System identification via nuclear norm regularization for simulated moving bed processes from incomplete data sets

The application of nuclear norm regularization to system identification was recently shown to be a useful method for identifying low order linear models. In this paper, we consider nuclear norm regularization for identification of simulated moving bed processes from data sets with missing entries. The missing data problem is of ongoing interest because the need to analyze incomplete data sets arises frequently in diverse fields such as chemistry, psychometrics and satellite imaging. By casting system identification as a convex optimization problem, nuclear norm regularization can be applied to identify the system in one step, i.e., without imputation of the missing data. Our exploratory work compares the proposed method named NucID to the standard techniques N4SID, prediction error minimization, subspace identification and expectation conditional maximization via linear regression and a linearized first principles model. NucID is found to consistently identify systems with missing data within the imposed error tolerance, a task for which the standard methods sometimes fail, and to be particularly effective when the data is missing with patterns, e.g., on multi-rate systems, where it significantly outperforms existing procedures.