Abstract
Recently published results of Gift (Ref. 1) are concerned with the necessary conditions for singular optimal control problems (in the sense of Pontryagin's minimum principle). However, those results are incorrect. An illustrative counterexample is given here.
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References
Gift, S. J. G.,Second-Order Optimality Principle for Singular Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 76, pp. 477–484, 1993.
Mizukami, K., andWu, H. S.,New Necessary Conditions for Optimality of Singular Controls in Optimal Control Problems, International Journal of Systems Science, Vol. 23, pp. 1335–1345, 1992.
Zhou, Q.,Comment on “New Necessary Conditions for Optimality of Singular Controls in Optimal Control Problems,” International Journal of Systems Science (to appear).
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Communicated by L. D. Berkovitz
This paper was written while the author studied at Fudan University. The author wishes to thank Professor X. J. Li for his guidance and encouragement. The research was partially supported by NSF of China and the Chinese State Education Commission NSF.
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Zhou, Q. Second-order optimality principle for singular optimal control problems. J Optim Theory Appl 88, 247–249 (1996). https://doi.org/10.1007/BF02192033
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DOI: https://doi.org/10.1007/BF02192033