Identification of nonlinear dynamical system equations using dynamic mode decomposition under invariant quantity constraints

Florian De Vuyst; Pierre Villon

doi:10.1016/j.crme.2019.11.013

Identification of nonlinear dynamical system equations using dynamic mode decomposition under invariant quantity constraints

Florian De Vuyst ¹ ; Pierre Villon ²

¹ Laboratoire de mathématiques appliquées de Compiègne, EA 2222, Université de technologie de Compiègne, Alliance Sorbonne Université, 60200 Compiègne, France
² Laboratoire Roberval, FRE UTC–CNRS, Université de technologie de Compiègne, Alliance Sorbonne Université, 60200 Compiègne, France

Comptes Rendus. Mécanique, Data-Based Engineering Science and Technology, Volume 347 (2019) no. 11, pp. 882-890.

Abstract

In this paper, an algorithm for identifying equations representing a continuous nonlinear dynamical system from a noise-free state and time-derivative state measurements is proposed. It is based on a variant of the extended dynamic mode decomposition. A particular attention is paid to guarantee that the physical invariant quantities stay constant along the integral curves. The numerical methodology is validated on a two-dimensional Lotka–Volterra system. For this case, the differential equations are perfectly retrieved from data measurements. Perspectives of extension to more complex systems are discussed.

Received: 2019-07-11
Accepted: 2019-09-09
Published online: 2019-11-01

DOI: 10.1016/j.crme.2019.11.013

Mots-clés : Dynamical system, Identification, Invariant quantity, Symplectic, Dynamic mode decomposition, Lyapunov equations, Lotka–Volterra system

Author's affiliations:

Florian De Vuyst ¹; Pierre Villon ²

¹ Laboratoire de mathématiques appliquées de Compiègne, EA 2222, Université de technologie de Compiègne, Alliance Sorbonne Université, 60200 Compiègne, France
² Laboratoire Roberval, FRE UTC–CNRS, Université de technologie de Compiègne, Alliance Sorbonne Université, 60200 Compiègne, France

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     author = {Florian De Vuyst and Pierre Villon},
     title = {Identification of nonlinear dynamical system equations using dynamic mode decomposition under invariant quantity constraints},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {882--890},
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     number = {11},
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     doi = {10.1016/j.crme.2019.11.013},
     language = {en},
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Florian De Vuyst; Pierre Villon. Identification of nonlinear dynamical system equations using dynamic mode decomposition under invariant quantity constraints. Comptes Rendus. Mécanique, Data-Based Engineering Science and Technology, Volume 347 (2019) no. 11, pp. 882-890. doi : 10.1016/j.crme.2019.11.013. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.11.013/

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