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On the nonuniqueness and instability of solutions of tracking-type optimal control problems
Mathematical Control and Related Fields ( IF 1.2 ) Pub Date : 2022-01-01 , DOI: 10.3934/mcrf.2021028 Constantin Christof 1 , Dominik Hafemeyer 1
Mathematical Control and Related Fields ( IF 1.2 ) Pub Date : 2022-01-01 , DOI: 10.3934/mcrf.2021028 Constantin Christof 1 , Dominik Hafemeyer 1
Affiliation
<p style='text-indent:20px;'>We study tracking-type optimal control problems that involve a non-affine, weak-to-weak continuous control-to-state mapping, a desired state <inline-formula><tex-math id="M1">\begin{document}$ y_d $\end{document}</tex-math></inline-formula>, and a desired control <inline-formula><tex-math id="M2">\begin{document}$ u_d $\end{document}</tex-math></inline-formula>. It is proved that such problems are always nonuniquely solvable for certain choices of the tuple <inline-formula><tex-math id="M3">\begin{document}$ (y_d, u_d) $\end{document}</tex-math></inline-formula> and instable in the sense that the set of solutions (interpreted as a multivalued function of <inline-formula><tex-math id="M4">\begin{document}$ (y_d, u_d) $\end{document}</tex-math></inline-formula>) does not admit a continuous selection.</p>
更新日期：2022-01-01
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