Cristina Stoica

Wilfred Laurier University, Waterloo, Ont. Canada

Control on Lie groups via Energy Shape Change

This talk concerns control methods based on alterations of the inertia metric for motions on Lie groups.

First, I will discuss a satellite attitude control problem. Satellite attitude control is typically achieved via reaction wheels (i.e. rotors) or magnets, which leave the moment of inertia fixed. I will present an alternative control mechanism: sliding point masses, which change the moment of inertia and thus the angular velocity, while leaving angular momentum fixed. This work involves a normal form parametrization of the phase space of the rigid body, which in its turn is based on a constructive symplectic slice theorem.

Second, I will explore similar control methods for ideal (Euler) fluids equations.  In particular, I will refer to Lagrangian averaged-\alpha models associated to second-grade fluids with zero viscosity. For these fluids, the inertia operator depends on  \alpha,  a material parameter related to the elastic response of the fluid.