Publication

Set-membership approach and Kalman observer based on zonotopes for discrete-time descriptor systems

Journal Article (2018)

Journal

Automatica

Pages

435-443

Volume

93

Doc link

https://doi.org/10.1016/j.automatica.2018.03.082

File

Download the digital copy of the doc pdf document

Abstract

This paper proposes a set-membership state estimator and a zonotopic Kalman observer for discrete-time descriptor systems. Both approaches are developed in a set-based context considering system disturbances, measurement noise, and unknown inputs. This set-membership state estimation approach determines the set of consistent states with the model and measurements by constructing a parameterized intersection zonotope. Two methods to minimize the size of this intersection zonotope are provided: one inspired by Kalman ltering and the other based on solving an optimization problem involving a series of linear matrix inequalities. Additionally, we propose a zonotopic Kalman observer for discrete-time descriptor systems. Moreover, the relationship between both approaches is discussed. In particular, it is proved that the zonotopic Kalman observer in the current estimation type is equivalent to the set-membership approach. Finally, a numerical example is used to illustrate and compare the effectiveness of the proposed approaches.

Categories

control theory, optimisation.

Author keywords

Set-membership approach; Kalman observer; Zonotopes; Discrete-time descriptor systems; Unknown inputs

Scientific reference

Y. Wang, V. Puig and G. Cembrano. Set-membership approach and Kalman observer based on zonotopes for discrete-time descriptor systems. Automatica, 93: 435-443, 2018.