Control Co-design of systems with parabolic PDE 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 first derive a sufficient stability condition for the PDE.

By spatially discretizing the PDE and using the sufficient stability condition, we propose a computationally tractable approximate CCD problem.

We solve the approximate CCD problem using a gradient-based method.

Finally, we justify our proposed approach through an example.