Data-driven estimation of Gramian based interaction measures for control structure selection

Interaction measures quantify the input-output relations in MIMO processes and can support the selection of control structures (CSS). Interaction measures are typically computed based on an existing process models. The study of inputoutput interactions based on data can complement missing information on a model, e.g., revealing unknown relations in a complex system or adjusting for a time dependent behavior. This paper presents a unified approach for datadriven estimation of Gramian based interaction measures from input-output data. Given open or closed-loop data, a high-order Vector ARX (VARX) model is identified and its parameters are used to calculate predictor Markov parameters, together with a covariance estimate. Three interaction measures based on the Hankel, Hilbert-Schmidt-Hankel and H2 norms are calculated from the estimated predictor Markov parameters and uncertainty estimates are provided for the last two, allowing for robust CSS. A solution which is recursive in the data points is presented, making it practical for applications to large datasets. The approach is verified through simulations and several possible extensions are discussed. As the method is suitable for open and closed-loop data and for large datasets, it opens up for data-driven control structure selection based on operational data from entire plants.