Training quasi-ARX neural network model by homotopy approach

Quasi-ARX neural networks (NN) are NN based nonlinear models that not only have linear structures similar to linear ARX models, but also have useful interpretation in part of their parameters. However when applying an ordinary backpropagation (BP) for the training, it has potential risk that the BP algorithm is stuck at a local minimum, which results in a poorly trained model. In this paper, a homotopy continuation method is introduced to improve the convergence performance of BP training. The idea is to start the BP training with the criterion function for linear ARX model, which is gradually deformed first into one for quasi-ARX NN model with linear node functions, and then into the actual one for quasi-ARX NN with sigmoid node functions. By building the deformation into a usual recursive procedure for BP training of quasi-ARX NN model with adaptable node functions so that the proposed homotopy based BP algorithm is able to achieve improved convergence performance without much increase in the computation load. Numerical simulation results show that the proposed homotopy based BP has better performance than an ordinary BP.