Adaptive stabilization of a saddle state of a conservative dynamical system: a spacecraft at the Lagrange point L2 of the Sun-Earth system

Abstract

An adaptive feedback method for tracking and stabilizing unknown or slowly varying saddle type steady states of conservative dynamical systems is proposed. We demonstrate that a conservative saddle point can be stabilized with neither unstable nor stable filter technique. The suggested controller involves both filters working in parallel. As a specific example, the Lagrange point L2 of the Sun-Earth system is discussed and a general second order saddle model is considered.