Stochastic gradient-based hyperbolic orthogonal neural networks for nonlinear dynamic systems identification

Orthogonal neural networks (ONNs) are some  powerful types of the neural networks in the modeling of non-linearity. They are constructed by the usage  of orthogonal functions sets. Piecewise continuous orthogonal functions (PCOFs) are some important classes of orthogonal functions. In this work, based on a set of hyperbolic PCOFs, we propose the hyperbolic ONNs  to identify the nonlinear dynamic systems. We train the proposed neural models with the stochastic gradient descent learning algorithm. Then, we prove the stability of this algorithm. Simulation results show the efficiencies of proposed model.