Journal of Zhejiang University-SCIENCE A

, Volume 7, Issue 12, pp 1984–1988 | Cite as

Predictive control of a class of bilinear systems based on global off-line models

  • Zhang Ri-dong 
  • Wang Shu-qing 


A new multi-step adaptive predictive control algorithm for a class of bilinear systems is presented. The structure of the bilinear system is converted into a simple linear model by using nonlinear support vector machine (SVM) dynamic approximation with analytical control law derived. The method does not need on-line parameters estimation because the system’s internal model has been transformed into an off-line global model. Compared with other traditional methods, this control law reduces on-line parameter estimating burden. In addition, its overall linear behavior treating method allows an analytical control law available and avoids on-line nonlinear optimization. Simulation results are presented in the article to illustrate the efficiency of the method.

Key words

Bilinear systems Model predictive control (MPC) Adaptive control Support vector machine (SVM) 

CLC number



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bloemen, H.H.J., van den Boom, T.J.J., Verbruggen, H.B., 2001. An Optimization Algorithm Dedicated to a MPC Problem for Discrete Time Bilinear Models. Proceedings of the American Control Conference, Arlington, VA, p.2371–2381.Google Scholar
  2. Clarke, D.W., Mohtadi, C., Tuffs, P.S., 1987. Generalized predictive control—part I. the basic algorithm. Automatica, 23(2):137–148. [doi:10.1016/0005-1098(87)90087-2]CrossRefMATHGoogle Scholar
  3. Fontes, A.B., Maitelli, A.L., Cavalcanti, A.L.O., 2004. Bilinear Compensed Generalized Predictive Control: An Adaptive Approach. 5th Asian Control Conference, Melbourne, Australia, p.1781–1785.Google Scholar
  4. He, J.C., Yang, M.Y., Yu, L., Chen, G.D., 1999. Predictive control of a class of generalized bilinear systems. Mechatronic Engineering, 16(5):225–226 (in Chinese).Google Scholar
  5. Jin, Y.Y., Gu, X.Y., 1990. Improved generalized predictive control. Information and Control., (3):8–14 (in Chinese).MathSciNetGoogle Scholar
  6. Lakhdari, Z., Mokhtari, M., Lecluse, Y., Provost, J., 1995. Adaptive Predictive Control of a Class of Nonlinear Systems—A Case Study. IFAC Proceedings: Adaptive Systems in Control and Signal Processing, Budapest, Hungary, p.209–214.Google Scholar
  7. Liu, G.Z., Li, P., 2004. Generalized Predictive Control for a Class of Bilinear Systems. IFAC 7th Symposium on Advanced Control of Chemical Processes, Hong Kong, China, p.952–956.Google Scholar
  8. Peng, H., Ozaki, T., Toyoda, Y., Haggan-Ozaki, V., 2002. Nonlinear Predictive Control Based on a Global Model Identified Off-line. Proceedings of the American Control Conference, Anchorage, AK, p.8–10.Google Scholar
  9. Priestley, M.B., 1980. State dependent models: a general approach to nonlinear time series analysis. Journal of Time Series Analysis, 1:57–71.MathSciNetCrossRefGoogle Scholar
  10. Suykens, J.A.K., Vandewalle, J., 1999. Least square support vector machine classifiers. Neural Processing Letters, 9(3):293–300. [doi:10.1023/A:1018628609742]MathSciNetCrossRefGoogle Scholar
  11. Yao, X.Y., Qian, J.X., 1997. Generalized predictive control of algorithm of bilinear system. Journal of Zhejiang University: Engineering Science, 31(2):231–236 (in Chinese).Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Zhang Ri-dong 
    • 1
  • Wang Shu-qing 
    • 1
  1. 1.Institute of Advanced Process Control, National Key Laboratory of Industrial Control TechnologyZhejiang UniversityHangzhouChina

Personalised recommendations