Abstract

The turnpike phenomenon concerns structural properties of the solutions of optimal control problems where the state is governed by an evolution equation over a certain time horizon and the objective functional is of integral type, for example the sum of a tracking term and a control cost.

In this situation for large time horizons the optimal controls and optimal states often come close to the solution of the corresponding static problem, where the feasible states are the static states corresponding to the evolution equation.

In particular, the influence of the given initial state becomes smaller as time proceeds.

Turnpike results provide valuable insights about the types of optimal controls that we can expect in a wide range of applications.