Deep Koopman learning of nonlinear time-varying systems

Wenjian Hao, Bowen Huang, Wei Pan, Di Wu, Shaoshuai Mou

Research output: Contribution to journalArticlepeer-review


This paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which results from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach.

Original languageEnglish
Article number111372
Early online date21 Oct 2023
Publication statusPublished - Jan 2024


  • Deep neural networks
  • Koopman operator
  • Nonlinear time-varying systems


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