Data-driven Construction of Finite Abstractions for Interconnected Systems: A Compositional Approach

Abstract

Finite-state abstractions (a.k.a. symbolic models) present a promising avenue for the formal verification and synthesis of controllers in continuous-space control systems. These abstractions provide simplified models that capture the fundamental behaviors of the original systems. However, the creation of such abstractions typically relies on the availability of precise knowledge concerning system dynamics, which might not be available in many real-world applications. In this work, we introduce a novel data-driven and compositional approach for constructing finite abstractions for interconnected systems comprised of discrete-time control subsystems with partially unknown dynamics. These subsystems interact through a partially unknown static interconnection map. Our methodology for abstracting the interconnected system involves constructing abstractions for individual subsystems and incorporating an abstraction of the interconnection map.