On the Sample Complexity of Set Membership Estimation for Linear Systems with Disturbances Bounded by Convex Sets Article Swipe

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YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2406.00574

This paper revisits the set membership identification for linear control systems and establishes its convergence rates under relaxed assumptions on (i) the persistent excitation requirement and (ii) the system disturbances. In particular, instead of assuming persistent excitation exactly, this paper adopts the block-martingale small-ball condition enabled by randomly perturbed control policies to establish the convergence rates of SME with high probability. Further, we relax the assumptions on the shape of the bounded disturbance set and the boundary-visiting condition. Our convergence rates hold for disturbances bounded by general convex sets, which bridges the gap between the previous convergence analysis for general convex sets and the existing convergence rate analysis for $\ell_\infty$ balls. Further, we validate our convergence rates by several numerical experiments. This manuscript contains supplementary content in the Appendix.

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Bounded function Convergence (economics) Mathematics Set (abstract data type) Estimation Regular polygon Convex set Rate of convergence Applied mathematics Mathematical optimization Computer science Convex optimization Economics Mathematical analysis Geometry Programming language Channel (broadcasting) Management Computer network Economic growth

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2406.00574
PDF: https://arxiv.org/pdf/2406.00574
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DOI: https://doi.org/10.48550/arxiv.2406.00574

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Title: On the Sample Complexity of Set Membership Estimation for Linear Systems with Disturbances Bounded by Convex Sets

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Language: en

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Publication year: 2024

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Publication date: 2024-06-01

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Authors: Haonan Xu, Yingying Li

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Landing page: https://arxiv.org/abs/2406.00574

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Concepts: Bounded function, Convergence (economics), Mathematics, Set (abstract data type), Estimation, Regular polygon, Convex set, Rate of convergence, Applied mathematics, Mathematical optimization, Computer science, Convex optimization, Economics, Mathematical analysis, Geometry, Programming language, Channel (broadcasting), Management, Computer network, Economic growth

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