Structure-preserving Observers for port-Hamiltonian systems via contraction analysis

Mario Spirito (1, 2) , Yann Le Gorrec (3) , Bernhard Maschke (4)

1 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique
2 UCBL - Université Claude Bernard Lyon 1
3 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
4 LAGEP - Laboratoire d'automatique et de génie des procédés

We address the design of structure preserving observers for port-Hamiltonian systems. Despite what is done in the literature on nonlinear observers for this class of systems, we consider a Luenberger-like identity observer dynamics with an output injection term. We provide an analysis on the passivity properties of the observer dynamics and of the system-observer cascade. We then consider the convergence properties of the observer scheme by exploiting the contraction theory (or convergent dynamics) approach, and we show the exponential convergence rate of the state reconstruction. We conclude the work by applying the proposed technique to a velocity observation of a PMSM system with only current measurements.

Mots clés: Structure-preserving Observer; convergent dynamics; port-Hamiltonian systems; Contraction theory

Domaines: Systèmes dynamiques [math.DS]

Mario Spirito, Yann Le Gorrec, Bernhard Maschke. Structure-preserving Observers for port-Hamiltonian systems via contraction analysis. 2024. ⟨hal-04344593v2⟩