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

For pt.I, see ibid., vol.45, p.2253-70 (2000). We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserv...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2001-10, Vol.46 (10), p.1556-1571
Main Authors: Bloch, A.M., Dong Eui Chang, Leonard, N.E., Marsden, J.E.
Format: Article
Language:English
Subjects:
Aerodynamics
Asymptotic properties
Automatic control
Carts
Complement
Control systems
Dissipation
Equations
Kinetic theory
Lagrangian functions
Linear feedback control systems
Mechanical systems
Mechanical variables control
Nonlinear control systems
Shape control
Stabilization
Symmetry
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Summary:For pt.I, see ibid., vol.45, p.2253-70 (2000). We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.956051