Equivalence of three different kinds of optimal control problems for heat equations and its applications (Q2840121)

The main purpose of the work is to prove an equivalence theorem for three different kinds of optimal control problems, which are optimal target control problems, optimal time control problems, and optimal norm control problems. Controlled systems in this study are internally controlled heat equations of the form NEWLINE\[NEWLINE\left\{ \begin{matrix} \l & \l \\ \partial_t y - \Delta y = \chi_{\omega}\chi_{(\tau,T)}u &\;\;\text{in}\;\Omega\times(0,T),\\ y=0&\;\;\text{on}\;\partial\Omega\times(0,T),\\ y(0)=y_0&\;\;\text{in}\;\Omega. \end{matrix}\right. NEWLINE\]NEWLINE With the aid of this theorem, the authors establish an optimal norm feedback law and build up some explicit algorithms for solutions of optimal norm and optimal time control problems.