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Fast and Robust Stability Region Estimation for Nonlinear Dynamical Systems

Eloïse Berthier 1, 2 Justin Carpentier 3, 2 Francis Bach 1, 2 
1 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique - ENS Paris, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
3 WILLOW - Models of visual object recognition and scene understanding
DI-ENS - Département d'informatique - ENS Paris, Inria de Paris
Abstract : A linear quadratic regulator can stabilize a nonlinear dynamical system with a local feedback controller around a linearization point, while minimizing a given performance criteria. An important practical problem is to estimate the region of attraction of such a controller, that is, the region around this point where the controller is certified to be valid. This is especially important in the context of highly nonlinear dynamical systems. In this paper, we propose two stability certificates that are fast to compute and robust when the first, or second derivatives of the system dynamics are bounded. Associated with an efficient oracle to compute these bounds, this provides a simple stability region estimation algorithm compared to classic approaches of the state of the art. We experimentally validate its application to both polynomial and non-polynomial systems of various dimensions, including standard robotic systems, for estimating region of attractions around equilibrium points, as well as for trajectory tracking.
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https://hal.archives-ouvertes.fr/hal-02984348
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Submitted on : Thursday, September 2, 2021 - 4:55:36 PM
Last modification on : Wednesday, June 8, 2022 - 12:50:06 PM

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Eloïse Berthier, Justin Carpentier, Francis Bach. Fast and Robust Stability Region Estimation for Nonlinear Dynamical Systems. European Control Conference (ECC) 2021, Jun 2021, Rotterdam, Netherlands. ⟨hal-02984348v2⟩

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