The turnpike property is an asymptotic-stability-like property of solutions of optimal control problems. It was first observed in the 1920s and 1930s by Ramsey and von Neumann and extensively studied in the 1960s and 1970s in mathematical economy. In recent years, it has attracted a lot of renewed attention in the Model Predictive Control (MPC) community on the one hand and in the Partial Differential Equation (PDE) control community on the other hand.

In this talk we start by explaining the turnpike property with simple examples. We will then briefly point out how this property relates to  classical systems theoretic properties such as dissipativity, stabilizability, and detectability. After explaining why this property is useful in MPC, in the last part of the talk we explain two recent developments: We show that for PDE-governed optimal control problems the turnpike property can be seen as a particular instance of a more general sensitivity property and we present first results for the turnpike  property in stochastic control problems.