On sampled-data optimization in distributed parameter systems

A system of parabolic partial differential equations is transformed into ordinary differential equations in a Hilbert space, where the system operator is the infinitesimal generator of a semigroup of operators. A sampled-data problem is then formulated and converted into an equivalent discrete-time problem. The existence and uniqueness of an optimal sampled-data control is proved. The optimal control is given by a linear sampled-states feedback law where the feedback operator is shown to be the bounded seff-adjoint positive semidefinite solution of a Riccati operator difference equation.