TY - GEN
T1 - Controllability of Sobolev-Type Linear Ensemble Systems
AU - Zhang, Wei
AU - Tie, Lin
AU - Li, Jr Shin
N1 - Funding Information:
This work was supported in part by the National Science Foundation under the awards CMMI-1933976 and ECCS-1810202.
Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - Systems composed of large ensembles of isolated or interacted dynamic units are prevalent in nature and engineered infrastructures. Linear ensemble systems are inarguably the simplest class of ensemble systems and have attracted intensive attention to control theorists and practionars in the past years. Comprehensive understanding of dynamic properties of such systems yet remains far-fetched and requires considerable knowledge and techniques beyond the reach of modern control theory. In this paper, we explore the classes of linear ensemble systems with system matrices that are not globally diagonalizable. In particular, we focus on analyzing their controllability properties under a Sobolev space setting and develop conditions under which uniform controllability of such ensemble systems is equivalent to that of their diagonalizable counterparts. This development significantly facilitates controllability analysis for linear ensemble systems through examining diagonalized linear systems.
AB - Systems composed of large ensembles of isolated or interacted dynamic units are prevalent in nature and engineered infrastructures. Linear ensemble systems are inarguably the simplest class of ensemble systems and have attracted intensive attention to control theorists and practionars in the past years. Comprehensive understanding of dynamic properties of such systems yet remains far-fetched and requires considerable knowledge and techniques beyond the reach of modern control theory. In this paper, we explore the classes of linear ensemble systems with system matrices that are not globally diagonalizable. In particular, we focus on analyzing their controllability properties under a Sobolev space setting and develop conditions under which uniform controllability of such ensemble systems is equivalent to that of their diagonalizable counterparts. This development significantly facilitates controllability analysis for linear ensemble systems through examining diagonalized linear systems.
UR - http://www.scopus.com/inward/record.url?scp=85126052290&partnerID=8YFLogxK
U2 - 10.1109/CDC45484.2021.9683659
DO - 10.1109/CDC45484.2021.9683659
M3 - Conference contribution
AN - SCOPUS:85126052290
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4097
EP - 4102
BT - 60th IEEE Conference on Decision and Control, CDC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 60th IEEE Conference on Decision and Control, CDC 2021
Y2 - 13 December 2021 through 17 December 2021
ER -