Optimal control problem governed by y’ = Ay + Bu, y(0) = epsilon y(T), epsilon = +/-1 are studied, where A is the infinitesimal generator of a nonasymptotically stable C-0 semigroup and B is a linear operator from a controller space U into a state space H. Both distributed (B is an element of L(U, H)) and boundary cases (B is an element of L(U, (D(A*))’)) are investigated. Some applications to periodic control of wave equations are given.