Stability analysis of neural net controllers using fuzzy neural networks

Abstract

Neural networks can only be trained with a crisp and finite data set. Therefore, the approximation quality of a trained network is hard to verify. So, a common way in proving stability of a trained neural net controller is to demonstrate the existence of a Lyapunov function. In this article we propose a new method how stability of a neural net controller, used as a closed-loop feedback controller, can be proven. Instead of finding a Lyapunov function, conditions for a fuzzy training set are developed. If a fuzzy neural net is trained using this training set special properties of fuzzy neural nets can be used for estimating the generalization error. After defuzzification of the fuzzy net finite stability of the process can be concluded.