Published June 12, 2018
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The Dimension Estimation Problem for Nonlinear Systems
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We consider the dimension estimation problem for nonlinear systems, that is, the problem of finding the least possible dimension of the state space of a (minimal) realization of a nonlinear system from given input-output measurements. Exploiting tools from nonlinear realization theory and free Lie algebras, we develop algorithms to solve the dimension estimation problem both for bilinear and for general nonlinear systems, provided sufficient measurements are available. Simple worked-out examples illustrate the theory.
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2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. A. Padoan and A. Astolfi, "The Dimension Estimation Problem for Nonlinear Systems," European Control Conference (ECC), Limassol, Cyprus, June 2018, pp. 184-189. doi: 10.23919/ECC.2018.8550340.
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