Abstract:

Robust Controllable (RC) sets enable safe control of dynamical systems under constraints and uncertainty. Existing approaches typically rely on polytopic representations for the computation of these sets, which suffer from conser- vativeness and scalability issues. Recently, Constrained Convex Generators (CCGs) were proposed to allow set-based control and analysis in presence of both ellipsoidal and polytopic state- input constraints. However, the computation of RC sets using CCGs is currently hindered because the Pontryagin difference set operation has not been developed for CCGs. In this paper, we provide theory and algorithms to address this challenge, and enable safe control under uncertainty using RC sets and CCGs. Specifically, we propose an inner approximation for the RC set using a CCG description. We show in simulations that the proposed approach improves accuracy and memory usage when compared to computations with polytopic approximations.