Training fuzzy neural networks using sliding mode theory with adaptive learning rate

This paper proposes an online training method for the parameters of a fuzzy neural network (FNN) using sliding mode systems theory with an adaptive learning rate. The implemented control structure consists of a conventional controller in parallel with a FNN. The former is provided both to guarantee global asymptotic stability in compact space and acts as a sliding surface to guide the states of the system towards zero. The output of the conventional controller is used to update the parameters of the FNN. The output of the FNN gradually replaces the conventional controller. The adaptive learning rate makes it possible to control the system without priori knowledge about the upper bound of the states of the system and their derivatives. An appropriate Lyapunov function approach is used to analyze the stability of the adaptation law of parameters of FNN. Sufficient conditions to guarantee the boundedness of the parameters are derived. The proposed approach is tested on the velocity control of an electro hydraulic servo system in presence of flow nonlinearities and internal friction.