Control of infinite behaviour is studied within the conceptual framework of the control theory for discrete-event systems (DES) of Ramadge and Wonhani. The extension to infinite behaviour broadens the scope of the original theory by permitting the expression of a larger class of behavioural properties. In addition it establishes formal links with other branches of DES theory.

The thesis consists of two main parts. The first concerns a model of DES as controlled generators of formal languages consisting of both finite and infinite strings. A notion of deadlock-freedom is given. Achievable closed-loop behaviour is characterized. A prototypical control synthesis problem (SCP^ω) is formulated and the existence of solutions is analyzed.

The second part of the thesis concerns effective solution of SCP^ω in cases where all relevant languages are represented by finite automata. The results of this part can be interpreted as algorithms for the control of finite automata on infinite strings. A key technique is the use of a calculus of extremal fixpoints of monotone transformations, similar to notations used in programming theory, to characterize various state subsets of control-theoretic significance. The resulting procedures represent new approaches to problems encountered in other areas of DES theory, such as Church’s problem, the emptiness problem for automata on infinite trees, and extensions of these.