Abstract
In this paper, iterative learning control is presented to a dynamic neural network modelling process for nonlinear (stochastic) dynamical systems. When (B-spline) neural networks are used to model a nonlinear dynamical functional such as the output stochastic distributions in the repetitive processes or the batch processes, the parameters in the basis functions will be tuned using the generalized iterative learning control (GILC) scheme. The GILC scheme differs from the classical model-based ILC laws, with no dynamical input-output differential or difference equations given a prior. For the “model free” GILC problem, we propose an optimal design algorithm for the learning operators by introducing an augmented difference model in state space. A sufficient and necessary solvable condition can be given where a robust optimization solution with an LMI-based design algorithm can be provided.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chen, S., Wu, Y., Luk, B.L.: Combined Genetic Algorithm Optimization and Regularized Orthogonal Least Squares Learning for RBF Networks. IEEE Trans. on Neural Networks 10, 1239–1244 (1999)
Hong, X., Brown, M., Chen, S., Harris, C.J.: Sparse Model Identification Using Orthogonal Forward Regression with Basis Pursuit and D-Optimality. IEE Proc.-Control Theory Appl. 151, 491–498 (2004)
Wang, H.: Bounded Dynamic Stochastic Systems: Modelling and Control. Springer, London (2000)
Guo, L., Wang, H.: PID Controller Design for Output PDFs of Stochastic Systems using Linear Matrix Inequalities. IEEE Trans on Systems, Man and Cybernetics, Part-B 35, 65–71 (2005)
Guo, L., Wang, H.: Applying Constrained Nonlinear Generalized PI Strategy to PDF Tracking Control through Square Root B-Spline Models. International Journal of Control 77, 1481–1492 (2004)
Guo, L., Wang, H.: Fault Detection and Diagnosis for General Stochastic Systems Using B-Spline Expansions and Nonlinear Filters. IEEE Trans. on Circuits and Systems-I: Regular Papers 52, 1644–1652 (2005)
Wang, H., Zhang, J.F., Yue, H.: Iterative Learning Control of Output Shaping in Stochastic Systems. In: Wang, H., Zhang, J.F., Yue, H. (eds.) Proceedings of the 2005 IEEE International Symposium on Intelligent Control, Cyprus, pp. 1225–1230 (2005)
Xu, J.X., Tan, Y.: Linear and Nonlinear Iterative Control. Springer, London (2003)
Norrlof, M., Gunnarsson, S.: Experimental Comparison of Some Classical Iterative Learning Control Algorithms, Technical report from the Control & Communication group in Linkoping (2002), http://www.control.isy.liu.se/publications
Amann, N., Owens, D.H., Rogers, E.: Predictive Optimal Iterative Learning Control. International Journal of Control 69, 203–226 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Guo, L., Wang, H. (2006). An Optimal Iterative Learning Scheme for Dynamic Neural Network Modelling. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_74
Download citation
DOI: https://doi.org/10.1007/11759966_74
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34439-1
Online ISBN: 978-3-540-34440-7
eBook Packages: Computer ScienceComputer Science (R0)