Kalman-like Observer for Hybrid Systems with Linear Maps and Known Jump Times (Full Version) - Automatique et systèmes (CAS) Access content directly
Conference Papers Year : 2023

Kalman-like Observer for Hybrid Systems with Linear Maps and Known Jump Times (Full Version)

Gia Quoc Bao Tran
Pauline Bernard

Abstract

We propose a hybrid Kalman-like observer for general hybrid systems with linear (time-varying) dynamics and output maps, where the solutions' jump times are exactly known. After defining a hybrid observability Gramian and the corresponding hybrid uniform complete observability, we show that the estimate provided by this observer converges asymptotically to the system solution if this observability holds together with some boundedness and invertibility conditions along the considered system solution. Then, under additional uniformity and strictness of the forgetting factors, we show exponential stability of the estimation error with an arbitrarily fast rate. The robust stability of this error against input disturbances and measurement noise is also studied. The results are illustrated on several benchmark examples, including switched systems, hybrid systems with discontinuous solutions, and continuoustime systems with multi-rate sporadic outputs.
Fichier principal
Vignette du fichier
Hybrid_Kalman (1).pdf (1.47 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04196352 , version 1 (05-09-2023)
hal-04196352 , version 2 (14-12-2023)

Identifiers

  • HAL Id : hal-04196352 , version 2

Cite

Gia Quoc Bao Tran, Pauline Bernard. Kalman-like Observer for Hybrid Systems with Linear Maps and Known Jump Times (Full Version). 62nd IEEE Conference on Decision and Control, Dec 2023, Singapore, Singapore. ⟨hal-04196352v2⟩
293 View
112 Download

Share

Gmail Facebook X LinkedIn More