State feedback control of asynchronous sequential machines with adversarial inputs

The problem of controlling an asynchronous sequential machine in the presence of adversarial inputs is considered. Here, an adversarial input is an unknown and unauthorised input that attempts to interfere with the operation of the machine. The objective is to develop automatic state feedback controllers that counteract the effects of the adversarial input and restore desirable behaviour to the controlled machine. Necessary and sufficient conditions for the existence of such controllers are presented in terms of an inequality condition between two numerical matrices. Whenever a controller exists, an algorithm for its design is provided.