Nonlinear model-based dynamic recurrent neural network

In this study, a model-based dynamic recurrent neural network (MBDRNN) is made use of to model and control nonlinear dynamic systems. It is primordial to have a priori analytic knowledge of the system since the MBDRNN has a partially fixed structure that is defined according to one or more linearized state-space operating points of the system. Such a requirement places the system in the "gray-box" category. Initially, the nodes of the MBDRNN have unity gains, which makes it just a simple block diagram of the linearized model. Afterwards, the MBDRNN is trained to represent the system\´s nonlinearities through modifying the weights of its node activation functions, which are expansion coefficients over judiciously selected sets of hump functions. Humps were chosen because of their localizing and shifting properties both in the time and the frequency domains. Training the MBDRNN was accomplished using back propagation and involved adjusting the weights of the activation functions in order to adapt to the contours representing the system\´s nonlinearities