Prediction Error Method for Identification of Subnetworks of Dynamical Systems

This paper considers prediction-error identification of a subnetwork embedded in a dynamic network. Measured boundary signals entering the subnetwork are appended to the exogenous inputs. Consistency requires that the part of these boundary signals generated by the subnetwork be reconstructible from the measured history; the subnetwork may be enlarged to obtain a simple structural sufficient condition. Under the stated model, stability, delay, disturbance-separation, informativity, and identifiability assumptions, the resulting criterion yields consistent estimates of the subnetwork transfer functions. The predictor may depend nonlinearly on the open-loop transfer functions, allowing consistent estimation with fewer measured internal signals than methods based on predictors that are linear in those transfer functions.