메뉴 건너뛰기




Volumn 7, Issue 3, 2001, Pages 385-423

Morse properties for the minimum time function on 2-D manifolds

Author keywords

Minimum time; Morse function; Optimal control

Indexed keywords

FUNCTION EVALUATION; GEOMETRY; INTEGRAL EQUATIONS; TOPOLOGY; TWO DIMENSIONAL; VECTORS;

EID: 0035412738     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1013190914234     Document Type: Article
Times cited : (4)

References (24)
  • 4
    • 0000401789 scopus 로고
    • Sufficient condition for optimality and the justification of the dynamic programming principle
    • V. Boltianski, Sufficient condition for optimality and the justification of the dynamic programming principle. SIAM J. Control Optim. 4 (1966), 326-361.
    • (1966) SIAM J. Control Optim. , vol.4 , pp. 326-361
    • Boltianski, V.1
  • 5
    • 84955868449 scopus 로고
    • Theorie des singularites de l'application entree/sortie et optimalite des singulieres dans le probleme du temps minimal
    • B. Bonnard and I. Kupka, Theorie des singularites de l'application entree/sortie et optimalite des singulieres dans le probleme du temps minimal. Forum Mathematicum 5 (1993) 111-159.
    • (1993) Forum Mathematicum , vol.5 , pp. 111-159
    • Bonnard, B.1    Kupka, I.2
  • 6
    • 0035323824 scopus 로고    scopus 로고
    • Extremal syntheses for generic planar systems
    • U. Boscain and B. Piccoli, Extremal syntheses for generic planar systems. J. Dynam. Control Systems 7 (2001), No. 2, 209-258.
    • (2001) J. Dynam. Control Systems , vol.7 , Issue.2 , pp. 209-258
    • Boscain, U.1    Piccoli, B.2
  • 9
    • 0031673673 scopus 로고    scopus 로고
    • A generic classification of time optimal planar stabilizing feedbacks
    • _, A generic classification of time optimal planar stabilizing feedbacks. SIAM J. Control Optim. 36 (1998), No. 1, 12-32.
    • (1998) SIAM J. Control Optim. , vol.36 , Issue.1 , pp. 12-32
  • 10
    • 0031344540 scopus 로고    scopus 로고
    • A generic classification of time optimal planar stabilizing feedbacks
    • San Diego, California, USA
    • _, A generic classification of time optimal planar stabilizing feedbacks. In: Proc. 36th IEEE Conf. Decision and Control, San Diego, California, USA (1997), 1397-1402.
    • (1997) Proc. 36th IEEE Conf. Decision and Control , pp. 1397-1402
  • 11
    • 0000195155 scopus 로고
    • Existence of regular syntheses for general problems
    • P. Brunovsky, Existence of regular syntheses for general problems. J. Differential Equations 38 (1980), 317-343.
    • (1980) J. Differential Equations , vol.38 , pp. 317-343
    • Brunovsky, P.1
  • 12
    • 0031316771 scopus 로고    scopus 로고
    • Regularity results for solutions of a class of Hamilton Jacobi equations
    • P. Cannarsa, A. Mennucci, and C. Sinestrari, Regularity results for solutions of a class of Hamilton Jacobi equations. Arch. Ration. Mech. Anal. 140 (1997), 197-223.
    • (1997) Arch. Ration. Mech. Anal. , vol.140 , pp. 197-223
    • Cannarsa, P.1    Mennucci, A.2    Sinestrari, C.3
  • 15
    • 0011737544 scopus 로고
    • Topological classification of the germ of functions of the maximum and minimax functions of a family of functions in general position
    • V. I. Matov, Topological classification of the germ of functions of the maximum and minimax functions of a family of functions in general position. Usp. Mat. Nauk (Russian) 37 (1982), No. 4, 167-168.
    • (1982) Usp. Mat. Nauk (Russian) , vol.37 , Issue.4 , pp. 167-168
    • Matov, V.I.1
  • 16
    • 0001919611 scopus 로고
    • On the classification of flows on 2-manifolds
    • (M. M. Peixoto, ed.), Academic Press, New York
    • M. M. Peixoto, On the classification of flows on 2-manifolds. In: Dynamical Systems, (M. M. Peixoto, ed.), Academic Press, New York (1973), pp. 389-419.
    • (1973) Dynamical Systems , pp. 389-419
    • Peixoto, M.M.1
  • 17
    • 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), 59-79.
    • (1996) Rend. Sem. Mat. Univ. Padova , vol.95 , pp. 59-79
    • Piccoli, B.1
  • 18
    • 0030289481 scopus 로고    scopus 로고
    • Classifications of generic singularities for the planar time-optimal synthesis
    • _, Classifications of generic singularities for the planar time-optimal synthesis. SIAM J. Control Optim. 34 (1996), No. 6, 1914-1946.
    • (1996) SIAM J. Control Optim. , vol.34 , Issue.6 , pp. 1914-1946
  • 19
    • 0034453280 scopus 로고    scopus 로고
    • Regular synthesis and sufficiency conditions for optimality
    • B. Piccoli and H. J. Sussmann, Regular synthesis and sufficiency conditions for optimality. SIAM J. Control Optim. 39 (2000), 359-410.
    • (2000) SIAM J. Control Optim. , vol.39 , pp. 359-410
    • Piccoli, B.1    Sussmann, H.J.2
  • 21
    • 0023383491 scopus 로고
    • The structure of time-optimal trajectories for single-input systems in the plane: The general real-analytic case
    • H. J. Sussmann, The structure of time-optimal trajectories for single-input systems in the plane: the general real-analytic case. SIAM J. Control Optim. 25 (1987), 868-904.
    • (1987) SIAM J. Control Optim. , vol.25 , pp. 868-904
    • Sussmann, H.J.1
  • 22
    • 0023422486 scopus 로고
    • Regular synthesis for time optimal control of single-input real-analytic systems in the plane
    • _, Regular synthesis for time optimal control of single-input real-analytic systems in the plane. SIAM J. Control Optim. 25 (1987), 1145-1162.
    • (1987) SIAM J. Control Optim. , vol.25 , pp. 1145-1162
  • 23
    • 0002671270 scopus 로고    scopus 로고
    • Geometry and optimal control
    • Springer-Verlag, New York
    • _, Geometry and optimal control. In: Math. Control Theory, Springer-Verlag, New York (1998), pp. 140-198.
    • (1998) Math. Control Theory , pp. 140-198
  • 24
    • 0001222585 scopus 로고    scopus 로고
    • Some properties of the value function and its level sets for affine control systems with quadratic cost
    • E. Trelat, Some properties of the value function and its level sets for affine control systems with quadratic cost. J. Dynam. Control Systems 6 (2000), No. 4, 511-541.
    • (2000) J. Dynam. Control Systems , vol.6 , Issue.4 , pp. 511-541
    • Trelat, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.