Lie symmetries of nonlinear systems with unknown inputs

It has been revealed that a dynamical system being unobservable or unidentifiable for a given set of observations is fundamentally related to the existence of Lie symmetries. Lie symmetries thus have the potentiality of providing useful tools to analyze and improve the observability and identifiabil...

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Main Authors: Shi, Xiaodong, Chatzis, Manolis N.
Other Authors: School of Civil and Environmental Engineering
Format: Article
Language:English
Published: 2023
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Online Access:https://hdl.handle.net/10356/172782
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1727822023-12-20T01:17:40Z Lie symmetries of nonlinear systems with unknown inputs Shi, Xiaodong Chatzis, Manolis N. School of Civil and Environmental Engineering Engineering::Civil engineering Lie Symmetries Unknown Inputs It has been revealed that a dynamical system being unobservable or unidentifiable for a given set of observations is fundamentally related to the existence of Lie symmetries. Lie symmetries thus have the potentiality of providing useful tools to analyze and improve the observability and identifiability properties of dynamical systems from a fundamental perspective. This work proposes a computational framework for finding general Lie symmetries of nonlinear systems in the presence of unknown inputs. The occurring framework does not rely on mathematical Ansatz as the typical setting in the existing methods, and it is therefore capable of computing all the groups of Lie symmetries admitted by the system of interest. To alleviate the computation burden of the general framework, an alternative method is developed which is based on a priori assumptions on the functional forms of Lie symmetries to be calculated. The two proposed computation methods can be used as complementary tools to handle real engineering systems efficiently and robustly. Furthermore, utilization of the calculated Lie symmetries to detect and improve observability properties (with identifiability being the observability of unknown model parameters) is systematically discussed. Effective strategies of changing sensor placement, transforming system model and adding model assumptions are introduced to improve observability, and optimally render an unobservable system observable. The concept, computation and application of Lie symmetries are illustrated through several examples of linear, nonlinear and non-smooth dynamical systems. The first author would like to gratefully acknowledge the financial support from the China Scholarship Council (CSC) for his Ph.D. studies. 2023-12-20T01:17:40Z 2023-12-20T01:17:40Z 2023 Journal Article Shi, X. & Chatzis, M. N. (2023). Lie symmetries of nonlinear systems with unknown inputs. Mechanical Systems and Signal Processing, 188, 110027-. https://dx.doi.org/10.1016/j.ymssp.2022.110027 0888-3270 https://hdl.handle.net/10356/172782 10.1016/j.ymssp.2022.110027 2-s2.0-85144378418 188 110027 en Mechanical Systems and Signal Processing © 2022 Elsevier Ltd. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Civil engineering
Lie Symmetries
Unknown Inputs
spellingShingle Engineering::Civil engineering
Lie Symmetries
Unknown Inputs
Shi, Xiaodong
Chatzis, Manolis N.
Lie symmetries of nonlinear systems with unknown inputs
description It has been revealed that a dynamical system being unobservable or unidentifiable for a given set of observations is fundamentally related to the existence of Lie symmetries. Lie symmetries thus have the potentiality of providing useful tools to analyze and improve the observability and identifiability properties of dynamical systems from a fundamental perspective. This work proposes a computational framework for finding general Lie symmetries of nonlinear systems in the presence of unknown inputs. The occurring framework does not rely on mathematical Ansatz as the typical setting in the existing methods, and it is therefore capable of computing all the groups of Lie symmetries admitted by the system of interest. To alleviate the computation burden of the general framework, an alternative method is developed which is based on a priori assumptions on the functional forms of Lie symmetries to be calculated. The two proposed computation methods can be used as complementary tools to handle real engineering systems efficiently and robustly. Furthermore, utilization of the calculated Lie symmetries to detect and improve observability properties (with identifiability being the observability of unknown model parameters) is systematically discussed. Effective strategies of changing sensor placement, transforming system model and adding model assumptions are introduced to improve observability, and optimally render an unobservable system observable. The concept, computation and application of Lie symmetries are illustrated through several examples of linear, nonlinear and non-smooth dynamical systems.
author2 School of Civil and Environmental Engineering
author_facet School of Civil and Environmental Engineering
Shi, Xiaodong
Chatzis, Manolis N.
format Article
author Shi, Xiaodong
Chatzis, Manolis N.
author_sort Shi, Xiaodong
title Lie symmetries of nonlinear systems with unknown inputs
title_short Lie symmetries of nonlinear systems with unknown inputs
title_full Lie symmetries of nonlinear systems with unknown inputs
title_fullStr Lie symmetries of nonlinear systems with unknown inputs
title_full_unstemmed Lie symmetries of nonlinear systems with unknown inputs
title_sort lie symmetries of nonlinear systems with unknown inputs
publishDate 2023
url https://hdl.handle.net/10356/172782
_version_ 1787136535183753216