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Volumn , Issue 9780817643850, 2005, Pages 3-19

Polytopic approximations of reachable sets applied to linear dynamic games and a class of nonlinear systems

Author keywords

Convex Polytope; Disturbance Input; Hybrid System; Linear Dynamical System; Protected Zone

Indexed keywords


EID: 84959089048     PISSN: 23249749     EISSN: 23249757     Source Type: Book Series    
DOI: 10.1007/0-8176-4409-1_1     Document Type: Chapter
Times cited : (47)

References (29)
  • 2
    • 0033100636 scopus 로고    scopus 로고
    • Controllers for reachability specifications for hybrid systems
    • J. Lygeros, C.J. Tomlin, and S. Sastry, Controllers for reachability specifications for hybrid systems, Automatica, 35 (3):349–370, 1999.
    • (1999) Automatica , vol.35 , Issue.3 , pp. 349-370
    • Lygeros, J.1    Tomlin, C.J.2    Sastry, S.3
  • 3
    • 0000274688 scopus 로고    scopus 로고
    • A game theoretic approach to controller design for hybrid systems
    • July
    • C.J. Tomlin, J. Lygeros, and S. Sastry, A game theoretic approach to controller design for hybrid systems, Proceedings of the IEEE, 88 (7):949–970, July 2000.
    • (2000) Proceedings of the IEEE , vol.88 , Issue.7 , pp. 949-970
    • Tomlin, C.J.1    Lygeros, J.2    Sastry, S.3
  • 4
    • 84944194723 scopus 로고    scopus 로고
    • Validating a Hamilton-Jacobi approximation to hybrid system reachable sets
    • M.D. DiBenedetto and A. Sangiovanni-Vincentelli, Eds, Springer-Verlag
    • I. Mitchell, A. Bayen, and C.J. Tomlin, Validating a Hamilton-Jacobi approximation to hybrid system reachable sets, In M.D. DiBenedetto and A. Sangiovanni-Vincentelli, Eds., Hybrid Systems: Computation and Control, LNCS 2034:418–431, Springer-Verlag, 2001.
    • (2001) Hybrid Systems: Computation and Control, LNCS , vol.2034 , pp. 418-431
    • Mitchell, I.1    Bayen, A.2    Tomlin, C.J.3
  • 6
    • 84945271493 scopus 로고    scopus 로고
    • Series of abstraction for hybrid automata
    • C.J. Tomlin and M.R. Greenstreet, Eds, Springer-Verlag
    • A. Tiwari and G. Khanna, Series of abstraction for hybrid automata, In C.J. Tomlin and M.R. Greenstreet, Eds., Hybrid Systems: Computation and Control, LNCS 2289:465–478, Springer-Verlag, 2002.
    • (2002) Hybrid Systems: Computation and Control, LNCS , vol.2289 , pp. 465-478
    • Tiwari, A.1    Khanna, G.2
  • 7
    • 84958171885 scopus 로고    scopus 로고
    • Reachability analysis of hybrid systems via predicate abstraction
    • C.J. Tomlin and M.R. Greenstreet, Eds, Springer-Verlag
    • R. Alur, T. Dang, and F. Ivančić, Reachability analysis of hybrid systems via predicate abstraction, In C.J. Tomlin and M.R. Greenstreet, Eds., Hybrid Systems: Computation and Control, LNCS 2289:35–48, Springer-Verlag, 2002.
    • (2002) Hybrid Systems: Computation and Control, LNCS , vol.2289 , pp. 35-48
    • Alur, R.1    Dang, T.2    Ivančić, F.3
  • 8
    • 33646168083 scopus 로고    scopus 로고
    • Reachability analysis of delta-notch lateral inhibition using predicate abstraction
    • S. Sahni, V.K. Prasanna and U. Shukla, Eds, Springer-Verlag
    • I. Hwang, H. Balakrishnan, R. Ghosh, and C.J. Tomlin, Reachability analysis of delta-notch lateral inhibition using predicate abstraction, In S. Sahni, V.K. Prasanna and U. Shukla, Eds., High Performance Computing-HiPC2002, LNCS 2552:715–724, Springer-Verlag, 2002.
    • (2002) High Performance Computing-Hipc2002, LNCS , vol.2552 , pp. 715-724
    • Hwang, I.1    Balakrishnan, H.2    Ghosh, R.3    Tomlin, C.J.4
  • 9
    • 84949433135 scopus 로고    scopus 로고
    • Verification of polyhedral-invariant hybrid automata using polygonal flow pipe approximations
    • F. Vaandrager and J.H. van Schuppen, Eds, Springer-Verlag
    • A. Chutinan and B.H. Krogh, Verification of polyhedral-invariant hybrid automata using polygonal flow pipe approximations, In F. Vaandrager and J.H. van Schuppen, Eds., Hybrid Systems: Computation and Control, LNCS 1569:76–90, Springer-Verlag, 1999.
    • (1999) Hybrid Systems: Computation and Control, LNCS , vol.1569 , pp. 76-90
    • Chutinan, A.1    Krogh, B.H.2
  • 10
    • 0037250532 scopus 로고    scopus 로고
    • Computational techniques for hybrid system verification
    • A. Chutinan and B.H. Krogh, Computational techniques for hybrid system verification, IEEE Transactions on Automatic Control, 48 (1):64–75, 2003.
    • (2003) IEEE Transactions on Automatic Control , vol.48 , Issue.1 , pp. 64-75
