Optimal feedback control for a semilinear evolution equation (Q1337222)

The authors study the semilinear control system \[ \begin{aligned} y_ j'(t) & = A_ j(t) y_ j(t)+ f_ j(t, y_ 1(t),\dots, y_ n(t),\;u(t))\qquad (1\leq j\leq n)\\ u(t) &\in V(t, y_ 1(t),\dots, y_ n(t)),\end{aligned} \] where \(y_ j(t)\in\) separable Banach space \(X_ j\) and \(u(t)\in\) Banach space \(Z\); \(V\) is a feedback set-valued map. The object is to construct a feedback solution of the problem of minimizing a cost functional subject to constraints on the initial and final point of the trajectory.