A graph learning approach for kernel-based system identification with manifold regularization

This paper proposes the use of graph learning techniques in kernel-based system identification with manifold regularization. Recent works in this direction all assume that the regressors graph, used to approximate the regressors manifold and to derive the manifold regularization term, is a priori known or derived by nearest neighbors rationales. In this work, we show that a regressors graph for system identification can be inferred from the inputs/outputs measurements from a dynamical system by means of modern smoothness-based graph learning techniques, without particular hypothesis on the graph topological structure. Leveraging on the dynamical nature of the data, we propose a way to map the measured signals in a form that is manageable for graph learning algorithms, along with a rationale for an effective graph edges selection. The identification approach is evaluated on an experimental switching system setup, where its effectiveness is especially relevant in a small-data regime.