Fuzzy Discrete Event Systems with Gradient-Based Online Learning

To make the fuzzy discrete event system theory more useful in a wide range of applications, it is crucial to equip it with learning capability, an issue that has hardly been touched upon in the literature. In this paper, we develop stochastic-gradient-decent-based algorithms for online learning of the event transition matrices and parameters of the fuzzy sets fuzzifying input variables of a fuzzy discrete event system modeled as a fuzzy automaton. We uncover an intrinsic obstacle in the algorithms that significantly impedes the learning owing to dependences of the fuzzy set parameters on the matrix. As a remedy, we modify the algorithms using the exponential penalty function. Preliminary computer simulation results are presented to illustrate learning performance of our final algorithms.