Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization

Bramburger JJ, Fantuzzi G (2024)


Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2024

Journal

Book Volume: 34

Article Number: 8

URI: https://arxiv.org/abs/2303.01483

DOI: 10.1007/s00332-023-09990-2

Open Access Link: https://arxiv.org/abs/2303.01483

Abstract

We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented as a semidefinite program that can be solved numerically. Furthermore, the method is agnostic of whether data are generated through a deterministic or stochastic process, so its implementation requires no prior adjustments by the user to accommodate these different scenarios. Rigorous convergence results justify the applicability of the method, while also extending and uniting similar results from across the literature. Examples on discovering Lyapunov functions, performing ergodic optimization, and bounding extrema over attractors for both deterministic and stochastic dynamics exemplify these convergence results and demonstrate the performance of the method.

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How to cite

APA:

Bramburger, J.J., & Fantuzzi, G. (2024). Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization. Journal of Nonlinear Science, 34. https://dx.doi.org/10.1007/s00332-023-09990-2

MLA:

Bramburger, Jason J., and Giovanni Fantuzzi. "Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization." Journal of Nonlinear Science 34 (2024).

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