Modeling and Control of Probabilistic Fuzzy Discrete Event Systems

We investigate modeling and control of probabilistic fuzzy discrete event systems (PFDES). PFDES is a new type of fuzzy discrete event systems. It allows the use of probabilities to describe the chances of occurrences of different events. Our new model for PFDES consists of a fuzzy automaton and a crisp automaton that specifies what sequences of events can occur and their probabilities of occurrences. Based on the new model, optimal control is designed using an on-line and limited lookahead method. Control is calculated one step at a time, after an occurrence of an event. At each step, a lookahead window of $N$ events is constructed. The performance measures for all states in the window are determined, which is a function of fuzzy states. Control is calculated to maximize the expected performance measure after the occurrences of $N$ events. To reduce computational complexity, a "dynamic-programming" approach is proposed. We prove that the control obtained is optimal. Examples are given in the paper to illustrate the results.