Bayesian Kernel-Based Linear Control Design

Anna Scampicchio, Alessandro Chiuso, Simone Formentin, Gianluigi Pillonetto

Abstract: Recent contributions have investigated the use of regularization in linear system identification. In particular, regularizing high-order FIR models to enforce stability while controlling complexity and regularity of the impulse response provides state-of-the-art performance in linear system identification. An advantage of such techniques is that they also enjoy a Bayesian interpretation that yields confidence intervals around the nominal system.In this work it is shown that these features can be useful for the design of a controller in a linear setting. In particular, the posterior distribution of the impulse response available from the Bayesian framework is exploited to perform control design using three different approaches; one of these is the minimization of the expected (posterior) distance from the desired closed loop system. Numerical studies illustrate the good performance of the proposed approaches.