Controlled Lagrangians and the Stabilization of Mechanical
Systems II: Potential Shaping
Bloch, A. M., D. Chang, N. Leonard and J. E. Marsden
Trans. IEEE on Auto. Control, 46, 1556-1571.
Abstract:
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.