Abstract
The problem of continuously dynamic multiobjective optimization, or multiobjective control, is discussed. The concepts of nondominated controls and viable controls are introduced. For a class of nonlinear dynamic systems, the convexity of their controlled Carathéodory trajectories is proved. Based on this convexity, sufficient conditions are given for the solution of a multiobjective control problem to be obtained in terms of solutions of weighting problems.
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Communicated by G. Leitmann
This work was partly done at the Huazhong University of Science and Technology, Wuhan, China. The author is indebted to Professor Chen Ting for his advice. The author wishes to thank Professor G. Leitmann for his favorable comments. The author is also grateful to Ms. Mary S. Linn at the University of Kansas, who helped him improve the English presentation of this paper.
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Liu, L.P. Characterization of nondominated controls in terms of solutions of weighting problems. J Optim Theory Appl 77, 545–561 (1993). https://doi.org/10.1007/BF00940449
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DOI: https://doi.org/10.1007/BF00940449