메뉴 건너뛰기




Volumn 52, Issue 5, 2007, Pages 782-798

Approximation metrics for discrete and continuous systems

Author keywords

Abstraction; Approximation; Bisimulation; Metrics; Transition systems

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; CONTINUOUS TIME SYSTEMS; LYAPUNOV FUNCTIONS;

EID: 34249005820     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.895849     Document Type: Article
Times cited : (388)

References (36)
  • 4
    • 0000333926 scopus 로고    scopus 로고
    • Discrete abstractions of hybrid systems
    • Jul
    • R. Alur, T. A. Henzinger, G. Lafferriere, and G. J. Pappas, "Discrete abstractions of hybrid systems," Proc. IEEE, vol. 88, no. 7, pp. 971-984, Jul. 2000.
    • (2000) Proc. IEEE , vol.88 , Issue.7 , pp. 971-984
    • Alur, R.1    Henzinger, T.A.2    Lafferriere, G.3    Pappas, G.J.4
  • 5
    • 0242366144 scopus 로고    scopus 로고
    • Bisimilar linear systems
    • Dec
    • G. J. Pappas, "Bisimilar linear systems," Automatica, vol. 39, no. 12, pp. 2035-2047, Dec. 2003.
    • (2003) Automatica , vol.39 , Issue.12 , pp. 2035-2047
    • Pappas, G.J.1
  • 6
    • 1842529968 scopus 로고    scopus 로고
    • Bisimilar control affine systems
    • P. Tabuada and G. J. Pappas, "Bisimilar control affine systems," Syst. Control Lett., vol. 52, pp. 49-58, 2004.
    • (2004) Syst. Control Lett , vol.52 , pp. 49-58
    • Tabuada, P.1    Pappas, G.J.2
  • 7
    • 11044229094 scopus 로고    scopus 로고
    • Equivalence of dynamical systems by bisimulation
    • Dec
    • A. van der Schaft, "Equivalence of dynamical systems by bisimulation," IEEE Trans. Autom. Control, vol. 49, no. 12, pp. 2160-2172, Dec. 2004.
    • (2004) IEEE Trans. Autom. Control , vol.49 , Issue.12 , pp. 2160-2172
    • van der Schaft, A.1
  • 8
    • 23944505464 scopus 로고    scopus 로고
    • Bisimulation relations for dynamical, control, and hybrid systems
    • September
    • E. Haghverdi, P. Tabuada, and G. J. Pappas, "Bisimulation relations for dynamical, control, and hybrid systems," Theor. Comp. Sc., vol. 342, no. 2-3, pp. 229-261, September 2005.
    • (2005) Theor. Comp. Sc , vol.342 , Issue.2-3 , pp. 229-261
    • Haghverdi, E.1    Tabuada, P.2    Pappas, G.J.3
  • 9
    • 34249023410 scopus 로고    scopus 로고
    • A behavioral framework for compositionality: Linear systems, discrete event systems and hybrid systems
    • A. A. Julius and A. J. van der Schaft, "A behavioral framework for compositionality: Linear systems, discrete event systems and hybrid systems," in Proc. MTNS, 2004.
    • (2004) Proc. MTNS
    • Julius, A.A.1    van der Schaft, A.J.2
  • 11
    • 33845452561 scopus 로고    scopus 로고
    • A survey of model reduction methods for large-scale systems
    • A. C. Antoulas, D. C. Sorensen, and S. Gugercin, "A survey of model reduction methods for large-scale systems," Contemp. Math., vol. 280, pp. 193-219, 2000.
    • (2000) Contemp. Math , vol.280 , pp. 193-219
    • Antoulas, A.C.1    Sorensen, D.C.2    Gugercin, S.3
  • 12
    • 84948956973 scopus 로고    scopus 로고
    • Toward an approximation theory for computerized control
    • Embedded Software. New York: Springer-Verlag
    • P. Caspi and A. Benveniste, "Toward an approximation theory for computerized control," in Embedded Software. New York: Springer-Verlag, 2002, vol. 2491, LNCS, pp. 294-304.
    • (2002) LNCS , vol.2491 , pp. 294-304
    • Caspi, P.1    Benveniste, A.2
  • 13
    • 35248857469 scopus 로고    scopus 로고
