Volume 27, 2021
|Number of page(s)||36|
|Published online||03 November 2021|
New perspectives on output feedback stabilization at an unobservable target*
Univ. Lyon, Université Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, 43 bd du 11 novembre 1918,
2 Université de Toulon, Aix Marseille Univ, CNRS, LIS, France.
3 Inria, Université Côte d’Azur, LJAD, CNRS, MCTAO team, Sophia Antipolis, France.
** Corresponding author: firstname.lastname@example.org
Accepted: 28 September 2021
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.
Mathematics Subject Classification: 93D15 / 93B07 / 93C10 / 22D10
Key words: Output feedback / stabilization / observability / nonlinear systems / dissipative systems / representation theory
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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