Runge-Kutta neural network for identification of dynamical systems in high accuracy
- 1 March 1998
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Neural Networks
- Vol. 9 (2) , 294-307
- https://doi.org/10.1109/72.661124
Abstract
This paper proposes Runge-Kutta neural networks (RKNNs) for identification of unknown dynamical systems described by ordinary differential equations (i.e., ordinary differential equation or ODE systems) with high accuracy. These networks are constructed according to the Runge-Kutta approximation method. The main attraction of the RKNNs is that they precisely estimate the changing rates of system states (i.e., the right-hand side of the ODE x/spl dot/=f(x)) directly in their subnetworks based on the space-domain interpolation within one sampling interval such that they can do long-term prediction of system state trajectories. We show theoretically the superior generalization and long-term prediction capability of the RKNNs over the normal neural networks. Two types of learning algorithms are investigated for the RKNNs, gradient-and nonlinear recursive least-squares-based algorithms. Convergence analysis of the learning algorithms is done theoretically. Computer simulations demonstrate the proved properties of the RKNNs.Keywords
This publication has 13 references indexed in Scilit:
- Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networksPublished by Elsevier ,2003
- High-order neural network structures for identification of dynamical systemsIEEE Transactions on Neural Networks, 1995
- Application of the recurrent multilayer perceptron in modeling complex process dynamicsIEEE Transactions on Neural Networks, 1994
- Memory neuron networks for identification and control of dynamical systemsIEEE Transactions on Neural Networks, 1994
- Introduction to Numerical AnalysisPublished by Springer Nature ,1993
- Neural networks for control systems—A surveyAutomatica, 1992
- Neural network application for direct feedback controllersIEEE Transactions on Neural Networks, 1992
- Universal Approximation Using Radial-Basis-Function NetworksNeural Computation, 1991
- Identification and control of dynamical systems using neural networksIEEE Transactions on Neural Networks, 1990
- Backpropagation through time: what it does and how to do itProceedings of the IEEE, 1990