A linear state space approach to a class of discrete-event systems

The paper addresses finite state machines which provide suitable mathematical models for discrete-event dynamical systems. This type of systems is considered to be one of the challenges in the present discussion of non-classical control problems. Boolean automata are of special interest. Different from classical automata theory, this paper makes use of an arithmetic representation of Boolean functions based on multilinear polynomials. These polynomials have the same structure as classical Shegalkin-polynomials, however Boolean algebra is replaced by arithmetic operations. By this technique finite automata can be imbedded in the Euklidean vector space which allows to detect a closer relationship between discrete-event systems and classical discrete-time systems since the same algebra is used. This type of modelling discrete-event systems enables a novel view on binary process control. The problem of self-regulation of binary dynamical processes can be interpreted in terms of feedback control structures. The degrees of freedom offered by the binary controller equation can be utilized for various purposes, e.g. attaining a specified cyclic operation or global linearization of the over-all system. Details will be reported elsewhere.