    • Quantitative relations and approximate process equivalences
    • Proc. CONCUR 2003
    • A. Di Pierro, C. Hankin, and H. Wiklicky, "Quantitative relations and approximate process equivalences," in Proc. CONCUR 2003, 2003, vol. 2761, LNCS, pp. 508-522.
    • (2003) LNCS , vol.2761 , pp. 508-522
    • Di Pierro, A.1    Hankin, C.2    Wiklicky, H.3
  • 14
    • 35248840029 scopus 로고    scopus 로고
    • An intrinsic characterization of approximate probabilistic bisintilarity
    • Foundations of Software Science and Computation Structures. New York: Springer-Verlag
    • F. van Breugel, M. Mislove, J. Ouaknine, and J. Worrell, "An intrinsic characterization of approximate probabilistic bisintilarity," in Foundations of Software Science and Computation Structures. New York: Springer-Verlag, 2003, vol. 2620, LNCS, pp. 200-215.
    • (2003) LNCS , vol.2620 , pp. 200-215
    • van Breugel, F.1    Mislove, M.2    Ouaknine, J.3    Worrell, J.4
  • 16
    • 33745439700 scopus 로고    scopus 로고
    • Linear and branching metrics for quantitative transition systems
    • Proc. ICALP'04
    • L. de Alfaro, M. Faella, and M. Stoelinga, "Linear and branching metrics for quantitative transition systems," in Proc. ICALP'04, 2004, vol. 3142, LNCS, pp. 1150-1162.
    • (2004) LNCS , vol.3142 , pp. 1150-1162
    • de Alfaro, L.1    Faella, M.2    Stoelinga, M.3
  • 17
    • 0025432462 scopus 로고
    • CCS expressions, finite-state processes, and three problems of equivalence
    • P. C. Kanellakis and S. A. Smolka, "CCS expressions, finite-state processes, and three problems of equivalence," Inform. Comput., vol. 86, pp. 43-68, 1990.
    • (1990) Inform. Comput , vol.86 , pp. 43-68
    • Kanellakis, P.C.1    Smolka, S.A.2
  • 18
    • 84958171885 scopus 로고    scopus 로고
    • Reachability analysis of hybrid systems via predicate abstraction
    • Proc. HSCC
    • R. Alur, T. Dang, and F. Ivancic, "Reachability analysis of hybrid systems via predicate abstraction," in Proc. HSCC, 2002, vol. 2289, LNCS, pp. 35-48.
    • (2002) LNCS , vol.2289 , pp. 35-48
    • Alur, R.1    Dang, T.2    Ivancic, F.3
  • 19
    • 84945271493 scopus 로고    scopus 로고
    • Series of abstractions for hybrid automata
    • Proc. HSCC
    • A. Tiwari and G. Khanna, "Series of abstractions for hybrid automata," in Proc. HSCC, 2002, vol. 2289, LNCS, pp. 465-478.
    • (2002) LNCS , vol.2289 , pp. 465-478
    • Tiwari, A.1    Khanna, G.2
  • 20
    • 84974731232 scopus 로고    scopus 로고
    • Approximate reachability analysis of piecewise linear dynamical systems
    • Proc. HSCC
    • E. Asarin, O. Bournez, T. Dang, and O. Maler, "Approximate reachability analysis of piecewise linear dynamical systems," in Proc. HSCC, 2000, vol. 1790, LNCS, pp. 21-31.
    • (2000) LNCS , vol.1790 , pp. 21-31
    • Asarin, E.1    Bournez, O.2    Dang, T.3    Maler, O.4
  • 21
    • 35248860724 scopus 로고    scopus 로고
    • Reachability of non-linear systems using conservative approximations
    • Proc. HSCC
    • E. Asarin, T. Dang, and A. Girard, "Reachability of non-linear systems using conservative approximations," in Proc. HSCC, 2003, vol. 2623, LNCS, pp. 22-35.
    • (2003) LNCS , vol.2623 , pp. 22-35
    • Asarin, E.1    Dang, T.2    Girard, A.3
  • 22
    • 84949433135 scopus 로고    scopus 로고
    • Verification of polyhedral invariant hybrid automata using polygonal flow pipe approximations
    • Proc. HSCC
