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Control and computation for linear ensemble systems using moment reduction
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DOI：10.1016/j.automatica.2025.112692.png)
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Abstract
En 中文
Ensemble systems, ubiquitous in science and engineering, present significant challenges for control analysis and design due to their large scale and underactuated nature. This paper develops a moment-based framework for conducting systems-theoretic analysis and computation of linear ensemble systems. We introduce the Legendre-moment transform, which maps a linear ensemble system on a Hilbert space to an equivalent moment system on its dual space, preserving controllability through a one-to-one correspondence. This equivalence enables a unified, sampling-free control design approach using truncated moment systems. In particular, we demonstrate that the system matrix of the moment system possesses a banded structure, allowing us to establish the convergence of the truncated systems to the full Legendre-moment system for a broad class of ensembles and derive explicit error bounds on control accuracy relative to the truncation order. Numerical examples illustrate the effectiveness of the presented method and validate the theoretical error estimates.
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5.9
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1.2W
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5.2W