Equation-free data-driven synchronization of rod-type plasma torch systems with a Koopman approach

This study explores equation-free data-driven synchronization of a rod-type plasma torch by employing the Koopman approach. In the data-driven methodology, we systematically extract information from driving-driven systems at fixed time intervals within a specific range. Utilizing the data, the Koopman operator is applied to attain observables for both driving and driven systems. Parameter estimation is employed to construct a flexible model capable of capturing subtle changes. The error system is derived from these models, and parameter optimization is performed to achieve synchronization. Leveraging Julia packages, system synchronization is achieved by dynamically controlling parameters, providing insights without relying on explicit equations.