University of Minnesota
Asymptotic Stabilization of Relative Equilibria
The application of fundamental methods of theoretical mechanics to nonlinear control problems has lead to new methods and insights into the solution of such problems over the last decade. In this talk we will discuss recent work in this area on the asymptotic stabilization of relative equilibria. The objective in this case is the stabilization of steady motion and the design of a feedback control scheme that leaves invariant a subset of conserved quantities of the system. Our viewpoint is that of mechanical systems with symmetries. The theory will be discussed in the context of specific examples including a rotating rigid body and an asymmetrical heavy top.