Comptes Rendus
Identification of nonlinear dynamical system equations using dynamic mode decomposition under invariant quantity constraints
Comptes Rendus. Mécanique, Volume 347 (2019) no. 11, pp. 882-890.

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.

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DOI: 10.1016/j.crme.2019.11.013
Keywords: Dynamical system, Identification, Invariant quantity, Symplectic, Dynamic mode decomposition, Lyapunov equations, Lotka–Volterra system

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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Florian De Vuyst; Pierre Villon. Identification of nonlinear dynamical system equations using dynamic mode decomposition under invariant quantity constraints. Comptes Rendus. Mécanique, 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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