2022/09/05 by Garcia-Tenorio, Camilo, Tellez-Castro, Duvan, Mojica-Nava, Eduardo +1
#FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2209.02028
This paper proposes an original methodology to compute the regions of attraction in hyperbolic and polynomial nonlinear dynamical systems using the eigenfunctions of the discrete-time approximation of the Koopman operator given by the extended dynamic mode decomposition algorithm. The proposed method relies on the spectral decomposition of the Koopman operator to build eigenfunctions that capture the boundary of the region of attraction. The algorithm relies solely on data that can be collected in experimental studies and does not require a mathematical model of the system. Two examples of dynamical systems, a population model and a higher dimensional chemical reaction system, allows demonstrating the reliability of the results.