# PDE Examples

Control of PDEs can be approached by the DyCon Toolbox for all evolutionary PDEs that can be written in a semidiscrete form leading to the following finite dimensional system

with $x(t)$ and $u(t)$ being the state and control variables respectively. The target is to find the control $u(t)$ that optimizes the functional $J(x(t),u(t))$ subject to the semidiscrete PDE.