Complete Abstractions of Monotone Control Systems: From Model-based to Data-Driven Systems

What the math gives to ML

The paper presents a constructive complete-abstraction mechanism for monotone control systems: an upper abstraction that supports sound controller refinement and a lower abstraction whose failure certifies infeasibility. Its transferable asset is a paired abstraction with a tunable conservativeness gap controlled by state discretization, extended to finite data without an explicit plant model. A strong neural-network transfer is to train and evaluate monotone policies or recurrent world models against paired interval abstractions, producing certified success, certified failure, or an explicit undecided band instead of relying only on nominal rollouts.