A new approach to the adaptation of fuzzy relations

Adaptive control proves to be an important eld of investigation as several control problems change its behaviour in time or there is no analytical model available at all. We present a new approach in this context: A fuzzy controller is adapted according to an evaluation function by a critic that is trained using reinforcement learning. In this paper we address the modeling and adaptation of the fuzzy controller. We use a combination of possibility and support distributions that is able to represent (partial) ignorance, to detect and resolve inconsistent knowledge. It is shown that the adaptation rule is stable and consistent with its task. I Introduction Neural controllers are very well suited for learning and adaptation. But in general, a neural network is a black box. We cannot explain how and why a neural controller works. This means, we cannot tell when a neural controller will fail, as well. Fuzzy controllers, on the contrary, allow the formalization and application of human knowledge. Therefore it is not only possible to interpret the way a fuzzy controller derives its output actions, but to incorporate a priori knowledge. From this point of view it is very interesting to directly tune fuzzy controllers. But comparing the importance of controller performance and controller interpretability, performance comes rst. We therefore propose a two step approach: (1) Adaptation: a given fuzzy controller is tuned without caring for a possible (2) Interpretation: afterwards, the adapted fuzzy knowledge is analyzed in order to extract a set of fuzzy rules that at least roughly represents the given knowledge base. This paper addresses adaptation only. In general, we want to control a process that has not been controlled before. This is, we cannot assume to have a teacher telling us in every input situation the appropriate action to be chosen. To cope with this problem reinforcement learning has been established ?, ?]. In reinforcement learning there is a critic evaluating each controller action. During controller adaptation, the critic is adapted, as well. The basic idea of our work is to implement the critic by a neural network, because the adaptation of the critic is more complex than the adaptation of the controller, whereas an understanding of the critic's behaviour is far less important. However, we do not address the realization of the critic here. In several applications a teacher is not available, as already mentioned above. A general problem results from …