Combining Prior Knowledge and Data for Robust Controller Design

We present a framework for systematically combining data of an unknown linear time-invariant system with prior knowledge on the system matrices or on the uncertainty for robust controller design. Our approach leads to linear matrix inequality (LMI)-based feasibility criteria that guarantee stability and performance robustly for all closed-loop systems consistent with the prior knowledge and the available data. The design procedures rely on a combination of multipliers inferred via prior knowledge and learnt from measured data, where for the latter, a novel and unifying disturbance description is employed. While large parts of the article focus on linear systems and input-state measurements, we also provide extensions to robust output-feedback design based on noisy input-output data and against nonlinear uncertainties. We illustrate through numerical examples that our approach provides a flexible framework for simultaneously leveraging prior knowledge and data, thereby reducing conservatism and improving performance significantly if compared to black-box approaches to data-driven control.