Design of Optimal Interval Observers Using Set-Theoretic Methods for Robust State Estimation

Feng Xu (1) , Junbo Tan (1) , Tarek Raissi (2) , Bin Liang (1)

1 THU - Tsinghua University [Beijing]
2 CEDRIC - LAETITIA - CEDRIC. Traitement du signal et architectures électroniques

This paper aims to design an optimal interval observer for discrete linear time-invariant (LTI) systems. Particularly, the proposed design method first transforms the interval observer into a zonotopic set-valued observer by establishing an explicit mathematical relationship between the interval observer and the zonoptopic set-valued observer. Then, based on the established mathematical relationship, a local optimal observer gain is designed for the interval observer via the equivalent zonotopic set-valued observer structure and the Frobenious norm (F-norm) based size of zonotopes. Third, considering that the dynamics of the optimal interval observer becomes a discrete linear time varying (LTV) system owing to the designed timevarying optimal gain, an optimization problem to obtain a coordinate transformation matrix and the local optimal observer gain for the interval observer is formulated and handled. Finally, a theoretic comparison on the conservatism of the interval observer and the zonotopic set-valued observer is made. At the end of this paper, a microbial growth bioprocess is used to illustrate the effectiveness of the proposed method.

Domaines: Automatique / Robotique

Feng Xu, Junbo Tan, Tarek Raissi, Bin Liang. Design of Optimal Interval Observers Using Set-Theoretic Methods for Robust State Estimation. International Journal of Robust and Nonlinear Control, 2020, ⟨10.1002/rnc.4960⟩. ⟨hal-02488500⟩