System Modelling Using Neural Networks with External Recurrence and Exponential Quadratic Cost Function

A novel cost function to improve the performance of neural networks in system modelling is proposed in this paper, the exponential quadratic cost function. This cost function combines the strength of penalizing errors exponentially and the feasibility of quadratic function in finding global minima. By applying the exponential quadratic cost function, the learning algorithm is expected to have an improved ability to minimize the difference between system output and model output. Simulations by using a test system with strong nonlinear dynamics were conducted to prove the effectiveness of the proposed cost function. The results show that the network trained using the exponential quadratic cost function performs better in emulating the test system in transient region.