Learning-based Robust Model Predictive Control for Sector-bounded Lur'e Systems

For dynamical systems with uncertainty, robust controllers can be designed by assuming that the uncertainty is bounded. The less we know about the uncertainty in the system, the more conservative the bound must be, which in turn may lead to reduced control performance. If measurements of the uncertain term are available, this data may be used to reduce the uncertainty in order to make bounds as tight as possible. In this paper, we consider a linear system with a sector-bounded uncertainty. We develop a model predictive control algorithm to control the system, and use a weighted Bayesian linear regression model to learn the least conservative sector condition using measurements collected in closed-loop. The resulting robust model predictive control algorithm therefore reduces the conservativeness of the controller, and provides probabilistic guarantees of asymptotic stability and constraint satisfaction. The efficacy of the proposed method is shown in simulation