Enforcing Detectability in Discrete Event Systems via Adaptive Control Sequences of Minimum Total Length

This paper studies the problem of eventually enforcing and maintaining exact knowledge of the current state of a given DES, modeled as a nondeterministic finite automaton with inputs and outputs. We assume that the system model is known and that we can choose the inputs to the system (i.e., the inputs are controllable and observable) but not the outputs; the latter are observable but not controllable as they depend on the unknown initial state and any nondeterministic actions taken by the system. Our goal is to devise an adaptive strategy that chooses the inputs to the system based on the outputs generated, in a way that allows us, after a minimal number of inputs, to (i) determine the exact current state of the system, and (ii) maintain knowledge of the exact state of the system for all its future behavior.