A Fixed-Time Stable Adaptation Law for Safety-Critical Control under Parametric Uncertainty.

Abstract

We present a novel technique for solving the problem of safe control for a class of nonlinear, control-affine systems subject to parametric model uncertainty. Invoking Lyapunov analysis and the notion of fixed-time stability (FxTS), we introduce a parameter adaptation law which guarantees convergence of the estimates of unknown parameters in the system dynamics to their true values within a fixed-time independent of the initial error. We then synthesize this law with a robust, adaptive control barrier function (RaCBF)-based quadratic program to compute safe control inputs despite the considered uncertainty. To corroborate our results, we undertake a comparative case study on the efficacy of this result versus other recent approaches in the literature to safe control under uncertainty, and close by highlighting the value of our method in the context of an automobile overtake scenario.

Bib

@inproceedings{DBLP:conf/eucc/BlackAP21,
  author       = {Mitchell Black and
                  Ehsan Arabi and
                  Dimitra Panagou},
  title        = {A Fixed-Time Stable Adaptation Law for Safety-Critical Control under
                  Parametric Uncertainty},
  booktitle    = {2021 European Control Conference, {ECC} 2021, Virtual Event / Delft,
                  The Netherlands, June 29 - July 2, 2021},
  pages        = {1328--1333},
  publisher    = {{IEEE}},
  year         = {2021},
  url          = {https://doi.org/10.23919/ECC54610.2021.9655080},
  doi          = {10.23919/ECC54610.2021.9655080},
  timestamp    = {Thu, 31 Mar 2022 11:10:43 +0200},
  biburl       = {https://dblp.org/rec/conf/eucc/BlackAP21.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}