A Notion of Approximation for Systems over Finite Alphabets

We consider the problem of approximating plants with discrete sensors and actuators (termed ‘systems over finite alphabets’) by deterministic finite memory systems for the purpose of certified-by-design controller synthesis. We propose a new, control-oriented notion of input/output approximation for these systems, that builds on ideas from robust control theory and behavioral systems theory. We conclude with a brief discussion of the key features of the proposed notion of approximation relative to those of two existing notions of finite state approximation and abstraction.