Towards Transparent Control of Large and Complex Systems

We first discuss the importance of making a controller interpretable and give an overview of the existing models and structures for that purpose. We then propose an approach to designing fuzzy controllers based on the B-spline model by learning. Unlike other normalised parametrised set functions for defining fuzzy sets, B-splines do not necessarily span membership values from zero to one but possess the property of "partition of unity". B-splines can be automatically determined after each input is partitioned. Learning of a fuzzy controller based on B-splines is then equivalent to the adaptation of a B-spline interpolator. Parameters of the controller output of each rule can be rapidly adapted by gradient descent. Optimal placements of the non-uniform B-splines for specifying each input can be found by Genetic Algorithms. Through comparative examples of function approximation we show that training of such a fuzzy controller generally provides results with minimal error. The approach can be extended to the problems of high-dimensional input by combining neural networks with a fuzzy control model.