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Volumn 42, Issue 2, 2003, Pages 513-531

On the local structure of optimal trajectories in R 3

Author keywords

Lie brackets; Optimal control

Indexed keywords

LIE BRACKETS; OPTIMAL CONTROL;

EID: 1942509708     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902409246     Document Type: Article
Times cited : (36)

References (23)
  • 1
    • 0346949167 scopus 로고
    • On regularity properties of extremals controls
    • A. A. AGRACHEV, On regularity properties of extremals controls, J. Dynam. Control Systems, 1 (1995), pp. 319-324.
    • (1995) J. Dynam. Control Systems , vol.1 , pp. 319-324
    • Agrachev, A.A.1
  • 2
    • 84957155683 scopus 로고
    • A second order optimality principle for a time-optimal problem
    • A. A. AGRACHEV AND R. V. GAMKRELIDZE, A second order optimality principle for a time-optimal problem, Math. USSR-Sb., 29 (1976), pp. 547-576.
    • (1976) Math. USSR-sb. , vol.29 , pp. 547-576
    • Agrachev, A.A.1    Gamkrelidze, R.V.2
  • 3
    • 85053529728 scopus 로고
    • Symplectic geometry for optimal control
    • Non-linear Controllability and Optimal Control, Hector J. Sussmann, ed., Marcel Dekker, New York
    • A. A. AGRACHEV AND R. V. GAMKRELIDZE, Symplectic geometry for optimal control, in Non-linear Controllability and Optimal Control, Pure Appl. Math. 133, Hector J. Sussmann, ed., Marcel Dekker, New York, 1990, pp. 263-277.
    • (1990) Pure Appl. Math. , vol.133 , pp. 263-277
    • Agrachev, A.A.1    Gamkrelidze, R.V.2
  • 4
  • 5
    • 0029376274 scopus 로고
    • Toward a geometric theory in the time-minimal control of chemical batch reactors
    • B. BONNARD AND J. DE MORANT, Toward a geometric theory in the time-minimal control of chemical batch reactors, SIAM J. Control Optim., 33 (1995), pp. 1279-1311.
    • (1995) SIAM J. Control Optim. , vol.33 , pp. 1279-1311
    • Bonnard, B.1    De Morant, J.2
  • 6
    • 0022674191 scopus 로고
    • The generic local time-optimal local stabilizing controls in dimension 3
    • A. BRESSAN, The generic local time-optimal local stabilizing controls in dimension 3, SIAM J. Control Optim., 24 (1986), pp. 177-190.
    • (1986) SIAM J. Control Optim. , vol.24 , pp. 177-190
    • Bressan, A.1
  • 7
    • 84954886334 scopus 로고
    • Study of an optimum nonlinear system
    • A. T. FULLER, Study of an optimum nonlinear system, J. Electronics Control, 15 (1963), pp. 63-71.
    • (1963) J. Electronics Control , vol.15 , pp. 63-71
    • Fuller, A.T.1
  • 9
    • 0024478824 scopus 로고
    • The structure of small-time reachable sets in low dimensions
    • A. J. KRENER AND H. SCHÄTTLER, The structure of small-time reachable sets in low dimensions, SIAM J. Control Optim., 27 (1989), pp. 120-147.
    • (1989) SIAM J. Control Optim. , vol.27 , pp. 120-147
    • Krener, A.J.1    Schättler, H.2
  • 10
    • 0002408866 scopus 로고
    • The ubiquity of Fuller's phenomenon
    • Nonlinear Controllability and Optimal Control, Hector J. Sussmann, ed., Marcel Dekker, New York
    • I. A. K. KUPKA, The ubiquity of Fuller's phenomenon, in Nonlinear Controllability and Optimal Control, Pure Appl. Math. 133, Hector J. Sussmann, ed., Marcel Dekker, New York, 1990, pp. 313-350.
    • (1990) Pure Appl. Math. , vol.133 , pp. 313-350
    • Kupka, I.A.K.1
  • 11
    • 0001883640 scopus 로고    scopus 로고
    • Regular time-optimal syntheses for smooth planar systems
    • B. PICCOLI, Regular time-optimal syntheses for smooth planar systems, Rend. Sem. Mat. Univ. Padova, 95 (1996), pp. 59-79.
    • (1996) Rend. Sem. Mat. Univ. Padova , vol.95 , pp. 59-79
    • Piccoli, B.1
  • 13
    • 0024036664 scopus 로고
    • The local structure of time-optimal trajectories in dimension three under generic conditions
    • H. SCHÄTTLER, The local structure of time-optimal trajectories in dimension three under generic conditions, SIAM J. Control Optim., 26 (1988), pp. 899-918.
    • (1988) SIAM J. Control Optim. , vol.26 , pp. 899-918
    • Schättler, H.1
  • 14
    • 85053552343 scopus 로고
    • Regularity properties of optimal trajectories: Recently developed techniques
