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 (M
³
) 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