Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Global optimization approach to nonlinear optimal control

  • 128 Accesses

  • 19 Citations


To determine the optimum in nonlinear optimal control problems, it is proposed to convert the continuous problems into a form suitable for nonlinear programming (NLP). Since the resulting finite-dimensional NLP problems can present multiple local optima, a global optimization approach is developed where random starting conditions are improved by using special line searches. The efficiency, speed, and reliability of the proposed approach is examined by using two examples.

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


  1. 1.

    Hicks, G. A., andRay, W. H.,Approximation Methods for Optimal Control Synthesis, Canadian Journal of Chemical Engineering, Vol. 49, pp. 522–528, 1971.

  2. 2.

    Sargent, R. W. H., andSullivan, G. R.,The Development of an Efficient Optimal Control Package, Optimization Techniques, Edited by J. Stoer, Springer-Verlag, Berlin, Germany, Part 2, pp. 158–168, 1978.

  3. 3.

    Rosen, O., andLuus, R.,Sensitivity of Optimal Control to Final State Specification by a Combined Continuation and Nonlinear Programming Approach, Chemical Engineering Science, Vol. 44, pp. 2527–2534, 1989.

  4. 4.

    Vlassenbroeck, J.,A Chebyshev Polynomial Method for Optimal Control with State Constraints, Automatica, Vol. 24, pp. 499–506, 1988.

  5. 5.

    Kraft, D.,On Converting Optimal Control Problems into Nonlinear Programming Problems, Computational Mathematical Programming, Edited by K. Schittkowski, Springer-Verlag, Berlin, Germany, pp. 261–280, 1985.

  6. 6.

    Litt, F. X., andDelcommune, J.,Implementation of Spline Approximation Algorithms in Numerical Optimal Control, Applications of Nonlinear Programming to Optimization and Control, Edited by H. E. Rauch, Pergamon Press, Oxford, England, pp. 121–128, 1984.

  7. 7.

    Cuthrell, J. E., andBiegler, L. T.,On the Optimization of Differential-Algebraic Process Systems, AIChE Journal, Vol. 33, pp. 1257–1270, 1987.

  8. 8.

    Gill, P. E., Murray, W., andWright, M. H.,Practical Optimization, Academic Press, London, England, 1981.

  9. 9.

    Luus, R., andCormack, D. E.,Multiplicity of Solutions Resulting from the Use of Variational Methods in Optimal Control Problems, Canadian Journal of Chemical Engineering, Vol. 50, pp. 309–311, 1972.

  10. 10.

    Dixon, L. C. W., andSzego, G. P., Editors,Toward Global Optimization, North-Holland Publishing Company, Amsterdam, Holland, 1975.

  11. 11.

    Dixon, L. C. W., andSzego, G. P., Editors,Toward Global Optimization 2, North-Holland Publishing Company, Amsterdam, Holland, 1978.

  12. 12.

    Torn, A. A.,A Search-Clustering Approach to Global Optimization, Toward Global Optimization 2, Edited by L. C. W. Dixon and G. P. Szego, North-Holland Publishing Company, Amsterdam, Holland, pp. 49–62, 1978.

  13. 13.

    Wang, B. C., andLuus, R.,Reliability of Optimization Procedures for Obtaining Global Optimum, AIChE Journal, Vol. 24, pp. 619–626, 1978.

  14. 14.

    Yeo, B. P.,A Modified Quasilinearization Algorithm for the Computation of Optimal Singular Control, International Journal of Control, Vol. 32, pp. 723–730, 1980.

  15. 15.

    Luus, R.,Optimal Control by Dynamic Programming Using Systematic Reduction in Grid Size, International Journal of Control, Vol. 51, pp. 995–1013, 1990.

  16. 16.

    Luus, R.,On the Optimization of Oil Shale Pyrolysis, Chemical Engineering Science, Vol. 33, pp. 1403–1404, 1978.

Download references

Author information

Additional information

Financial support from the Natural Science and Engineering Research Council under Grant A-3515 as well as an Ontario Graduate Scholarship are gratefully acknowledged. All the computations were done with the facilities of the University of Toronto Computer Centre and the Ontario Centre for Large Scale Computations.

Communicated by L. C. W. Dixon

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Rosen, O., Luus, R. Global optimization approach to nonlinear optimal control. J Optim Theory Appl 73, 547–562 (1992). https://doi.org/10.1007/BF00940055

Download citation

Key Words

  • Nonlinear optimal control
  • nonlinear programming
  • global optimization