata? J Comput Syst Sci 57:94-124
25. Henzinger TA, Wong-Toi H (1996) Linear phase-portrait approximations for nonlinear systems. In: Alur R, Henzinger T, Sontag ED (eds) Hybrid systems III. Lecture notes in computer science, vol 1066. Springer, Berlin, pp 377-388
26. Hong H (1990) An improvement of the projection operator in cylindrical algebraic decomposition. In: Proc ISAAC 90, pp 261-264
27. Krogh BH, Stursberg O On efficient representation and computation of reachable sets for hybrid systems. In Maler and Pnueli [31]
28. Lafferriere G, Pappas GJ, Yovine S (2001) Symbolic reachability computations for families of linear vector fields. J Symb Comput 32(3):231-253
29. Lazard D (1990) An improved projection for cylindrical algebraic decomposition. Technical report, Informatique, Universite Paris IV, F-75252 Paris Cedex 05, France
30. Loeser T, Iwasaki Y, Fikes R (1998) Safety verification proofs for physical systems. In: Proc of the 12th intl workshop on qualitative reasoning. AAAI Press, Menlo Park, pp 88-95. Also published as a Knowledge Systems Lab, Stanford University, technical report KSL-98-14
31. Maler O, Pnueli A (eds) (2003) In: Hybrid systems: computation and control, 6th international workshop, HSCC 2003 Prague, Czech Republic, April 3-5, 2003. Proceedings. Lecture notes in computer science, vol 2623. Springer, Berlin
32. McCallum S (1988) An improved projection operator for cylindrical algebraic decomposition of three dimensional space. J Symb Comput 5:141-161
33. Milner R (1971) An algebraic definition of simulation between programs. In: Proc. 2nd IJCAI, pp 481-489
34. Möller MO, Rueß H, Sorea M (2002) Predicate abstraction for dense real-time systems. Electron Notes Theor Comput Sci 65(6). http://www.elsevier.com/locate/entcs/volume65.html
35. Nicollin X, Olivero A, Sifakis J, Yovine S An approach to the description and analysis of hybrid systems. In Grossman et al [17], pp 149-178
36. Olivero A, Sifakis J, Yovine S (1994) Using abstractions for the verification of linear hybrid systems. In: Proc of the 6th computer-aided verification, CAV. Lecture notes in computer science, vol 818. Springer, Berlin, pp 81-94
37. Parrilo PA (2000) Structured semidefinite programs and semialgebraic geometric methods in robustness and optimization. PhD thesis, California Institute of Technology, Pasadena
38. Parrilo PA, Sturmfels B (2003) Minimizing polynomial functions. In: Algorithmic and quantitative real algebraic geometry. DIMACS series in discrete mathematics and theoretical computer science, vol 60, pp 83-99. http://www/arxiv.org/abs/math.OC/0103170
39. Prajna S (2003) Barrier certificates for nonlinear model validation. In: Proc IEEE conference on decision and control
40. Prajna S, Jadbabaie A Safety verification of hybrid systems using barrier certificates. In Alur and Pappas [6], pp 477-492
41. Prajna S, Papachristodoulou A, Parrilo PA (2002) SOSTOOLS: sum of square optimization toolbox for MATLAB, http://www.cds.caltech.edu/sostools
42. Puri A, Varaiya P (1995) Driving safely in smart cars. In: Proc of the 1995 American control conference
43. Raisch J, O'Young S (1997) A totally ordered set of discrete abstractions for a given hybrid or continuous system. In: Hybrid systems IV. Lecture notes in computer science, vol 1273. Springer, Berlin, pp 342-360
44. Shults B, Kuipers BJ (1997) Proving properties of continuous systems: qualitative simulation and temporal logic. AI J 92:91-129
45. Sokolsky O, Hong HS Qualitative modeling of hybrid systems. In: Proc of the Montreal workshop, 2001. Available from http://www.cis.upenn.edu/~rtg/ rtg_papers.htm
46. Tabuada P (2004) Flatness and finite bisimulations in continuous time. In: Proc 16th intl symp on mathematical theory of networks and systems
47. Tarski A (1948) A decision method for elementary algebra and geometry, 2nd edn. University of California Press, Berkeley
48. Tiwari A (2003) Abstraction based theorem proving: an example from the theory of reals. In: Proc CADE-19 workshop on pragmatics of decision procedures in automated deduction, PDPAR 2003. INRIA, Nancy, pp 40-52
49. Tiwari A Approximate reachability for linear systems. In Maler and Pnueli [31], pp 514-525
50. Tiwari A, Khanna G (2002) Series of abstractions for hybrid automata. In: Tomlin C, Greenstreet MR (eds) HSCC. Lecture notes in computer science, vol 2289. Springer, Berlin, pp 465-478
51. Tiwari A, Khanna G Nonlinear systems: approximating reach sets. In: Alur and Pappas [6], pp 600-614
52. Vidyasagar M (1993) Nonlinear systems analysis. Prentice Hall, New York
53. Yazarel H, Pappas GJ (2004) Geometric programming relaxations for linear system reachability. In: Proc 2004 American control conference
54. Yazarel H, Prajna S, Pappas GJ (2004) S.O.S. for safety. In: Proc 43rd IEEE conference on decision and control, vol 1, pp 461-466