Dirichlet boundary control problems for parabolic equations with quadratic cost: Analyticity and riccati's feedback synthesis

Riccati type feedback synthesis of optimal controls for Dirichlet boundary parabolic equations is considered. The functional cost penalizes the L2 -energy over [0,T] of state and control action u and also final state y(T) at t=T. This latter fact, makes the functional cost discontinuous on the space of admissible controls: L2(Σ); Σ=[0T] × Γ. After overcoming some technical difficulties related to the above mentioned discontinuity, we prove that the optimal control uO can be written in the desired feedback form: uO (t)=−CP (t) yO (t) for all 0≤t