Nonlinear System Modeling via Knot-Optimizing B-Spline Networks

In using the B-spline network for nonlinear system modeling, owing to a lack of suitable theoretical results, it is quite difficult to choose an appropriate set of knot points to achieve a good network structure for minimizing, say, a minimum error criterion. In this paper, a novel knot-optimizing B-spline network is proposed to approximate general nonlinear system behavior. The knot points are considered to be independent variables in the B-spline network and are optimized together with the B-spline expansion coefficients. A simulated annealing algorithm with an appropriate search strategy is used as an optimization algorithm for the training process in order to avoid any possible local minima. Examples involving dynamic systems up to six dimensions in the input space to the network are solved by the proposed method to illustrate the effectiveness of this approach.