Uncertainty Learning for LTI Systems with Stability Guarantees

We present a framework for learning of modeling uncertainties in Linear Time Invariant (LTI) systems to improve the predictive capacity of system models in the input-output sense. First, we propose a methodology to extend the LTI model with an uncertainty model. The proposed framework guarantees stability of the extended model. To achieve this, two semi-definite programs are provided that allow obtaining optimal uncertainty model parameters, given state and uncertainty data. Second, to obtain this data from available input-output trajectory data, we introduce a filter in which an internal model of the uncertainty is proposed. This filter is also designed via a semi-definite program with guaranteed robustness with respect to uncertainty model mismatches, disturbances, and noise. Numerical simulations are presented to illustrate the effectiveness and practicality of the proposed methodology in improving model accuracy, while guaranteeing model stability.