Ensemble control of linear systems

Jr Shin Li; Navin Khaneja

doi:10.1109/CDC.2007.4434971

Ensemble control of linear systems

Jr Shin Li, Navin Khaneja

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

18 Scopus citations

Abstract

In this article, we study ensemble control problems which involve controlling a continuum of dynamical systems with different dynamics by using the same control signal. In particular, we look into ensemble control of linear systems. From the standpoint of mathematical control theory, the challenge is to simultaneously steer a continuum of systems between points of interest with the same control signal. This raises some new and unexplored questions about controllability and optimal control of such systems. We analyze ensemble controllability and optimal control of linear systems and study in detail the problem of controlling an uncountable family of harmonic oscillators. We show how the ideas of polynomial approximation are in connection with the ensemble controllability. We also find the optimal ensemble control for this linear ensemble control system.

Original language	English
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3768-3773
Number of pages	6
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434971
State	Published - 2007
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	46th IEEE Conference on Decision and Control 2007, CDC
Country/Territory	United States
City	New Orleans, LA
Period	12/12/07 → 12/14/07

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10.1109/CDC.2007.4434971

Cite this

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title = "Ensemble control of linear systems",

abstract = "In this article, we study ensemble control problems which involve controlling a continuum of dynamical systems with different dynamics by using the same control signal. In particular, we look into ensemble control of linear systems. From the standpoint of mathematical control theory, the challenge is to simultaneously steer a continuum of systems between points of interest with the same control signal. This raises some new and unexplored questions about controllability and optimal control of such systems. We analyze ensemble controllability and optimal control of linear systems and study in detail the problem of controlling an uncountable family of harmonic oscillators. We show how the ideas of polynomial approximation are in connection with the ensemble controllability. We also find the optimal ensemble control for this linear ensemble control system.",

author = "Li, {Jr Shin} and Navin Khaneja",

year = "2007",

doi = "10.1109/CDC.2007.4434971",

language = "English",

isbn = "1424414989",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "3768--3773",

booktitle = "Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC",

note = "46th IEEE Conference on Decision and Control 2007, CDC ; Conference date: 12-12-2007 Through 14-12-2007",

}

Li, JS & Khaneja, N 2007, Ensemble control of linear systems. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434971, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 3768-3773, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434971

Ensemble control of linear systems. / Li, Jr Shin; Khaneja, Navin.
Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. p. 3768-3773 4434971 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Li, Jr Shin

AU - Khaneja, Navin

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N2 - In this article, we study ensemble control problems which involve controlling a continuum of dynamical systems with different dynamics by using the same control signal. In particular, we look into ensemble control of linear systems. From the standpoint of mathematical control theory, the challenge is to simultaneously steer a continuum of systems between points of interest with the same control signal. This raises some new and unexplored questions about controllability and optimal control of such systems. We analyze ensemble controllability and optimal control of linear systems and study in detail the problem of controlling an uncountable family of harmonic oscillators. We show how the ideas of polynomial approximation are in connection with the ensemble controllability. We also find the optimal ensemble control for this linear ensemble control system.

AB - In this article, we study ensemble control problems which involve controlling a continuum of dynamical systems with different dynamics by using the same control signal. In particular, we look into ensemble control of linear systems. From the standpoint of mathematical control theory, the challenge is to simultaneously steer a continuum of systems between points of interest with the same control signal. This raises some new and unexplored questions about controllability and optimal control of such systems. We analyze ensemble controllability and optimal control of linear systems and study in detail the problem of controlling an uncountable family of harmonic oscillators. We show how the ideas of polynomial approximation are in connection with the ensemble controllability. We also find the optimal ensemble control for this linear ensemble control system.

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U2 - 10.1109/CDC.2007.4434971

DO - 10.1109/CDC.2007.4434971

M3 - Conference contribution

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SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3768

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BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 46th IEEE Conference on Decision and Control 2007, CDC

Y2 - 12 December 2007 through 14 December 2007

ER -

Ensemble control of linear systems

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