Corrective control of asynchronous sequential machines with input disturbance I: Modeling

This paper presents the problem of controlling asynchronous sequential machines in the presence of input disturbances, which may be also regarded as an adversary in a game theoretic setting. The main objective is to develope a new methodology for including unpredictable behavior of input disturbance into models of asynchronous machines. The input disturbance, representing uncontrollable noise input, is embedded into a new model of asynchronous machines in form of input/state finite state machines. It is shown that the proposed modeling preserves the fundamental model and well-pose of asynchronous machines. The reachability matrix, an important performance index of asynchronous machines, is also adapted according to input disturbance and will be used for constructing corrective controllers in the companion paper.