Periodic optimal control in Hilbert space (Q1911772)

The authors have studied an optimal control problem governed by \(y' = Ay + Bu\), \(y(0) = \varepsilon y(\tau)\), \(\varepsilon = \pm 1\), where \(A\) is the infinitesimal generator of a nonasymptotically stable \(C_0\) semigroup and \(B\) is a linear operator from \(U\) to \(H\). Both, distributed, i.e., \(B \in L(U,H)\), and boundary, i.e., \(B \in L(U, (D(A^*)')\), cases are investigated. Some applications to periodic control \((\varepsilon = 1)\) are given.