Controllability issues of linear ensemble systems over multidimensional parameterization spaces

Xudong Chen

doi:10.1137/21M1418691

Controllability issues of linear ensemble systems over multidimensional parameterization spaces

Xudong Chen

Department of Electrical & Systems Engineering

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We address an open problem in ensemble control: Whether there exist controllable linear ensemble systems over multidimensional parameterization spaces? We provide a negative result: Any real-Analytic linear ensemble system is not Lp-controllable, for 2≤ p ≤ ∞ , if its parameterization space contains an open set in Rd for d ≥ 2.

Original language	English
Pages (from-to)	2425-2447
Number of pages	23
Journal	SIAM Journal on Control and Optimization
Volume	61
Issue number	4
DOIs	https://doi.org/10.1137/21M1418691
State	Published - 2023

Keywords

Approximation theory
Controllability
Ensemble control
Functional analysis
Infinite-dimensional systems
Operator theory

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10.1137/21M1418691

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title = "Controllability issues of linear ensemble systems over multidimensional parameterization spaces",

abstract = "We address an open problem in ensemble control: Whether there exist controllable linear ensemble systems over multidimensional parameterization spaces? We provide a negative result: Any real-Analytic linear ensemble system is not Lp-controllable, for 2≤ p ≤ ∞ , if its parameterization space contains an open set in Rd for d ≥ 2.",

keywords = "Approximation theory, Controllability, Ensemble control, Functional analysis, Infinite-dimensional systems, Operator theory",

author = "Xudong Chen",

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year = "2023",

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AB - We address an open problem in ensemble control: Whether there exist controllable linear ensemble systems over multidimensional parameterization spaces? We provide a negative result: Any real-Analytic linear ensemble system is not Lp-controllable, for 2≤ p ≤ ∞ , if its parameterization space contains an open set in Rd for d ≥ 2.

KW - Approximation theory

KW - Controllability

KW - Ensemble control

KW - Functional analysis

KW - Infinite-dimensional systems

KW - Operator theory

UR - https://www.scopus.com/pages/publications/85169669676

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JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 4

ER -

Controllability issues of linear ensemble systems over multidimensional parameterization spaces

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