We aim at developing a systematic turnpike theory for evolution PDEs. Our preliminary results show that this not only depends on the model under consideration but also on the cost functional and control target, and that the fulfillment of the turnpike property requires the system under consideration to be controllable or stabilisable.

The theory developed so far allows to handle, mostly, linear PDEs, but the problem is widely open in the **nonlinear** frame, where the existing results require smallness conditions on the objectives (probably of a purely technical nature), which restrict the scope of applications.

#### Available tutorials:

#### Rotors imbalance suppression by optimal control

Formulation of Optimal control problem for rotor imbalance. Explanation of the code to numerically solve the problem.

#### Riccati theory in LQ optimization with time-varying target

In this short tutorial, we explain how to use Riccati’s theory to solve an LQ control problem with targets.

#### Turnpike property for functionals involving $L^1$−norm

We want to study the following optimal control problem...

#### Long time control and the Turnpike property

The turnpike property improves the numerical methods used to solve optimal control problems