Constructing ρ/μ approximations from input/output snapshots for systems over finite alphabets

We consider discrete-time plants that interact with their controllers by sending and receiving binary valued sensor signals and finite valued control signals, respectively. In the absence of exogenous inputs, we propose a general procedure for constructing (finite state) ρ/μ approximations, starting from finite length sequences of input and output signal pairs. We show that the proposed construction satisfies desirable properties, thus leading to a hierarchy of finite state models that can be used for certified-by-design control synthesis.