    • Nonlinear Controllability and Optimal Control, Hector J. Sussmann, ed., Marcel Dekker, New York
    • H. SCHÄTTLER, Regularity properties of optimal trajectories: Recently developed techniques, in Nonlinear Controllability and Optimal Control, Pure Appl. Math. 133, Hector J. Sussmann, ed., Marcel Dekker, New York, 1990, pp. 351-381.
    • (1990) Pure Appl. Math. , vol.133 , pp. 351-381
    • Schättler, H.1
  • 15
    • 0343371999 scopus 로고
    • A synthesis of time-optimal controls in the presence of saturated singular arcs
    • H. SCHÄTTLER AND M. JANKOVIC, A synthesis of time-optimal controls in the presence of saturated singular arcs, Forum Math., 5 (1993), pp. 203-241.
    • (1993) Forum Math. , vol.5 , pp. 203-241
    • Schättler, H.1    Jankovic, M.2
  • 16
    • 0002438310 scopus 로고
    • Lie brackets, real analyticity and geometric control
    • R. W. Brockett, R. S. Millman, and H. J. Sussmann, eds., Birkhäuser, Boston
    • H. J. SUSSMANN, Lie brackets, real analyticity and geometric control, in Differential Geometric Control Theory, R. W. Brockett, R. S. Millman, and H. J. Sussmann, eds., Birkhäuser, Boston, 1983, pp. 1-116.
    • (1983) Differential Geometric Control Theory , pp. 1-116
    • Sussmann, H.J.1
  • 17
    • 0020302383 scopus 로고
    • Time-optimal control in the plane
    • Feedback Control of Linear and Nonlinear Systems, Springer-Verlag, Berlin
    • H. J. SUSSMANN, Time-optimal control in the plane, in Feedback Control of Linear and Nonlinear Systems, Lecture Notes in Control and Inform. Sci. 39, Springer-Verlag, Berlin, 1985, pp. 244-260.
    • (1985) Lecture Notes in Control and Inform. Sci. , vol.39 , pp. 244-260
    • Sussmann, H.J.1
  • 18
    • 0005335685 scopus 로고
    • Envelopes, conjugate points and optimal bang-bang extremals
    • M. Fliess and M. Hazewinkel, eds., D. Reidel Publishing Co., Dordrecht, The Netherlands
    • H. J. SUSSMANN, Envelopes, conjugate points and optimal bang-bang extremals, in Proceedings of the 1985 Paris Conference on Nonlinear Systems, M. Fliess and M. Hazewinkel, eds., D. Reidel Publishing Co., Dordrecht, The Netherlands, 1986, pp. 325-346.
    • (1986) Proceedings of the 1985 Paris Conference on Nonlinear Systems , pp. 325-346
    • Sussmann, H.J.1
  • 19
    • 0346395164 scopus 로고
    • A weak regularity for real analytic optimal control problems
    • H. J. SUSSMANN, A weak regularity for real analytic optimal control problems, Rev. Mat. Iberoamericana, 2 (1986), pp. 307-317.
    • (1986) Rev. Mat. Iberoamericana , vol.2 , pp. 307-317
    • Sussmann, H.J.1
  • 21
    • 0024914645 scopus 로고
    • Envelopes, high order optimality conditions and Lie brackets
    • IEEE Press, Piscataway, NJ
    • H. J. SUSSMANN, Envelopes, high order optimality conditions and Lie brackets, in Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 2, IEEE Press, Piscataway, NJ, 1989, pp. 1107-1112.
    • (1989) Proceedings of the 28th IEEE Conference on Decision and Control , vol.2 , pp. 1107-1112
    • Sussmann, H.J.1
  • 22
    • 0001859091 scopus 로고
    • Synthesis, presynthesis, sufficient conditions for optimality and subanalytic sets
    • Nonlinear Controllability and Optimal Control, Hector J. Sussmann, ed., Marcel Dekker, New York
    • H. J. SUSSMANN, Synthesis, presynthesis, sufficient conditions for optimality and subanalytic sets, in Nonlinear Controllability and Optimal Control, Pure Appl. Math. 133, Hector J. Sussmann, ed., Marcel Dekker, New York, 1990, pp. 1-19.
    • (1990) Pure Appl. Math. , vol.133 , pp. 1-19
    • Sussmann, H.J.1
  • 23
    • 0003740690 scopus 로고
    • Theory of Chattering Control. With Applications to Astronautics, Robotics, Economics, and Engineering
    • Birkhäuser, Boston
    • M. I. ZELIKIN AND V. F. BORISOV, Theory of Chattering Control. With Applications to Astronautics, Robotics, Economics, and Engineering, Systems and Control: Foundations and Applications, Birkhäuser, Boston, 1994.
    • (1994) Systems and Control: Foundations and Applications
    • Zelikin, M.I.1    Borisov, V.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.