## Time optimal control: Application to LCL filters

### Lukáš Adam, Václav Šmídl

We consider LCL filters which are important to remove unwanted frequencies or to enhance the wanted ones in a signal. Mathematically, we solve an optimal time control problem where we want to reach the prescribed state in minimal possible time. We rewrite the (controlled) differential equation into an (uncontrolled) differential inclusion and compute the reachable set based on convex duality. We discuss different viewpoints from mathematicians and engineers.