Controlled Lagrangians and the stabilization of mechanical systems II: Potential shaping

IEEE Transactions on Automatic Control

Volumn 46, Issue 10, 2001, Pages 1556-1571

  Bloch, Anthony M ^a,b   Chang, Dong Eui ^c   Leonard, Naomi Ehrich ^a,d   Marsden, Jerrold E ^c  

^a IEEE   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^d Princeton University   (United States)

Author keywords

Lyapunov methods; Mechanical systems; Non linear control; Stabilization; Tracking

Indexed keywords

CONTROLLED LAGRANGIANS; MECHANICAL SYSTEMS; POTENTIAL SHAPING; TRACKING;

ASYMPTOTIC STABILITY; CLOSED LOOP CONTROL SYSTEMS; FEEDBACK CONTROL; LYAPUNOV METHODS; MECHANISMS; NONLINEAR CONTROL SYSTEMS; PENDULUMS; STATE SPACE METHODS; SYSTEM STABILITY;

LAGRANGE MULTIPLIERS;

EID: 0035471689     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.956051     Document Type: Article

References (47)

1. Swinging up a pendulum by energy control
2. Control of nonlinear underactuated systems
3. Stable average motions of mechanical systems subject to periodic forcing
4. The geometry of controlled mechanical systems
5. Matching conditions and geometric invariants for second-order control systems
6. Potential and kinetic shaping for control of underactuated mechanical systems
7. Asymptotic stabilization of Euler-Poincaré mechanical systems
8. Stabilization of rigid body dynamics by internal and external torques
9. Stabilization of mechanical systems using controlled Lagrangians
10. Matching and stabilization by the method of controlled Lagrangians
11. Stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians
12. Potential shaping and the method of controlled Lagrangians
13. Controlled Lagrangians and the stabilization of mechanical systems I: The first matching theorem
14. Controlled Lagrangians and the stabilization of Euler-Poincaré mechanical systems
15. Controlling homoclinic orbits
16. Stabilization of relative equilibria of mechanical systems with symmetry
17. Tracking for fully actuated mechanical systems: A geometric framework
18. Lyapunov-based transfer between elliptic Keplerian orbits
19. Asymptotic stabilization of the heavy top using controlled Lagrangians
20. Dynamic inversion of nonlinear maps with applications to nonlinear control and robotics
21. Configuration manifolds and their applications to robotic dynamic modeling and control
22. General matching conditions in the theory of controlled Lagrangians
23. Controlled Lagrangians, symmetries and conditions for strong matching
24. Stabilization of relative equilibria II
25. Stabilization of relative equilibria
26. Robot navigation functions on manifolds with boundary
27. Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
28. Stabilization of underwater vehicle dynamics with symmetry-breaking potentials
29. The category of affine connection control systems
30. Adding integrations, saturated controls, and stabilization for feedforward systems
31. Energy-shaping of port-controlled Hamiltonian systems by interconnection
32. Robust stabilization of a heavy top
33. The control of underactuated mechanical systems
34. The swing up control problem for the acrobat
35. Energy based control of a class of underactuated mechanical systems
36. A nonlinear small gain theorem for the analysis of control systems with saturation
37. Stabilization of Hamiltonian Systems
38. Gyroscopic control and stabilization
39. Energy shaping and dissipation: Underwater vehicle stabilization using internal rotors
40. Physical dissipation and the method of controlled Lagrangians
41. Global asymptotic stabilization of an underwater vehicle using internal rotors
42. Matching and stabilization of the unicycle with rider
43. The energy momentum method for the stability of nonholonomic systems
44. Feedback stabilization of uniform rigid body rotation