Open AccessOn the nonuniqueness and instability of solutions of tracking-type optimal control problems
Author(s) -
Constantin Christof,
Dominik Hafemeyer
Publication year - 2022
Publication title -
mathematical control and related fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.658
H-Index - 21
eISSN - 2156-8472
pISSN - 2156-8499
DOI - 10.3934/mcrf.2021028
Subject(s) - mathematics , combinatorics , type (biology) , state (computer science) , arithmetic , discrete mathematics , algorithm , ecology , biology
We study tracking-type optimal control problems that involve a non-affine, weak-to-weak continuous control-to-state mapping, a desired state \begin{document}$ y_d $\end{document} , and a desired control \begin{document}$ u_d $\end{document} . It is proved that such problems are always nonuniquely solvable for certain choices of the tuple \begin{document}$ (y_d, u_d) $\end{document} and instable in the sense that the set of solutions (interpreted as a multivalued function of \begin{document}$ (y_d, u_d) $\end{document} ) does not admit a continuous selection.