Residual Dynamic Mode Decomposition with Control for Nonlinear Aeroservoelastic Applications

The Koopman theory has received increasing attention for constructing reduced-order models (ROMs) as it converts a nonlinear dynamical system to a linear one in a higher dimensional space. However, the conventional ROMs based on Koopman are often made more complicated, and sometimes inaccurate, by unnecessary spurious eigenvalue-eigenvector pairs. This paper leverages the recent method of Residual Dynamic Mode Decomposition (ResDMD) for autonomous systems, and extends its ϵ-pseudospectrum residual computation to Koopman with Inputs and Control (KIC), for systems with control. This novel ResDMD with Control (ResDMDc) procedure eliminates spurious eigenpairs and results in low-rank and accurate linear ROMs for nonlinear dynamics. The method was tested on a nonlinear aeroelastic panel problem with exogenous inputs, and demonstrated high accuracy with a mean error of 0.0327 in the worst case.