Citation: |
[1] |
J. Baillieul, The geometry of controlled mechanical systems, in "Mathematical Control Theory" (Eds. J. Baillieul and J. C. Willems), Springer Verlag, New York, (1998), 322-354. |
[2] |
A. M. Bloch, "Nonholonomic Mechanics and Control," Springer Verlag, 2003.doi: 10.1007/b97376. |
[3] |
A. M. Bloch, J. E. Marsden and D. V. Zenkov, Nonholonomic dynamics, Notices Amer. Math. Soc., 52 (2005), 324-333. |
[4] |
A. Bressan, Impulsive control of Lagrangian systems and locomotion in fluids, Discr. Cont. Dynam. Syst., 20 (2008), 1-35.doi: 10.3934/dcds.2008.20.1. |
[5] |
A. Bressan and F. Rampazzo, On differential systems with vector-valued impulsive controls, Boll. Un. Matem. Italiana, 2-B (1988), 641-656. |
[6] |
A. Bressan and F. Rampazzo, Impulsive control systems with commutative vector fields, J. Optim. Theory & Appl., 71 (1991), 67-84.doi: 10.1007/BF00940040. |
[7] |
A. Bressan and F. Rampazzo, On systems with quadratic impulses and their application to Lagrangian mechanics, SIAM J. Control, 31 (1993), 1205-1220.doi: 10.1137/0331057. |
[8] |
A. Bressan and F. Rampazzo, Moving constraints as stabilizing controls in classical mechanics, Arch. Rational Mech. Anal., 196 (2010), 97-141.doi: 10.1007/s00205-009-0237-6. |
[9] |
Aldo Bressan, Hyper-impulsive motions and controllizable coordinates for Lagrangean systems, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Natur. Mem., 19 (1989), 195–-246. (1991). |
[10] |
Aldo Bressan, On some control problems concerning the ski or swing, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Natur. Mem., 1 (1991), 147-196. |
[11] |
Aldo Bressan and M. Motta, A class of mechanical systems with some coordinates as controls. A reduction of certain optimization problems for them. Solution methods, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Mem., 9 (1993), 5-30. |
[12] |
F. Bullo and A. D. Lewis, "Geometric Control of Mechanical Systems," Springer Verlag, 2004. |
[13] |
F. Cardin and M. Favretti, Hyper-impulsive motion on manifolds, Dynam. Cont. Discr. Imp. Systems, 4 (1998), 1-21. |
[14] |
E. Cartan, Sur la possibilité de plonger un espace riemannien donné dans un espace euclidien, Ann. Soc. Polonaise Math., 6 (1927), 1-7. |
[15] |
P. S. Krishnaprasad and D. P. Tsakiris, Oscillations, SE(2)-snakes and motion control: A study of the roller racer, Dynamical Systems, 16 (2001), 347-397.doi: 10.1080/14689360110090424. |
[16] |
M. Levi, Geometry of vibrational stabilization and some applications, Int. J. Bifurc. Chaos, 15 (2005), 2747-2756.doi: 10.1142/S0218127405013745. |
[17] |
M. Levi and Q. Ren, Geodesics on vibrating surfaces and curvature of the normal family, Nonlinearity, 18 (2005), 2737-2743.doi: 10.1088/0951-7715/18/6/017. |
[18] |
W. S. Liu and H. J. Sussmann, Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories, in "Proc. 30-th IEEE Conference on Decision and Control" IEEE Publications, New York, (1991), 437-442. |
[19] |
C. Marle, Géométrie des systèmes mécaniques à liaisons actives, in "Symplectic Geometry and Mathematical Physics" (1991), 260-287, (Eds. P. Donato, C. Duval, J. Elhadad and G. M. Tuynman), Birkhäuser, Boston. |
[20] |
B. M. Miller, The generalized solutions of ordinary differential equations in the impulse control problems, J. Math. Syst. Estim. Control, 4 (1994), 385-388. |
[21] |
J. Nash, The imbedding problem for Riemannian manifolds, Annals of Math., 63 (1956), 20-63. |
[22] |
H. Nijmejer and A. J. van der Schaft, "Nonlinear Dynamical Control Systems," Springer Verlag, New York, 1990. |
[23] |
F. Rampazzo, On Lagrangian systems with some coordinates as controls, Atti Accad. Naz. Lincei, Classe di Scienze Mat. Fis. Nat. Serie 8, 82 (1988), 685-695. |
[24] |
F. Rampazzo, On the Riemannian structure of a Lagrangean system and the problem of adding time-dependent coordinates as controls, European J. Mechanics A/Solids, 10 (1991), 405-431. |
[25] |
F. Rampazzo, Lie brackets and impulsive controls: An unavoidable connection, Differential Geometry and Control, Proc. Sympos. Pure Math., (AMS, Providence) (1999), 279-296. |
[26] |
B. L. Reinhart, Foliated manifolds with bundle-like metrics, Annals of Math., 69 (1959), 119-132. |
[27] |
B. L. Reinhart, "Differential Geometry of Foliations. The Fundamental Integrability Problem," Springer-Verlag, Berlin, 1983. |
[28] |
H. J. Sussmann, On the gap between deterministic and stochastic ordinary differential equations, Ann. Prob., 6 (1978), 17-41. |