Data‐Based Refinement of Parametric Uncertainty Descriptions

We consider dynamical systems with a linear fractional representation involving parametric uncertainties which are either constant or varying with time. Given a finite‐horizon input‐state or input‐output trajectory of such a system, we propose a numerical scheme which iteratively improves the available knowledge about the involved constant parametric uncertainties. As its key feature, strong theoretical properties, including a structural invariance of the uncertainty's description, are preserved during the data‐based learning process. In particular, it facilitates any robustness analysis and robust controller synthesis by improving the guaranteed performance. Our technique can be viewed as a data‐dependent preprocessing step which supplements and enhances some recent direct data‐based analysis or design approaches.