Interval Predictor Models for Robust System Identification

Abstract

This paper proposes a framework for the quantification of structured uncertainty in a plant model according to multivariable input-output data. The only restriction imposed upon such a model is for its outputs to depend continuously on the parameters. An Interval Predictor Model (IPM) prescribes the parameters of a computational model as a bounded, path-connected set thereby making each predicted output an interval-valued function of the inputs. The formulation proposed seeks the parameter set leading to the tightest enclosure of the data. This set, which is modeled as a semi-algebraic set having a tunable complexity level, enables the characterization of parameter dependencies commonly found in practice. This representation of the uncertain parameters makes the resulting plant model amenable to robustness analysis and robust control techniques based on polynomial optimization. Furthermore, scenario theory is used to evaluate the generalization properties of the identified model. This evaluation yields a formally-verifiable, distribution-free upper bound on the probability of future data falling outside the predicted output intervals.