Corrective control of asynchronous sequential machines in the presence of adversarial input

The problem of controlling asynchronous sequential machines in the presence of input disturbances is presented, which may be also regarded as an adversary in a game theoretic setting. The adversarial input is supposed to be measurable but uncontrollable by outer control units. The main objective is to develop state-feedback controllers that eliminate the effect of the adversarial input, while controlling the machine so as to match a prescribed model. Necessary and sufficient conditions for the existence of appropriate controllers are derived in terms of inequality relation between two numerical matrices. Whenever controllers exist, algorithms for their design are outlined and a case study is provided.