ABSTRACT
This chapter deals with optimal control problems for partial differential equations of parabolic and hyperbolic type with boundary conditions (in the time variable) of periodic and antiperoidic type. It provides a set of results on the optical control of the heat and wave equations based on "tangent cones" technique and based on smooth approximations of such cones. The technique is mainly based on approximate penalization of cost functions. The chapter discusses the two point nonlinear boundary conditions of antiperiodic type using real Hilbert spaces. In order to give necessary conditions for optimality, one needs to introduce some smooth approximations of beta function.