    • Chutinan, A.1    Krogh, B.H.2
  • 11
    • 84974731232 scopus 로고    scopus 로고
    • Approximate reachability analysis of piecewise-linear dynamical systems
    • B. Krogh and N. Lynch, Eds, Springer-Verlag
    • E. Asarin, O. Bournez, T. Dang, and O. Maler, Approximate reachability analysis of piecewise-linear dynamical systems, In B. Krogh and N. Lynch, Eds., Hybrid Systems: Computation and Control, LNCS 1790:20–31, Springer-Verlag, 2000.
    • (2000) Hybrid Systems: Computation and Control, LNCS , vol.1790 , pp. 20-31
    • Asarin, E.1    Bournez, O.2    Dang, T.3    Maler, O.4
  • 12
    • 84957870468 scopus 로고    scopus 로고
    • Reachability analysis via face lifting
    • T.A. Henzinger and S. Sastry, Eds, Springer-Verlag
    • T. Dang and O. Maler. Reachability analysis via face lifting, In T.A. Henzinger and S. Sastry, Eds., Hybrid Systems: Computation and Control, LNCS 1386:96–109, Springer-Verlag, 1998.
    • (1998) Hybrid Systems: Computation and Control, LNCS , vol.1386 , pp. 96-109
    • Dang, T.1    Maler, O.2
  • 13
    • 0346640326 scopus 로고    scopus 로고
    • Overapproximating reachable sets by Hamilton- Jacobi projections
    • December
    • I. Mitchell and C.J. Tomlin, Overapproximating reachable sets by Hamilton- Jacobi projections, Journal of Scientific Computing, 19 (1–3):323–346, December 2003.
    • (2003) Journal of Scientific Computing , vol.19 , Issue.1-3 , pp. 323-346
    • Mitchell, I.1    Tomlin, C.J.2
  • 14
    • 35048857940 scopus 로고    scopus 로고
    • Abstraction by projection and application to multi-affine systems
    • R. Alur and G.J. Pappas, Eds, Springer-Verlag
    • E. Asarin and T. Dang. Abstraction by projection and application to multi-affine systems, In R. Alur and G.J. Pappas, Eds., Hybrid Systems: Computation and Control, LNCS 2993:32–47, Springer-Verlag, 2004.
    • (2004) Hybrid Systems: Computation and Control, LNCS , vol.2993 , pp. 32-47
    • Asarin, E.1    Dang, T.2
  • 15
    • 0031645586 scopus 로고    scopus 로고
    • State estimation for dynamic systems via parallelotopes
    • E.K. Kostousova, State estimation for dynamic systems via parallelotopes, Optimization Methods and Software, 9:269–306, 1998.
    • (1998) Optimization Methods and Software , vol.9 , pp. 269-306
    • Kostousova, E.K.1
  • 18
    • 84974735953 scopus 로고    scopus 로고
    • Verification of hybrid systems with linear differential inclusions using ellipsoidal approximations
    • B. Krogh and N. Lynch, Eds, Springer-Verlag
    • O. Botchkarev and S. Tripakis, Verification of hybrid systems with linear differential inclusions using ellipsoidal approximations, In B. Krogh and N. Lynch, Eds., Hybrid Systems: Computation and Control, LNCS 1790:73–88, Springer-Verlag, 2000.
    • (2000) Hybrid Systems: Computation and Control, LNCS , vol.1790 , pp. 73-88
    • Botchkarev, O.1    Tripakis, S.2
  • 22
    • 85048491169 scopus 로고    scopus 로고
    • On some nonstandard dynamic programming problems of control theory
    • F. Giannessi and A. Maugeri, Eds., Kluwer Academic Publishers, New York
    • A.B. Kurzhanski and P. Varaiya, On some nonstandard dynamic programming problems of control theory, In F. Giannessi and A. Maugeri, Eds., Variational Analysis and Applications, Kluwer Academic Publishers, New York, 2004.
    • (2004) Variational Analysis and Applications
    • Kurzhanski, A.B.1    Varaiya, P.2
  • 23
    • 0142255879 scopus 로고
    • Exact description of reachable sets and global optimality conditions
    • M.M. Khrustalev, Exact description of reachable sets and global optimality conditions, Avtomatika i Telemekhanika, (5):62–70, 1988.
    • (1988) Avtomatika I Telemekhanika , Issue.5 , pp. 62-70
    • Khrustalev, M.M.1
  • 24
    • 44749084234 scopus 로고
    • Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • S. Osher and J.A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, 79:12–49, 1988.
    • (1988) Journal of Computational Physics , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 28
    • 2942550882 scopus 로고    scopus 로고
    • Decentralized overlapping control of a formation of unmanned aerial vehicles
    • D.M. Stipanović, G. İnalhan, R. Teo, and C.J. Tomlin, Decentralized overlapping control of a formation of unmanned aerial vehicles, Automatica, 40:1285– 1296, 2004.
    • (2004) Automatica , vol.40 , pp. 1285-1296
    • Stipanović, D.M.1    İnalhan, G.2    Teo, R.3    Tomlin, C.J.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.