    • A. Chutinan and B. H. Krogh, "Verification of polyhedral invariant hybrid automata using polygonal flow pipe approximations," in Proc. HSCC, 1999, vol. 1569, LNCS, pp. 76-90.
    • (1999) LNCS , vol.1569 , pp. 76-90
    • Chutinan, A.1    Krogh, B.H.2
  • 23
    • 84974693322 scopus 로고    scopus 로고
    • Ellipsoidal tehcniques for reachability analysis
    • Proc. HSCC
    • A. Kurzhanski and P. Varaiya, "Ellipsoidal tehcniques for reachability analysis," in Proc. HSCC, 2000, vol. 1790, LNCS.
    • (2000) LNCS , vol.1790
    • Kurzhanski, A.1    Varaiya, P.2
  • 24
    • 84974725120 scopus 로고    scopus 로고
    • Level set methods for computation in hybrid systems
    • proc. HSCC
    • I. Mitchell and C. Tomlin, "Level set methods for computation in hybrid systems," in proc. HSCC, 2000, vol. 1790, LNCS.
    • (2000) LNCS , vol.1790
    • Mitchell, I.1    Tomlin, C.2
  • 25
    • 24344472268 scopus 로고    scopus 로고
    • Reachability of uncertain linear systems using zonotopes
    • Proc. HSCC
    • A. Girard, "Reachability of uncertain linear systems using zonotopes," in Proc. HSCC, 2005, vol. 3414, LNCS, pp. 291-305.
    • (2005) LNCS , vol.3414 , pp. 291-305
    • Girard, A.1
  • 26
    • 35048844766 scopus 로고    scopus 로고
    • Safety verification of hybrid systems using barrier certificates
    • Proc. HSCC
    • S. Prajna and A. Jadbabaie, "Safety verification of hybrid systems using barrier certificates," in Proc. HSCC, 2004, vol. 2993, LNCS, pp. 477-492.
    • (2004) LNCS , vol.2993 , pp. 477-492
    • Prajna, S.1    Jadbabaie, A.2
  • 27
    • 8744232867 scopus 로고    scopus 로고
    • Reachability of hybrid control systems using reduced-order models
    • Z. Han and B. H. Krogh, "Reachability of hybrid control systems using reduced-order models," in Proc. Amer. Control Conf., 2004, pp. 1183-1189.
    • (2004) Proc. Amer. Control Conf , pp. 1183-1189
    • Han, Z.1    Krogh, B.H.2
  • 28
    • 35048857940 scopus 로고    scopus 로고
    • Abstraction by projection and application to multi-affine systems
    • Proc. HSCC
    • E. Asarin and T. Dang, "Abstraction by projection and application to multi-affine systems," in Proc. HSCC, 2004, vol. 2993, LNCS, pp. 32-47.
    • (2004) LNCS , vol.2993 , pp. 32-47
    • Asarin, E.1    Dang, T.2
  • 31
    • 34247609933 scopus 로고    scopus 로고
    • Approximate simulation relations for hybrid systems
    • A. Girard, A. A. Juluis, and G. J. Pappas, "Approximate simulation relations for hybrid systems," in Proc. ADHS, 2006, pp. 106-111.
    • (2006) Proc. ADHS , pp. 106-111
    • Girard, A.1    Juluis, A.A.2    Pappas, G.J.3
  • 34
    • 34249006340 scopus 로고    scopus 로고
    • A. Gerard and G. J. Pappas, Approximation metrics for discrete and continuous systems Dept. CIS, Univ. Pennsylvania, Philadelphia, PA, Techn. Rep. MS-CIS-05-10, May 2005.
    • A. Gerard and G. J. Pappas, Approximation metrics for discrete and continuous systems Dept. CIS, Univ. Pennsylvania, Philadelphia, PA, Techn. Rep. MS-CIS-05-10, May 2005.
  • 35
    • 33847000790 scopus 로고    scopus 로고
    • Non-deterministic temporal logics for general flow systems
    • Proc. HSCC
    • J.M. Davoren, V. Coulthard, N. Markey, and T. Moor, "Non-deterministic temporal logics for general flow systems," in Proc. HSCC, 2004, vol. 2993, LNCS, pp. 280-295.
    • (2004) LNCS , vol.2993 , pp. 280-295
    • Davoren, J.M.1    Coulthard, V.2    Markey, N.3    Moor, T.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.