On “an improved approach for nonlinear system identification using neural networks”

Nonlinear system identification and prediction is a complex task, and often non-parametric models such as neural networks are used in place of intricate mathematics. To that cause, recently an improved approach to nonlinear system identification using neural networks was presented in Gupta and Sinha (J. Franklin Inst. 336 (1999) 721). Therein a learning algorithm was proposed in which both the slope of the activation function at a neuron, β, and the learning rate, η, were made adaptive. The proposed algorithm assumes that η and β are independent variables. Here, we show that the slope and the learning rate are not independent in a general dynamical neural nétwork, and this should be taken into account when designing a learning algorithm. Further, relationships between η and β are developed which helps reduce the number of degrees of freedom and computational complexity in an optimisation task of training a fully adaptive neural network. Simulation results based on Gupta and Sinha (1999) and the proposed approach support the analysis.