State estimation for flexible-joint manipulators using stable neural networks

A stable neural network based observer for general multivariable nonlinear system is presented in this paper. Unlike most previous neural network observers, the proposed observer uses nonlinear in parameter neural network (NLPNN). Therefore, it can be applied to systems with higher degrees of nonlinearity without any a priori knowledge of system dynamics. The learning rule of the neural network is based on backpropagation algorithm. Backpropagation is a well known algorithm, which is easy to implement, and it has been successfully applied to many engineering problems. However, previous works on backpropagation suffer from lack of mathematical proof of stability. An e-modification term is also added to guarantee the robustness of the observer. No SPR or any other strong assumption is imposed on the proposed approach. The stability of the recurrent neural network observer is shown by Lyapunov´s direct method. The proposed neural network observer is applied to a flexible-joint manipulator to evaluate its performance of the new scheme.