Solving nonlinear algebraic loops arising in input-saturated feedbacks - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes Accéder directement au contenu
Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2023

Solving nonlinear algebraic loops arising in input-saturated feedbacks

Résumé

We propose a dynamic augmentation scheme for the asymptotic solution of the nonlinear algebraic loops arising in well-known input saturated feedbacks typically designed by solving linear matrix inequalities (LMIs). We prove that the existing approach based on dynamic augmentation, which replaces the static loop by a dynamic one through the introduction of a sufficiently small time constant, works under some restrictive sufficient well-posedness conditions, requiring the existence of a diagonal Lyapunov matrix. However it can fail in general, even when the algebraic loop is well-posed. Then, we propose a novel approach whose effectiveness is guaranteed whenever wellposedness holds. We also show how this augmentation allows preserving the guaranteed region of attraction with Lyapunovbased designs, as long as a gain parameter is sufficiently large. We finally propose an adaptive version of the scheme where this parameter is adjusted online. Simulation results show the effectiveness of the proposed solutions.
Fichier principal
Vignette du fichier
final.pdf (2.77 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04148146 , version 1 (02-07-2023)

Identifiants

Citer

Franco Blanchini, Giulia Giordano, Francesco Riz, Luca Zaccarian. Solving nonlinear algebraic loops arising in input-saturated feedbacks. IEEE Transactions on Automatic Control, 2023, 68 (4), pp.2079-2093. ⟨10.1109/TAC.2022.3170858⟩. ⟨hal-04148146⟩
14 Consultations
56 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More