A Set-based Approach for Synthesizing Controllers Enforcing ω-Regular Properties over Uncertain Linear Control Systems

In this work, synthesizing controllers against ω-regular properties is investigated for linear control systems affected by bounded disturbances. Our results show that synthesizing such controllers can be reduced to computing so-called hybrid controlled invariant (HCI) sets. Accordingly, we propose a set-based approach for computing the maximal HCI set over a product system which is constructed using the linear system and the deterministic Rabin automata (DRA) representing the negation of the given desired property. We also provide an alternative iterative scheme to compute an approximation of the maximal HCI set, which is guaranteed to be terminated within a finite number of iterations. Finally, we present a control problem for a buck converter as a case study to show the effectiveness of our proposed approaches.