Skip to main content
SpringerLink
Log in

Satisfactory solutions approach to parameter optimization of dynamic systems with vector performance index

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

A novel approach to parameter optimization of large dynamic systems using vector performance index is described. The approach entails characterizing and determining a set of satisfactory solutions to the multiobjective optimization problem. The satisfactory solutions are defined with respect to a prespecified and satisfactory set of bounds on the indices. A theoretical basis is provided to obtain a compact and connected set of satisfactory solutions in the parameter space. Compactness and connectedness are essential requirements, since they assure a range of values for the parameters. An expedient numerical technique for determining the range of satisfactory values for the parameters is illustrated with an example. The satisfactory solutions approach provides a basis for designing a system with multiple requirements when all of them cannot be formulated in the framework of a composite vector index problem.

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. Mayne, D. Q.,Decentralized Control and Large-Scale Systems, Directions in Large-Scale Systems, Edited by Y. C. Ho and S. K. Mitter, Plenum Press, New York, New York, 1976.

    Google Scholar 

  2. Zadeh, L. A.,Optimality and Nonscalar-Valued Performance Criteria, IEEE Transactions on Automatic Control, Vol. AC-8, pp. 59–60, 1963.

    Google Scholar 

  3. Geoffrion, A. M.,Proper Efficiency and the Theory of Vector Minimization, Journal of Mathematical Analysis and Applications, Vol. 22, pp. 618–630, 1968.

    Google Scholar 

  4. Reid, R. W., andCitron, S. J.,On the Noninferior Performance Index Vectors, Journal of Optimization Theory and Applications, Vol. 7, pp. 11–28, 1971.

    Google Scholar 

  5. Lin, J. G.,Three Methods for Determining Pareto-Optimal Solutions of Multiple Objective Problems, Directions in Large-Scale Systems, Edited by Y. C. Ho and S. K. Mitter, Plenum Press, New York, New York, 1976.

    Google Scholar 

  6. Yu, P. L., andLeitmann, G.,Compromise Solutions, Dominated Structures, and Salukvadze's Solution, Journal of Optimization Theory and Applications, Vol. 13, pp. 362–378, 1974.

    Google Scholar 

  7. Hoffman, K.,Analysis in Euclidean Space, Prentice-Hall, Englewood Cliffs, New Jersey, 1975.

    Google Scholar 

  8. Pearson, A. E., andNoonan, F.,On the Model Reference Adaptive Control Problem, Proceedings of the Joint Automatic Control Conference, Ann Arbor, Michigan, pp. 538–545, 1968.

  9. Franklin, J. M.,Matrix Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1968.

    Google Scholar 

  10. Teo, K. L., andMoore, E. J.,On Directional Derivative Methods for Solving Optimal Parameter Selection Problems, International Journal of Systems Science, Vol. 9, pp. 1029–1041, 1978.

    Google Scholar 

  11. Hasdorf, L.,Gradient Optimization and Nonlinear Control, Wiley, New York, New York, 1976.

    Google Scholar 

  12. Luenberger, D. G.,Introduction to Linear and Nonlinear Programming, Addison-Wesley, Reading, Massachusetts, 1973.

    Google Scholar 

  13. Rosen, J. B.,The Gradient Projection Method for Nonlinear Programming, Part 1, SIAM Journal on Applied Mathematics, Vol. 8, pp. 181–217, 1960.

    Google Scholar 

  14. Kirsch, L. W.,Feedback Control of a Steam Generator Using Vector Performance Index, University of Illinois at Chicago, PhD Thesis, 1974.

  15. Perkins, W. R., andCruz, J. B.,Engineering of Dynamic Systems, Wiley, New York, New York, 1969.

    Google Scholar 

  16. Gopalsami, N.,Satisfactory Solutions Approach to Control and Optimization of Large-Scale Systems, University of Illinois at Chicago, PhD Thesis, 1981.

  17. Lane, N. M.,Goal Programming and Satisficing Models in Economic Analysis, University of Texas, Austin, PhD Thesis, 1970.

  18. Benson, R. G.,Interactive Multiple Criteria Optimization Using Satisfactory Goals, University of Iowa, Iowa City, PhD Thesis, 1975.

Download references

Author information

Authors and Affiliations

  1. Components Technology Division, Argonne National Laboratory, Argonne, Illinois

    N. Gopalsami (Electrical Engineer)

  2. University of Illinois at Chicago, Chicago, Illinois

    C. K. Sanathanan (Professor of Electrical Engineering and Computer Science)

Authors
  1. N. Gopalsami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. K. Sanathanan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by G. Leitmann

This work constitutes part of the first author's doctoral dissertation in the Department of Electrical Engineering and Computer Science, University of Illinois at Chicago, Chicago, Illinois. It was supported in part by the National Science Foundation, Grant No. ENG-76-09930. The first author is indebted to Drs. A. C. Raptis and T. P. Mulcahey of Argonne National Laboratory for their support and encouragement.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gopalsami, N., Sanathanan, C.K. Satisfactory solutions approach to parameter optimization of dynamic systems with vector performance index. J Optim Theory Appl 47, 301–319 (1985). https://doi.org/10.1007/BF00941496

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00941496

Key Words

Search

Navigation