ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
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Proceedings of the Estonian Academy of Sciences. Physics. Mathematics

Nonessential functionals in multiobjective optimal control problems; 336-346

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Authors
Agnieszka B. Malinowska, Delfim F. M. Torres

Abstract

We address the problem of obtaining well-defined criteria for multiple criteria optimal control problems. Necessary and sufficient conditions for an objective functional to be nonessential are proved. The results provide effective tools for determining nonessential objectives in multiobjective optimal control problems.


References

1. Aubin, J.-P. and Frankowska, H. Set-Valued Analysis, Systems & Control: Foundations & Applications, Vol. 2. Birkhäuser Boston, Boston, MA, 1990.

2. Hamel, A. H. Optimal control with set-valued objective function. In Proceedings of the 6th Portuguese Conference on Automatic Control – Controlo 2004, Faro, Portugal. 2004, 648–652.

3. Torres, D. F. M. A Noether theorem on unimprovable conservation laws for vector-valued optimization problems in control theory. Georgian Math. J., 2006, 1, 173–182.

4. Mordukhovich, B. S. Variational Analysis and Generalized Differentiation, II. Springer, New York, 2006.
doi:10.1007/3-540-31247-1_4

5. Salukvadze, M. E. Vector-Valued Optimization Problems in Control Theory. Academic Press, New York, 1979.

6. Gal, T. and Hanne, T. Nonessential objectives within network approaches for MCDM. European J. Oper. Res., 2006, 2, 584–592.
doi:10.1016/j.ejor.2004.04.045

7. Malinowska, A. B. Nonessential objective functions in linear vector optimization problems. Control Cybern., 2006, 35, 873–880.

8. Leitmann, G. The Calculus of Variations and Optimal Control. Plenum, New York, 1981.

9. Gal, T. and Leberling, H. Redundant objective functions in linear vector maximum problems and their determination. European J. Oper. Res., 1977, 1, 176–184.
doi:10.1016/0377-2217(77)90025-X

10. Malinowska, A. B. Changes of the set of efficient solutions by extending the number of objectives and its evaluations. Control Cybern., 2002, 31, 964–974.

11. Pontryagin, L. S. and Boltyanskii, V. G. The Mathematical Theory of Optimal Processes. Interscience Publishers John Wiley & Sons, Inc., New York, 1962.

12. Chang, S. S. L. General theory of optimal processes. SIAM J. Control, 1966, 4, 46–55.
doi:10.1137/0304005

13. Liu, L. P. Characterization of nondominated controls in terms of solutions of weighting problems. J. Optim. Theory Appl., 1993, 77, 545–561.
doi:10.1007/BF00940449

14. Reid, R. W. and Citron, S. J. On noninferior performance index vectors. J. Optim. Theory Appl., 1971, 7, 11–28.
doi:10.1007/BF00933589

15. Macki, J.W. and Strauss, A. Introduction to Optimal Control Theory. Springer, New York, 1982.

16. Pedregal, P. Introduction to Optimization. Springer, New York, 2004.

17. Ferreira, M. M. and de Pinho, M. d. R. Optimal Control Problems with Constraints. Editura Electus, Bucharest, 2002.

18. Athans, M. and Falb, P.-L. Optimal Control: An Introduction to the Theory and Its Applications. McGraw-Hill, New York, 1966.

 

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