Using symbolic computation to solve algebraic Riccati equations arising in invariant filtering

Utilisation de méthodes symboliques pour la résolution d'équations algébriques de Riccati apparaissant en filtrage invariant

Axel Barrau (1) , Guillaume Rance (2) , Yacine Bouzidi (3) , Alban Quadrat (3) , Arnaud Quadrat (4)

1 Safran Tech
2 SAFRAN Electronics & Defense
3 GAIA - Géométrie, Algèbre, Informatique, Applications
4 SAGEM Défense Sécurité [Massy]

This paper proposes a new step in the development of invariant observers. In the past, this theory led to impressive simplifications of the error equations encountered in estimation problems, especially those related to navigation. This was used to reduce computation load or derive new theoretical properties. Here, we leverage this advantage to obtain closed-form solutions of the underlying algebraic Riccati equations through advanced symbolic computation methods.

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique; Calcul formel [cs.SC]

Axel Barrau, Guillaume Rance, Yacine Bouzidi, Alban Quadrat, Arnaud Quadrat. Using symbolic computation to solve algebraic Riccati equations arising in invariant filtering. ECC2018 - European Control Conference, Jun 2018, Limassol, Cyprus. ⟨hal-01667341⟩