Nonlinear system modeling via knot-optimizing B-Spline networks

In using the B-spline network for nonlinear system modeling, owing to a lac k of suitable theoretical results, it is quite difficult to choose an appro priate set of knot points to achieve a good network structure for minimizin g, say, a minimum error criterion. In this paper, a novel knot-optimizing B -spline network is proposed to approximate general nonlinear system behavio r. The knot points are considered to be independent variables in the B-spli ne network and are optimized together with the B-spline expansion coefficie nts. A simulated annealing algorithm with an appropriate search strategy is used as an optimization algorithm for the training process in order to avo id any possible local minima. Examples involving dynamic systems up to six dimensions in the input space to the network are solved by the proposed met hod to illustrate the effectiveness of this approach.