Rule-based Boolean control of discrete-event systems-an arithmetic approach

The paper addresses finite state machines which provide suitable mathematical models for discrete-event dynamical systems. Boolean automata are of particular interest. Different from classical automata theory, an arithmetic representation of Boolean functions is used based on multilinear polynomials. By this technique finite automata are imbedded in the Euclidean vector space which allows to detect a closer relationship between discrete-event systems and classical discrete-time systems. The problem of self-regulation of binary dynamical systems is interpreted in terms of feedback control structures. As a special class, systems which are linear in the controls are considered. It is shown that multilinear state feedback can be utilized to globally linearize the over-all system. The design equations turn out to be linear with respect to the controller parameters in this case. An illustrative example is included