Multilayer minimum projection method with singular point assignment for nonsmooth control Lyapunov function design

Abstract

Control Lyapunov functions (CLFs) design on manifolds is a difficult control problem. For the problem, we have proposed the multilayer minimum projection method. The method requires control Lyapunov functions (CLF) on other manifolds. For the case of “another single-manifold,” we relaxed the condition by desingularization of the function on the other manifold. However, the “multilayer-case” is not discussed. This paper focuses on the problem of desingularization via the multilayer minimum projection method. We show that the functions on other manifolds need not to be CLFs on these manifolds by considering desingularization. Based on the advantage of desingularization, we propose a CLF design method by singular point assignment. The method enables us to merge local CLFs into the global CLF. We confirm the effectiveness of the proposed CLF design method by an example of obstacle avoidance control of a mobile robot.