Title :
Stabilization of relative equilibria for systems on Riemannian manifolds
Author :
Bullo, Francesco
Author_Institution :
Coordinated Sci. Lab., Illinois Univ., Urbana, IL, USA
Abstract :
Describes a systematic procedure to exponentially stabilize relative equilibria of mechanical systems. We review the notion of relative equilibria and their stability in a Riemannian geometry context. Potential shaping and dissipation are employed to obtain full exponential stabilization to the desired trajectory. Two necessary conditions are that the effective potential be positive definite over a specified subspace and that the system be linearly controllable
Keywords :
Lyapunov methods; asymptotic stability; control system synthesis; controllability; geometry; Riemannian geometry; Riemannian manifolds; dissipation; exponential stabilisation; linearly controllable system; mechanical systems; necessary conditions; potential shaping; relative equilibria; Control systems; Convergence; Geometry; Lyapunov method; Manifolds; Mechanical systems; Remotely operated vehicles; Stability; Underwater vehicles; Velocity control;
Conference_Titel :
American Control Conference, 1999. Proceedings of the 1999
Conference_Location :
San Diego, CA
Print_ISBN :
0-7803-4990-3
DOI :
10.1109/ACC.1999.786104
