Online Self-Learning Fuzzy Discrete Event Systems

The fuzzy discrete event system theory is unique in that it is capable of modeling a class of event-driven systems as fuzzy automata with states and event-invoked state transitions being ambiguous. At present, the theory lacks a self-learning component, an important topic that has hardly been touched in the literature. In this article, we use stochastic gradient descent to develop online learning algorithms for the fuzzy automata. We uncover an inherent obstacle in the initial derived algorithms that fundamentally restricts their learning capability owing to dependences of the model parameters to be learned. We develop a novel mechanism to not only overcome the obstacle but also make the learning adaptive. Our final algorithms can learn an event transition matrix based on automaton's states before and after the occurrence of a fuzzy event, and learn the transition matrix and multidimensional Gaussian fuzzy sets yielding initial automaton states from relevant input variables and target states. Computer simulation results are presented to show learning performance of the final algorithms.