A direct lyapunov approach for a class of underactuated mechanical systems

Proceedings of the American Control Conference

Volumn 2006, Issue , 2006, Pages 103-110

  White, Warren N ^a   Foss, Mikil ^b   Guo, Xin ^a  

^a Kansas State University   (United States)

^b UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; DEGREES OF FREEDOM (MECHANICS); FEEDBACK; LYAPUNOV FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; TORQUE;

LYAPUNOV DIRECT METHOD; MASS/INERTIA MATRIX; MECHANICAL SYSTEMS;

DYNAMICAL SYSTEMS;

EID: 34047228942     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (30)

1. Andreev, Fedor, Dave Auckly, Shekhar Gosavi, Lev Kapitanski, Atul G. Kelkar, Warren White; "Matching, Linear Systems, and the Ball and Beam," Automatica, v 38, n 12, December, 2002a, p. 2147-2152.
2. Andreev, F., D. Auckly, L. Kapitanski, A.G. Kelkar, W.N. White; "Matching and digital control implementation for underactuated Systeme" American Control Conference, 2000. Proceedings of the 2000, Volume: 6, 28-30 June 2000b Pages:3934 - 3938 vol.6.
3. Auckly, D, L. Kapitanski, and W. White; "Control of Nonlinear Underactuated Systems" Comm. Pure Appl. Math, 53, number 3, 2000a, pp.354-369.
4. Auckly, D. and L. Kapitanski; "Mathematical Problems in the Control of Underactuated Systems," CRM Proceedings and Lecture Notes," v 27, 2000b, p. 41 - 52.
5. Auckly, D. and L. Kapitanski; "On The λ-Equations for Matching Control Laws," SIAM Journal Control and Optimization, 41 2002c, number 5, pp 1372-1388.
6. Blankenstein, Guido, Romeo Ortega, and Arjan J Van Der Schaft; "The Matching Conditions of Controlled Lagrangians and IDA Passivity Based Control," International Journal of Control, v 75, n 9, Jun 15, 2002, p 645-665.
7. Bloch, Anthony M., Naomi Enrich Leonard, and Jerrold E. Marsden; "Controlled Lagrangians and the Stabilization of Mechanical Systems. I: The First Matching Theorem," IEEE Transactions on Automatic Control, v 45, n 12, Dec, 2000, p 2253-2270.
8. Bloch, A.M., Dong Eui Chang, N.E. Leonard, J.E. Marsden; "Controlled Lagrangians and the stabilization of mechanical systems. II. Potential Shaping" IEEE Transactions on Automatic Control, Volume: 46, Issue: 10, Oct. 2001, p. 1556 - 1571.
9. Brocket, R.W.; "Feedback Invariants for Nonlinear Systems" Proceedings IFAC Congress, Vol. 6, 1978, p. 115-1120.
10. Chang, Dong Eui, Anthony M. Bloch, Naomi E.Leonard, Jerrold E. Marsden, and Craig A. Woolsey; "The Equivalence of Controlled Lagrangians and Controlled Hamiltonian Systems," ESIAM: Control, Optimisation, and Calculus of Variations, preprint, 2001.
11. Hamberg, Johan; "General Matching Conditions in the Theory of Controlled Lagrangians," Proceedings of the IEEE Conference on Decision and Control, v 3, 1999, p 2519-2523.
12. Hamberg, Johan, "Simplified Conditions for Matching and for Generalized Matching in the Theory of Controlled Lagrangians," Proceedings of the American Control Conference, v 6, 2000, p 3918-3923.
13. Hermann, Robert and Arthur J. Krener; "Nonlinear Controllability and Observability," IEEE Transactions on Automatic Control, 22, number 5, p 728-740, Oct. 1977.
14. Isidori, A., A. J. Krener, G. C. Gori-Giorgi, and 8. Monaco; "Nonlinear Decoupling via Feedback-' A Differential Geometric Approach," IEEE Transactions on Automatic Control, 26, number 2, p. 331-345, April 1981.
15. Jakubczyk, B. and W. Respondek; "On Linearization of Control Systems" Bull. Acad. Polonaise Sci. Ser. Sci. Math., 28, p. 517522, 1980.
16. Kelkar, Atul G., Bo Fang, Warren White, Xin Guo; "Feedback Stabilization of Underactuated Nonlinear Pendulum Cart System Using Matching Conditions," Proceedings of the American Control Conference, v 6, 2002, p 4696-4701.
17. Khalil, Hassan K.; Nonlinear Systems, Upper Saddle River, NJ: Prentice-Hall, 2002.
18. Mazenc, F., A. Astolfi, and R. Lozanoi "Lyapunov Function for the Ball and Beam: Robustness Property," Proceedings of the 1999 IEEE Conference on Decision and Control, Phoenix, AZ USA, Dec. 1999, pp. 1208-1213.
19. st Ed., Englewood Cliffs, NJ: 1970.
20. Olfati-Saber, Reza and Alexandre Megretski; "Control for a Class of Underactuated Nonlnear Systems" Proceedings of the IEEE Conference on Decision and Control, 1998, p. 4182-4187.
21. Olfati-Saber, Reza; "Control of Underactuated Mechanical Systems with Two Degrees of Freedom and Symmetry" Proceedings of the American Control Conference, v 6, 2000, p 4092-4096.
22. Olfati-Saber, Reza; Nonlinear Control of Underactuated Systems with Application to Robotics and Aerospace Vehicles, Ph.D. thesis, Massachusetts Institute of Technology, Department of Electrical and Computer Science, Feb. 2001a.
23. Olfati-Saber, Reza; "Nonlinear Control and Reduction of Underactuated Systems with Symmetry," Actuated Shape Variables Case" Proceedings of the IEEE Conference on Decision and Control, v 5, 2001b, p 4158-4163.
24. Olfati-Saber, Reza; "Nonlinear Control and Reduction of Underactuated Systems with Symmetry II- Unactuated Shape Variables Case" Proceedings of the IEEE Conference on Decision and Control, v 5, 2001c, p 4164-4169.
25. Olfati-Saber, Reza; "Nonlinear Control and Reduction of Underactuated Systems with Symmetry III-' Input Coupling Case," Proceedings of the IEEE Conference on Decision and Control, v 5, 2001d, p 3778-3783.
26. Ortega, Romeo; Arjan van der Schaft, Bernhard Maschke and Gerardo Escobari "Interconnection and Damping Assignment Passivity-Based Control of Port-Controlled Hamiltonian Systems" Automatica, 38, 2002a, p 585 - 596.
27. Ortega, Romeo, Mark W. Spong, Fabio Gomez-Estern, and Guido Blankensteini "Stabilization of a Class of Underactuated Mechanical Systems via Interconnection and Damping Assignment," IEEE Transactions on Automatic Control, v 47, n 8, August, 2002b, p 1218-1233.
28. Spong, Mark W.; "Underactuated Mechanical Systems,"from Control Problems in Robotics and Automation by B. Siciliano and K.P. Valavanis, eds. New York: Springer, 1998. p. 135-150.
29. Su, R.; "On the Linear Equivalents of Nonlinear Systems" Systems & Control Letters, 2, number 1, p. 48-52, July 1982.
30. Zenkov, Dmitry V., Bloch, Anthony M., Marsen, Jerrold E.; "Flat Nonholonomic Matching," Proceedings of the American Control Conference, v 4, 2002, p 2812-2817.