Etale backstepping for control Lyapunov function design on manifold

摘要

Backstepping is one of the most popular nonlinear controller and differentiable control Lyapunov function (CLF) design techniques. However, for asymptotic stabilization of systems defined on noncontractible manifolds, there exists no differentiable CLF; the semiconcave CLF design problem based on the back stepping has not been discussed. In this paper, we propose a backstepping based controller design method for asymptotic stabilization of systems defined on noncontractible manifolds. In the method, we design a controller and a CLF on an etale space. Then, we obtain a semiconcave CLF on the original space by the minimum projection method. The effectiveness of the proposed method is confirmed by computer simulation. (C) 2017 Published by Elsevier Ltd.