Optimal Discrete-Event Supervisory Control in a Setting of Real-Time Artificial Intelligence

Using a discrete event finite state model of the unsupervised plant, this paper presents a concept of optimal supervisory control of dynamical systems in a setting of real-time artificial intelligence (AI), based on a real signed measure of regular languages. In contrast to the seminal work of Ramadge & Wonham as well as those of others in this field, the proposed language measure allows total ordering on a set of partially ordered sublanguages of regular languages of the supervised plant for a (quantitative) performance evaluation and comparison of different supervisors. Given a (homogeneous) probabilistic finite-state automaton (PFSA) model of the unsupervised plant, reward/penalty characterization of the individual PFSA states is used to construct the performance cost functional to be maximized. In this setting, the optimal DES control system yields superior performance in the sense that the controlled plant is more likely to reach a good (i.e., desirable) state and less likely to terminate at a bad (i.e., undesirable) state than other DES control systems. This optimal DES control algorithm requires at most (2n+1) iterations, and its computational complexity is polynomial in n, where n is the number of states in the plant PFSA model; this property suggests that the DES control concept would be ideally suited for real-time AI operations, such as those built upon a stimulus-response procedure. As an example, the proposed concept has been validated on a PFSA model of an (airborne) twin engine unmanned autonomous vehicle (UAV).