Design of input assignment and feedback gain for re-stabilizing undirected networks with High-Dimension Low-Sample-Size data

There exists a critical transition before dramatic deterioration of a complex dynamical system. Recently, a method to predict such shifts based on High-Dimension Low-Sample-Size (HDLSS) data has been developed. Thus based on the prediction, it is important to make the system more stable by feedback control just before such critical transitions, which we call re-stabilization. However, the re-stabilization cannot be achieved by traditional stabilization methods such as pole placement method because the available HDLSS data is not enough to get a mathematical system model by system identification. In this article, a model-free pole placement method for re-stabilization is proposed to design the optimal input assignment and feedback gain for undirected network systems only with HDLSS data. The proposed method is validated by numerical simulations.