Data-Driven Controller Synthesis via Co-Büchi Barrier Certificates With Formal Guarantees

In this letter, we introduces a data-driven framework for synthesizing controllers that enforce properties expressed by so-called
$\ell $
universal co-Büchi automata (
$\ell $
-UCA) over control systems with finite input sets and unknown mathematical models. The proposed framework leverages the notion of co-Büchi control barrier certificates (CBC). These certificates, together with their corresponding controllers, guarantee that a region in the state set is visited finitely often as the system evolves, limiting visits to at most
$\ell $
times. The CBC is defined over a domain that augments the system and the
$\ell $
-UCA, incorporating a counter variable to track the number of visits to the accepting states of
$\ell $
-UCA. However, constructing these CBCs typically requires precise knowledge of the dynamics of the system, which is often unavailable in real-world applications. Therefore, we propose a data-driven scheme where we initially formulate the CBC conditions as a robust optimization program (ROP). Since the unknown model appears in some of the ROP constraints, we employ sampled data points collected from the system’s trajectories to formulate a scenario optimization program (SOP) associated with the ROP. By solving the corresponding SOP, we construct CBCs and controllers that enforce
$\ell $
-UCA properties for the unknown system with a formal correctness guarantee. The efficacy of our data-driven approach is demonstrated by applying it to a three-tank system whose dynamics is assumed to be unknown.