Optimal Control of Dynamical Systems Governed by Partial Differential Equations: A Perspective from Real-life Applications

This survey article summarizes some ideas of the two principle procedures for solving optimal control problems governed by partial differential (algebraic) equations: the indirect method or first-optimize-then-discretize approach based on first-order necessary conditions, and the direct method or first-discretize-then-optimize approach based on non-linear programming software. The focus of this paper is to discuss some pros and cons when applications come from real-life problems. It also glances at the main method which currently may have the best chance for online applications in PDE constrained optimization. The demonstrator example deals with the optimal control of a certain type of high temperature fuel cell system.