Control Problems of Hydrodynamic Type

摘要

It has been known for some time that the classical work of Kirchhoff, Love, and Birkhoff on rigid bodies in incompressible, irrotational flows provides effective models for treating control problems for underwater vehicles. This has also lead to a better appreciation of the dynamics of such systems. In this paper, we develop results based on geometric mechanics and center manifold theory to solve controllability and stabilization questions for a class of under-actuated left invaiant mechanical systems on Lie groups that include approximate models of underwater vehicles and surface vehicles. We also provide numerical evidence to capture the global properties of certain interesting feedback laws.