Control Co-design of systems with parabolic partial differential equation dynamics

In this paper we study the control co-design (CCD) synthesis problem for a class of systems with parabolic partial differential equation (PDE) dynamics. We formulate CCD problem and finally derive an approximate CCD problem with matrix algebraic constraint. We then solve this approximate problem with gradient-based method and prove that the optimal solution also stabilizes the PDE system. We justify approach through numerical examples.