On Finite Memory Approximations Constructed from Input/Output Snapshots

The problem of approximating systems with finite input and output alphabets by finite memory systems for verification or certified control has received much deserved attention in the recent past. The present paper is a further step in that direction, building upon a robust control inspired notion of approximation we recently proposed. A constructive algorithm for deriving deterministic finite state machine (DFM) approximations of a given system over finite alphabets is proposed, based on a partitioning of its input/output behavior into equivalence classes of finite length snapshots. The algorithm is analyzed, and the resulting nominal models and corresponding approximation errors are shown to have desirable properties. An algorithm for conservatively quantifying the resulting approximation error in a manner consistent with the objective of control synthesis is also proposed. Several simple illustrative examples are presented to demonstrate the approach.