MODEL-ORDER REDUCTION OF SINGULARLY PERTURBED SYSTEMS BASED ON ARTIFICIAL NEURAL ESTIMATION AND LMI-BASED TRANSFORMATION

Othman M-K. Alsmadi, Za'er S. Abo-Hammour, Mohammad S. Saraireh

2009

Abstract

A new method for model order reduction with eigenvalue preservation is presented in this paper. The new technique is formulated based on the system state matrix transformation which preserves the system eigenvalues and is accomplished using an artificial neural network training. A linear matrix inequality (LMI) numerical algorithm technique is used to obtain the complete system transformation. Model order reduction is then obtained utilizing the singular perturbation method. Simulation results show that the LMI-based transformed reduced model order is superior to other reduction methods.

References

  1. Alsmadi, O., Abdalla, M., 2007. Model order Reduction for Two-Time-Scale Systems Based on Neural Network Estimation. Proceedings of the 15th Mediterranean Conference on Control & Automation. Athens, Greece.
  2. Benner, P., 2007. Model Reduction at ICIAM'07. SIAM News, V. 40, N. 8.
  3. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., 1994. Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics (SIAM).
  4. Bui-Thanh, T., Willcox, K., 2005. Model Reduction for Large-Scale CFD Applications using the Balanced Proper Orthogonal Decomposition. 17th American Institute of Aeronautics and Astronautics Computational Fluid Dynamics Conference. Toronto, Canada.
  5. Franklin, G., Powell, J., Emami-Naeini, A., 1994. Feedback Control of Dynamic Systems, AddisonWesley, 3rd edition.
  6. Garsia, G., Dfouz, J., Benussou, J., 1998. H2 Guaranteed Cost Control for Singularly Perturbed Uncertain Systems. IEEE Transactions on Automatic Control, Vol. 43, pp. 1323-1329.
  7. Haykin, S., 1994. Neural Networks: a Comprehensive Foundation, Macmillan College Publishing Company, New York.
  8. Hinton, G., Salakhutdinov, R., 2006. Reducing the Dimensionality of Data with Neural Networks. Science, pp. 504-507.
  9. Horn, R., Johnson, C., 1985. Matrix Analysis. Cambridge, UK.
  10. Kokotovic, P., Khalil, H., O'Reilly, J., 1986. Singular Perturbation Methods in Control: Analysis and Design, Academic Press. Orlando, Florida.
  11. Williams, R., Zipser, D., 1989. A Learning Algorithm for Continually Running Full Recurrent Neural Networks. Neural Computation, 1(2), pp. 270-280.
  12. Zhou, W., Shao, S., Gao, Z., 2009. A Stability Study of the Active Disturbance Rejection Control Problem by a Singular Perturbation Approach. Applied Mathematical Science, Vol. 3, no. 10, pp. 491-508.
  13. Zurada, J., 1992. Artificial Neural Systems, West Publishing Company, New York.
Download


Paper Citation


in Harvard Style

M-K. Alsmadi O., S. Abo-Hammour Z. and S. Saraireh M. (2009). MODEL-ORDER REDUCTION OF SINGULARLY PERTURBED SYSTEMS BASED ON ARTIFICIAL NEURAL ESTIMATION AND LMI-BASED TRANSFORMATION . In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 978-989-8111-99-9, pages 173-180. DOI: 10.5220/0002187801730180


in Bibtex Style

@conference{icinco09,
author={Othman M-K. Alsmadi and Za'er S. Abo-Hammour and Mohammad S. Saraireh},
title={MODEL-ORDER REDUCTION OF SINGULARLY PERTURBED SYSTEMS BASED ON ARTIFICIAL NEURAL ESTIMATION AND LMI-BASED TRANSFORMATION },
booktitle={Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2009},
pages={173-180},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002187801730180},
isbn={978-989-8111-99-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - MODEL-ORDER REDUCTION OF SINGULARLY PERTURBED SYSTEMS BASED ON ARTIFICIAL NEURAL ESTIMATION AND LMI-BASED TRANSFORMATION
SN - 978-989-8111-99-9
AU - M-K. Alsmadi O.
AU - S. Abo-Hammour Z.
AU - S. Saraireh M.
PY - 2009
SP - 173
EP - 180
DO - 10.5220/0002187801730180