Stable identification of nonlinear systems using neural networks: theory and experiments

This paper presents an approach for stable identification of multivariable nonlinear system dynamics using a multilayer feedforward neural network. Unlike most of the previous neural network identifiers, the proposed identifier is based on a nonlinear-in-parameters neural network (NLPNN). Therefore, it is applicable to systems with higher degrees of nonlinearities. Both parallel and series-parallel models are used with no a priori knowledge about the system dynamics. The method can be considered both as an online identifier that can be used as a basis for designing a neural network controller as well as an offline learning scheme for monitoring the system states. A novel approach is proposed for the weight updating mechanism based on the modification of the backpropagation (BP) algorithm. The stability of the overall system is shown using Lyapunov´s direct method. To demonstrate the performance of the proposed algorithm, an experimental setup consisting of a three-link macro-micro manipulator (M³) is considered. The proposed approach is applied to identify the dynamics of the experimental robot. Experimental and simulation results are given to show the effectiveness of the proposed learning scheme