Controllability Issues of Linear Ensemble Systems over Multi-dimensional Parameterization Spaces

Xudong Chen

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arXiv · 2003.04529

Controllability Issues of Linear Ensemble Systems over Multi-dimensional Parameterization Spaces

Xudong Chen

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Abstract

We address an open problem in ensemble control: Whether there exist controllable linear ensemble systems over multi-dimensional parameterization spaces? We provide a negative result: Any real-analytic linear ensemble system is not $\mathrm{L}^p$-controllable, for $2\leq p \leq \infty$, if its parameterization space contains an open set in $\mathbb{R}^d$ for $d \geq 2$.

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Xudong Chen. 2020-03-10. Controllability Issues of Linear Ensemble Systems over Multi-dimensional Parameterization Spaces. https://arxiv.org/abs/2003.04529

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