Adaptive-Graph Semi-Supervised Dynamical System Identification

In this paper, we present a novel adaptive-graph semi-supervised dynamical system identification (AG-SSI) for the challenging nonlinear dynamical system identification. AG-SSI constructs the regressors in the Reproducing Kernel Hilbert Spaces (RKHS) leveraging on both input-output data and input-only data. Then, a manifold regularization with adaptive graph structure is introduced for semi-supervised learning. AG-SSI can jointly learn the optimal affinity graph and identify the unknown dynamical system. An efficient iteration method is proposed to solve this challenging problem, which promotes graph matrix learning and system identification in a mutual reinforcement mode. Experiments are conducted on three nonlinear dynamical systems and the results demonstrate the superiority of the proposed method compared with the existing semi-supervised system identification algorithms.