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

TL;DR

This paper develops a control co-design framework for systems governed by parabolic PDEs, formulating an approximate problem solved via gradient methods, ensuring system stability and validated through numerical examples.

Contribution

It introduces an approximate control co-design formulation for parabolic PDE systems and demonstrates stability guarantees using gradient-based solutions.

Findings

The approximate CCD problem can be effectively solved with gradient methods.

Optimal solutions from the approximate problem stabilize the PDE system.

Numerical examples confirm the approach's validity and stability.

Abstract

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.