Skip to main content
SpringerLink
Log in

Fuzzy Optimal Control for Bilinear Stochastic Systems with Fuzzy Parameters

  • Published:
Dynamics and Control

Abstract

In this paper we consider the control problem for a class of partially observed bilinear stochastic systems with fuzzy parameters. Using Takagi–Sugeno fuzzy model, the problem is described by three sets of fuzzy stochastic differential equations: one for the state process, one for the observed process and one for the controller which is assumed to be driven by the observed process. With this formulation, the original stochastic control problem can be treated as a deterministic identification problem in which the controller parameters and the corresponding membership functions are the unknowns. Using a suitable performance index, we have developed a set of necessary conditions for determining the parameters of the controller and the corresponding membership functions. Finally, some numerical simulations are presented to illustrate the effectiveness of the proposed fuzzy control scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ahmed, N. U., Elements of Finite Dimensional Systems and Control Theory, Longman Sci. Tech.: New York, 1988.

    Google Scholar 

  2. Ahmed, N. U., Optimization, Identification and Control of Systems Governed by Evolution Equations on Banach Space, Pitman Research Notes in Mathematics Series, Vol. 184, Longman Sci. Tech.: New York, 1988.

    Google Scholar 

  3. Ahmed, N. U., “Computer aided design of optimal feedback controls for partially observed systems driven by martingale processes, ” in 14th IFIP on System Modeling and Optimization, Leipzig, July 1989.

  4. Ahmed, N. U., “Identification of operators in systems governed by evolution equations on Banach space, ” in Breudez (ed.), Control of Partial Differential Equations, Lecture Notes in Control and Information Science Vol. 114, pp. 73–83, 1989.

  5. Äström, L. and Wittenmark, B., Computer Controlled Systems: Theory and Design, 2nd ed., Prentice-Hall: Englewood Cliffs, NJ, 1990.

  6. Äström, L. and Wittenmark, B., “On self-tuning regulators, ” Automatica, Vol. 9, pp. 185–199, 1973.

    Google Scholar 

  7. Becker, A., Kumar, P. and Wei, C., “Adaptive control with the stochastic approximation algorithm: Geometry and convergence, ” IEEE Trans. Automat. Control, Vol. 30, pp. 330–338, 1985.

    Google Scholar 

  8. Chen, G., Tseng, C. and Uang, H., “Robustness design of nonlinear dynamic systems via fuzzy linear control, ” IEEE Trans. Fuzzy Systems, Vol. 7, No. 5, pp. 571–585, 1999.

    Google Scholar 

  9. Chen, G., Wang, J. and Sheih, L., “Fuzzy Kalman filtering, ” J. Inform. Sci., Vol. 109, pp. 197–209, 1998.

    Google Scholar 

  10. Dabbous, T. E., “Optimal control for a class of partially observed bilinear stochastic systems, ” in 29th IEEE Conf. on Decision and Control, Hawaii, pp. 1416–1417, 1990.

  11. Dabbous, T. E. and Ahmed, N. U., “Parameter identification for partially observed diffusions, ” J. Opt. Theory Appl., Vol. 75, No. 1, pp. 33–49, 1992.

    Google Scholar 

  12. Goodwin, G. and Sin, K., Adaptive Filtering, Prediction, and Control, Prentice-Hall: Englewood Cliffs, NJ, 1984.

    Google Scholar 

  13. Goodwin, G., Sin, K. and Saluja, K., “Stochastic adaptive control and prediction, the general delay-colored noise case, ” IEEE Trans. Automat. Control, Vol. 25, pp. 946–949, 1980.

    Google Scholar 

  14. Kumar, P., “A survey of some results in stochastic adaptive control, ” SIAM J. Control Optim., Vol. 23, pp. 329–380, 1985.

    Google Scholar 

  15. Kumar, P. and Becker, A., “A new family of optimal adaptive controllers for Markov chains, ” IEEE Trans. Automat. Control, Vol. 27, pp. 137–146, 1982.

    Google Scholar 

  16. Kumar, P. and Praly, L., “Self-tuning tractors, ” SIAM J. Control Optim., Vol. 25, pp. 1053–1071, 1987.

    Google Scholar 

  17. Kumar, P. and Varaiya, P., Stochastic Systems: Estimation, Identification and Adaptive Control, Prentice-Hall: Englewood Cliffs, NJ, 1984.

    Google Scholar 

  18. Ren, W. and Kumar, P., “Stochastic adaptive prediction and model reference control, ” IEEE Trans. Automat. Control, Vol. 39, No. 10, pp. 2047–2060, 1994.

    Google Scholar 

  19. Schuppen, V., “Tuning of Gaussian stochastic control systems, ” IEEE Trans. Automat. Control, Vol. 39, No. 11, pp. 2178–2190, 1994.

    Google Scholar 

  20. Sin, K., Goodwin, G. and Bitmead, R., “An adaptive D-step ahead predictor based on least squares, ” IEEE Trans. Automat. Control, Vol. 25, pp. 1161–1164, 1980.

    Google Scholar 

  21. Teo, K. L. and Wu, Z. S., Computational Methods for Optimizing Distributed Systems, Appendix V, Academic Press: New York, 1984.

    Google Scholar 

  22. Wang, L., Adaptive Fuzzy Systems and Control, Prentice-Hall: Englewood Cliffs, NJ, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Elec. & Comp. Engineering, Higher Technological Institute, Ramadan 10th City, Egypt

    T. E. Dabbous

Authors
  1. T. E. Dabbous
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dabbous, T.E. Fuzzy Optimal Control for Bilinear Stochastic Systems with Fuzzy Parameters. Dynamics and Control 11, 243–259 (2001). https://doi.org/10.1023/A:1015224002970

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015224002970

Search

Navigation