Transfer operator-based approach for domain of attraction computation and experimental data analysis

We present novel transfer operator-based methods for domain of attraction computation and experimental data analysis of nonlinear systems. The problem of domain of attraction (DA) computation is of great practical interest with applications in various engineering and physical systems such as power system, chemical processes, aircraft control, and biological systems. We propose linear transfer operator-based set-oriented numerical method for DA computation of nonlinear systems. The proposed method overcomes some of the shortcoming of the existing methods of DA computation; in particular the proposed method can be used for DA computation of non-polynomial vector fields and for systems with non-equilibrium dynamics.;Proper orthogonal decomposition (POD) is one of the most popular methods currently used for experimental data analysis and reduced order modeling of fluid flow systems. The basic idea behind POD is to decompose the experimental data into dominant energy modes. We present an alternate numerical scheme for spectral-based decomposition of the experimental time series data. The new method is based on the spectral analysis of linear transfer operator constructed from the experimental data. Application of this method is demonstrated on a time series data obtained from the flapping wing micro-aerial vehicle experiment. Future research efforts will focus on application of this method for reduced order modeling of time series data.