Language-measure-theoretic optimal control of probabilistic finite-state systems

Supervisory control theory for discrete event systems, introduced by Ramadge and Wonham, is based on a non-probabilistic formal language framework. Building on the concept of signed real measure of regular languages, this paper formulates a comprehensive theory for optimal control of finite-state probabilistic processes. It is shown that the resulting discrete-event supervisor is optimal in the sense of elementwise maximizing the renormalized language measure vector for the controlled plant behavior and is efficiently computable.