TY - JOUR
T1 - Sampled Observability and State Estimation of Linear Discrete Ensembles
AU - Zeng, Shen
AU - Ishii, Hideaki
AU - Allgower, Frank
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2017/5
Y1 - 2017/5
N2 - We consider the problem of reconstructing the initial states of a finite group of structurally identical linear systems in the situation that output measurements of the individual systems are received at discrete time steps and in an anonymized manner: While we do know all output measurements of the individual systems in the group, we do not know which output measurement corresponds to which system. This state estimation problem addresses the essence of state estimation problems for populations, in which the output measurements of the individual systems are given only as statistics. We adopt a measure theoretical approach in which the group is modelled by an LTI system describing the structure of the individual systems and an initial state which is expressed by a discrete measure. In this framework we derive a geometric characterization for the state estimation to admit a unique solution, which combined with a result on the observability of linear systems under irregular sampling, yields a sufficient condition for the sampled observability of discrete ensembles. As a supplement to our theoretical findings, we provide illustrations by means of simulation examples. Furthermore we consider the practical state estimation problem under noisy output measurements.
AB - We consider the problem of reconstructing the initial states of a finite group of structurally identical linear systems in the situation that output measurements of the individual systems are received at discrete time steps and in an anonymized manner: While we do know all output measurements of the individual systems in the group, we do not know which output measurement corresponds to which system. This state estimation problem addresses the essence of state estimation problems for populations, in which the output measurements of the individual systems are given only as statistics. We adopt a measure theoretical approach in which the group is modelled by an LTI system describing the structure of the individual systems and an initial state which is expressed by a discrete measure. In this framework we derive a geometric characterization for the state estimation to admit a unique solution, which combined with a result on the observability of linear systems under irregular sampling, yields a sufficient condition for the sampled observability of discrete ensembles. As a supplement to our theoretical findings, we provide illustrations by means of simulation examples. Furthermore we consider the practical state estimation problem under noisy output measurements.
KW - Ensemble observability
KW - linear systems
KW - observability
KW - sampled data control
UR - http://www.scopus.com/inward/record.url?scp=85010720128&partnerID=8YFLogxK
U2 - 10.1109/TAC.2016.2613478
DO - 10.1109/TAC.2016.2613478
M3 - Article
AN - SCOPUS:85010720128
SN - 0018-9286
VL - 62
SP - 2406
EP - 2418
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 5
ER -