Compositional Synthesis of Controllers via Co-Büchi Barrier Certificates

Abstract

The success of barrier certificates to ensure the safety of control systems has led to their adoption in designing controllers to guarantee more general ω-regular automata specifications. Recent developments in co-Büchi barrier certificates propose the direct construction of the product of the system and the automaton, ensuring that the accepting states of the automaton are visited finitely often. Despite the benefits, challenges arise when finding these certificates for large-scale systems. To overcome such challenges, we introduce a compositional controller synthesis via co-Büchi barrier certificates. We decompose the large-scale system into an interconnection of smaller subsystems, construct local certificates for these subsystems, and utilize a dissipativity-type condition to guarantee the existence of a certificate for the large-scale system. We design controllers for the subsystems that, when concatenated, act as a formally correct controller for the large-scale system. Finally, we illustrate our approach with a numerical example.