Free end points linear-quadratic problems of optimal control

The authors consider linear-quadratic optimal control problems with free end points, i.e., end points which are restricted to belong to a certain subset of the state space (in particular this set may be a linear manifold). Necessary and sufficient conditions are presented which enable an infinite-dimensional linear-quadratic optimal control problem to be reduced to a quadratic minimization problem in a finite-dimensional Euclidian space, and to present necessary and sufficient optimality conditions for the original infinite-dimensional optimization problem.<>