Deep Koopman Learning of Nonlinear Time-Varying Systems
This addresses modeling complex dynamic systems for control applications, but appears incremental as it builds on existing Koopman operator methods.
The paper tackles approximating nonlinear time-varying systems with linear ones using Koopman operators and deep neural networks, achieving small approximation errors in simulations, including on quadcopters.
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 is resulted 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.