TY - JOUR
T1 - A moment-based approach to ensemble controllability of linear systems
AU - Zeng, Shen
AU - Allgöwer, Frank
N1 - Funding Information:
The authors thank the German Research Foundation (DFG) for financial support of the project under grant number AL316/14-1 and within the Cluster of Excellence in Simulation Technology (EXC 310/2) at the University of Stuttgart. The authors would like to thank Roger Brockett for hosting the research stay of the first author at Harvard University, during which parts of this work were carried out.
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - In this paper we introduce a new perspective on the L2-ensemble controllability problem of linear time-invariant systems using an ℓ2-framework. The reformulation results from focussing on the controllability of the ensemble's moments, which evolve under a linear system defined on the space of square-summable sequences. For a specific class of ensembles, a necessary and sufficient condition can be stated in terms of truncations of infinite Kalman matrices. We illustrate the analysis in this framework on several examples which highlight the possibility of using elementary structural arguments in proving or disproving the controllability of an ensemble's moments, as well as essential differences to the uniform ensemble controllability property which is mostly considered in the literature.
AB - In this paper we introduce a new perspective on the L2-ensemble controllability problem of linear time-invariant systems using an ℓ2-framework. The reformulation results from focussing on the controllability of the ensemble's moments, which evolve under a linear system defined on the space of square-summable sequences. For a specific class of ensembles, a necessary and sufficient condition can be stated in terms of truncations of infinite Kalman matrices. We illustrate the analysis in this framework on several examples which highlight the possibility of using elementary structural arguments in proving or disproving the controllability of an ensemble's moments, as well as essential differences to the uniform ensemble controllability property which is mostly considered in the literature.
KW - Approximate controllability
KW - Ensemble controllability
KW - Linear systems
UR - http://www.scopus.com/inward/record.url?scp=84994247347&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2016.09.020
DO - 10.1016/j.sysconle.2016.09.020
M3 - Article
AN - SCOPUS:84994247347
SN - 0167-6911
VL - 98
SP - 49
EP - 56
JO - Systems and Control Letters
JF - Systems and Control Letters
ER -