Formal Synthesis of Controllers for Uncertain Linear Systems against $ω$-Regular Properties: A Set-based Approach

Abstract

In this paper, we present how to synthesize controllers to enforce ω-regular properties over linear control systems affected by bounded disturbances. In particular, these controllers are synthesized based on socalled hybrid controlled invariant (HCI) sets. To compute these sets, we first construct a product system using the linear control system and the deterministic Rabin automata (DRA) modeling the negation of the desired property. Then, we compute the maximal HCI set over the state set of the product system by leveraging a set-based approach. To ensure termination of the computation of the HCI sets within a finite number of iterations, we also propose two iterative schemes to compute approximations of the maximal HCI set. Finally, we show the effectiveness of our approach on two case studies.