Identification of Nonlinear Systems Using the Infinitesimal Generator of the Koopman Semigroup—A Numerical Implementation of the Mauroy–Goncalves Method
Abstract
Inferring the latent structure of complex nonlinear dynamical systems in a data driven setting is a challenging mathematical problem with an ever increasing spectrum of applications in sciences and engineering. Koopman operator-based linearization provides a powerful framework that is suitable for identification of nonlinear systems in various scenarios. A recently proposed method by Mauroy and Goncalves is based on lifting the data snapshots into a suitable finite dimensional function space and identification of the infinitesimal generator of the Koopman semigroup. This elegant and mathematically appealing approach has good analytical (convergence) properties, but numerical experiments show that software implementation of the method has certain limitations. More precisely, with the increased dimension that guarantees theoretically better approximation and ultimate convergence, the numerical implementation may become unstable and it may even break down. The main sources of numerical difficulties are the computations of the matrix representation of the compressed Koopman operator and its logarithm. This paper addresses the subtle numerical details and proposes a new implementation algorithm that alleviates these problems.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 27, 2021
- Source ID
- 10.3390/math9172075
Entities
People
- Igor Mezić
- Ryan Mohr
- Zlatko Drmač
Organizations
- Defense Advanced Research Projects Agency