Optimal control for holonomic and nonholonomic mechanical systems with symmetry and Lagrangian reduction

SIAM Journal on Control and Optimization

Volumn 35, Issue 3, 1997, Pages 901-929

  Koon, Wang Sang ^a,b   Marsden, Jerrold E ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Constraints; Lagrangian reduction; Mechanical systems with symmetry; Nonholonomic; Optimal control

Indexed keywords

CONSTRAINT THEORY; MATHEMATICAL OPERATORS; MAXIMUM PRINCIPLE; MECHANICAL CONTROL EQUIPMENT; OPTIMAL CONTROL SYSTEMS;

HOLONOMIC SYSTEM;

MECHANICAL VARIABLES CONTROL;

EID: 0031145153     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012995290367     Document Type: Article

References (25)

1. A. M. BLOCH AND P. CROUCH (1992), On the dynamics and control of nonholonomic systems on Riemannian manifolds, in Proc. NOLCOS '92, Bordeaux, France, pp. 368-372.
2. A. M. BLOCH AND P. CROUCH (1994), Reduction of Euler Lagrange problems for constrained variational problems and relation with optimal control problems, in Proc. 33rd CDC, IEEE, pp. 2584-2590.
3. A. M. BLOCH AND P. CROUCH (1995), Nonholonomic control systems on Riemanman manifolds, SIAM J. Control Optim., 33, pp. 126-148.
4. A. M. BLOCH, P. CROUCH, AND T. S. RATIU (1994), Sub-Riemannian optimal control problems, Fields Inst. Commun., 3, pp. 35-48.
5. A. M. BLOCH, P. S. KRISHNAPRASAD, J. E. MARSDEN, AND R. MURRAY (1996), Nonholonomic mechanical systems with symmetry, Arch. Rational Mech. Anal., to appear.
6. A. M. BLOCH, P. S. KRISHNAPRASAD, J. E. MARSDEN, AND T. S. RATIU (1996), The Euler-Poincaré equations and double bracket dissipation, Comm. Math. Phys., 175, pp. 1-42.
7. A. M. BLOCH, P. S. KRISHNAPRASAD, J. E. MARSDEN, AND G. SÁNCHEZ DE ALVAREZ (1992), Stabilization of rigid body dynamics by internal and external torques, Automatica J. IFAC, 28, pp. 745-756.
8. R. W. BROCKETT AND L. DAI (1992), Nonholonomic kinematics and the role of elliptic functions in constructive controllability, in Nonholonomic Motion Planning, Z. Li and J. F. Canny, eds., Kluwer International Series in Engineering and Science, Kluwer, Amsterdam, pp. 1-22.
9. V. JURDJEVIC (1993), The geometry of the plate-ball problem, Arch. Rational Mech. Anal., 124, pp. 305-328.
10. V. JURDJEVIC (1996), Optimal control problems on Lie groups: Crossroads between geometry and mechanics, in Geometry and Feedback Control, Marcel Dekker, New York.
11. S. D. KELLY AND R. M. MURRAY (1995), Geometric phases and robotic locomotion, J. Robotic Systems, to appear.
12. P. S. KRISHNAPRASAD (1993), Optimal Control and Poisson Reduction, Institute for Systems Research Technical report 93-87, University of Maryland, College Park, MD, pp. 1-16.
13. P. S. KRISHNAPRASAD, R. YANG, AND W. DAYAWANSA (1991), Control problems on principal bundles and nonholonomic mechanics, in Proc. 30th CDC, IEEE, pp. 1133-1138.
14. J. E. MARSDEN (1992), Lectures on Mechanics, London Mathematical Society Lecture Note Series 174, Cambridge University Press.
15. J. E. MARSDEN AND T. S. RATIU (1994), An Introduction to Mechanics and Symmetry, Texts in Appl. Math. 17, Springer-Verlag, Berlin.
16. J. E. MARSDEN AND J. SCHEURLE (1993a), Lagrangian reduction and the double spherical pendulum, Z. Angew. Math. Phys., 44, pp. 17-43.
17. J. E. MARSDEN AND J. SCHEURLE (1993b), The reduced Euler-Lagrange equations, Fields Institute Comm., 1, pp. 139-164.
18. R. MONTGOMERY (1984), Canonical formulations of a particle in a Yang-Mills field, Lett. Math. Phys., 8, pp. 59-67.
19. R. MONTGOMERY (1990), Isoholonomic problems and some applications, Comm. Math. Phys., 128, pp. 565-592.
20. R. MONTGOMERY (1991), Optimal control of deformable bodies and its relation to gauge theory, in The Geometry of Hamiltonian Systems, T. Ratiu, ed., Springer-Verlag, Berlin.
21. R. MONTGOMERY (1993), Gauge theory of the falling cat, Fields Inst. Comm., 1, pp. 193-218.
22. Ju. I. NAIMARK AND N. A. FUFAEV (1972), Dynamics of Nonholonimic Systems, Translations of Mathematical Monographs 33, AMS, Providence, RI.
23. A. M. VERSHIK AND V. YA. GERSHKOVICH (1994), Nonholonomic dynamical systems, geometry of distributions and variational problems, in Dynamical Systems VII, V. Arnold and S. P. Novikov, eds., Springer-Verlag, New York, pp. 1-81.
24. G. WALSH, R. MONTGOMERY, AND S. SASTRY (1994), Optimal Path Planning on Matrix Lie Groups, preprint.
25. R. YANG (1992), Nonholonomic Geometry, Mechanics and Control, Institute for Systems Research Technical Report, 92-14, University of Maryland, College Park, MD.