We address the problem of dynamic output feedback stabilization at an unobservable target point. The challenge lies in according the antagonistic nature of the objective and the properties of the system: the system tends to be less observable as it approaches the target. We illustrate two main ideas: well chosen perturbations of a state feedback law can yield new observability properties of the closed-loop system, and embedding systems into bilinear systems admitting observers with dissipative error systems allows to mitigate the observability issues. We apply them on a case of systems with linear dynamics and nonlinear observation map and make use of an ad hoc finite-dimensional embedding. More generally, we introduce a new strategy based on infinite-dimensional unitary embeddings. To do so, we extend the usual definition of dynamic output feedback stabilization in order to allow infinite-dimensional observers fed by the output. We show how this technique, based on representation theory, may be applied to achieve output feedback stabilization at an unobservable target.
Keywords: Output feedback, stabilization, observability, nonlinear systems, dissipative systems, representation theory
@article{COCV_2021__27_1_A104_0,
author = {Brivadis, Lucas and Gauthier, Jean-Paul and Sacchelli, Ludovic and Serres, Ulysse},
title = {New perspectives on output feedback stabilization at an unobservable target},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021097},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021097/}
}
TY - JOUR AU - Brivadis, Lucas AU - Gauthier, Jean-Paul AU - Sacchelli, Ludovic AU - Serres, Ulysse TI - New perspectives on output feedback stabilization at an unobservable target JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021097/ DO - 10.1051/cocv/2021097 LA - en ID - COCV_2021__27_1_A104_0 ER -
%0 Journal Article %A Brivadis, Lucas %A Gauthier, Jean-Paul %A Sacchelli, Ludovic %A Serres, Ulysse %T New perspectives on output feedback stabilization at an unobservable target %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021097/ %R 10.1051/cocv/2021097 %G en %F COCV_2021__27_1_A104_0
Brivadis, Lucas; Gauthier, Jean-Paul; Sacchelli, Ludovic; Serres, Ulysse. New perspectives on output feedback stabilization at an unobservable target. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 102. doi: 10.1051/cocv/2021097
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Cité par Sources :
This research was partially funded by the French Grant ANR ODISSE (ANR-19-CE48-0004-01) and by the ANR SRGI (ANR-15-CE40-0018).
