New perspectives on output feedback stabilization at an unobservable target

Lucas Brivadis (1, 2) , Jean-Paul Gauthier (3, 4) , Ludovic Sacchelli (1, 2) , Ulysse Serres (1, 2)

1 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique
2 UCBL - Université Claude Bernard Lyon 1
3 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
4 UTLN - Université de Toulon

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.

Mots clés: Output feedback; Stabilization; Observability; Nonlinear systems; Luenberger observers; Dissipative systems; Representation theory

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Lucas Brivadis, Jean-Paul Gauthier, Ludovic Sacchelli, Ulysse Serres. New perspectives on output feedback stabilization at an unobservable target. ESAIM: Control, Optimisation and Calculus of Variations, 2021, 27 (2021) (102), ⟨10.1051/cocv/2021097⟩. ⟨hal-03021663v2⟩