Feedback Design Using Nonsmooth Control Lyapunov Functions: A Numerical Case Study for the Nonholonomic Integrator

Titelangaben

Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M.:
Feedback Design Using Nonsmooth Control Lyapunov Functions: A Numerical Case Study for the Nonholonomic Integrator.
In: Proceedings of the 56th IEEE Annual Conference on Decision and Control (CDC 2017), Melbourne, Australia. - Melbourne , 2017 . - S. 4890-4895
ISBN 978-1-5090-2873-3
DOI: https://doi.org/10.1109/CDC.2017.8264382

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Abstract

Theoretical results for the existence of (nonsmooth) control Lyapunov functions (CLFs) for nonlinear systems asymptotically controllable to the origin or a closed set have been available since the late 1990s. Additionally, robust feedback stabilizers based on such CLFs have also been available though, to the best of our knowledge, these stabilizers have not been implemented. Here, we numerically investigate the properties of the closed loop solutions of the nonholonomic integrator using three control techniques based on the knowledge of two different nonsmooth CLFs. In order to make the paper self-contained, we review theoretical results on the existence of nonsmooth CLFs.