Preliminary results on asymptotic stabilization of Hamiltonian systems with nonholonomic constraints

Abstract

This paper presents some preliminary results on asymptotic stabilization of nonholonomic mechanical systems using the Hamiltonian formulation proposed by van der Schaft and Maschke (1994). Our work seeks to establish a general formulation for designing time-varying controllers for some mechanical system described in the generalized coordinates (position and momentum). The paper gives the change of coordinates that transforms the Hamiltonian system to the form needed to apply the center manifold theorem. We also present a worked example for which stability is analyzed.