Uniting two Control Lyapunov Functions for affine systems (full version)
Résumé
The problem of piecing together two Control Lyapunov Functions (CLFs) is addressed. The first CLF characterizes a local asymptotic controllability property toward the origin, whereas the second CLF is related to a global asymptotic controllability property with respect to a compact set. A sufficient condition is expressed to obtain an explicit solution. This sufficient condition is shown to be always satisfied for a linear second order controllable system. In a second part, it is shown how this uniting CLF problem can be used to solve the problem of piecing together two stabilizing control laws. Finally, this framework is applied on a numerical example to improve local performance of a globally stabilizing state feedback. Note that this paper is the full version of a paper submitted to IEEE TAC.
Domaines
Automatique / Robotique
Origine : Fichiers produits par l'(les) auteur(s)