From Model-based to Data-driven LMI-based Controller Synthesis

This thesis uses Linear Matrix Inequalities (LMIs) to transition from model-based to data-driven control design, while preserving guarantees with regard to stability and performance of the resulting closed-loop system. In the model-based case, LMIs provide a unifying framework for both analysis and controller synthesis, in which key control problems are formulated as semidefinite programs. The first part of the thesis reviews established LMI-based methods for synthesizing stabilizing state-feedback controllers for discrete-time linear time-invariant systems, taking performance requirements based on common metrics such as H2 and H∞ norms into account. Recently, the LMI-based framework has been extended to data-driven settings, where model knowledge is replaced by finitely many (noisy) input-state samples. These extensions are the subject of the latter part of the thesis. A variant of the S-procedure is employed to derive data-dependent LMI synthesis conditions, which provide the same stability and performance guarantees as their model-based counterparts. Thereby, this thesis demonstrates that it is possible to design controllers directly from data while keeping rigorous theoretical guarantees, which are typically associated with model-based control design.