Casimir elements and optimal control

• Autorzy: V. Jurdjevic
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1995
• Tom: 32
• Numer: 1
• Strony: 261-275

Daty

wydano

1995

Twórcy

autor

V. Jurdjevic

• Department of Mathematics, University of Toronto, 100, St George Street, Toronto, Ontario, M5S 1A1 Canada

Bibliografia

• [1] V. I. Arnold, Méthodes Mathématiques de la Mécanique Classique, Editions Mir, 1976.
• [2] B. Bonnard, V. Jurdjevic, I. A. K. Kupka and G. Sallet, Transitivity of families of vector fields on the semi-direct products of Lie groups, Trans. Amer. Math. Soc. 275 (1982), 525-535.
• [3] J. D. Boissonat, A. Cereso, and J. LeBlond, On shortest paths in the plane subject to a constraint on the derivative of the curvature, a preprint.
• [4] L. E. Dubins, On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal position and tangents, Amer. J. Math. 79 (1957), 497-516.
• [5] V. Jurdjevic, Non-Euclidean elastica, Amer. J. Math. 117 (1995), 93-124.
• [6] V. Jurdjevic, The geometry of the plate-ball problem, Arch. Rational Mech. Anal. 124 (1993), 305-328.
• [7] V. Jurdjevic, Optimal Control Problems on Lie Groups: Crossroads between Geometry and Mechanics, in: The Geometry of Non-linear Feedback and Optimal Control, B. Jakubczyk and W. Respondek (eds.), Marcel Dekker, to appear.
• [8] V. Jurdjevic and I. Kupka, Control systems on semi-simple Lie groups and their homogeneous spaces, Ann. Inst. Fourier (Grenoble) 31 (4) (1981), 151-179.
• [9] C. Lobry, Controllability of non-linear systems on compact manifolds, SIAM J. Control 12 (1974), 1-4.
• [10] J. P. Laumonde et P. Souriat, Synthèse des plus courts chemins pour la voiture de Reeds et Shepp, Repport LAAS/CNRS 92234, Juin 1992.
• [11] J. A. Reeds and R. A. Shepp, Optimal paths for a car that goes both forward and backwards, Pacific J. Math. 145 (1990), 367-393.
• [12] H. J. Sussmann and G. Tang, Shortest paths for the Reeds-Shepp car: A worked out example of the use of geometric techniques in non-linear optimal control, a preprint.