Runge Kutta neural network for identification of continuous systems

This paper proposes Runge Kutta neural networks (RKNNs) for identification of continuous-time nonlinear systems. These networks are constructed according to the Runge Kutta approximation method. The RKNNs can thus precisely model continuous-time systems and do long-term prediction of system state trajectories. The RKNNs model continuous-time systems can incorporate available continuous relationship (physical laws) of the identified systems into their structures directly. Also, they are insensitive to the size of sampling interval in prediction. We also show theoretically the superior generalization and long-term prediction capability of the RKNNs over the normal neural networks. A class of novel recursive least square algorithms, called nonlinear recursive least square learning algorithms, are developed for the RKNNs. Computer simulations demonstrate the proved properties of the RKNNs