A LINEAR STATE-SPACE APPROACH TO A CLASS OF DISCRETE-EVENT SYSTEMS

The paper addresses finite state machines which provide suitable mathe matical models for discrete-event dynamical systems. This type of syst ems is considered to be one of the challenges in the present discussio n of non-classical control problems. Boolean automata are of special i nterest. Different from classical automata theory, this paper makes us e of an arithmetic representation of Boolean functions based on multil inear polynomials. These polynomials have the same structure as classi cal Shegalkin-polynomials, however Boolean algebra is replaced by arit hmetic operations. By this technique finite automata can be imbedded i n the Euklidean vector space which allows to detect a closer relations hip 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 o f self-regulation of binary dynamical processes can be interpreted in terms of feedback control structures. The degrees of freedom offered b y the binary controller equation can be utilized for various purposes, e.g. attaining a specified cyclic operation or global linearization o f the over-all system. Details will be reported elsewhere.