Speaker
Description
Nowadays, the turnpike phenomenon is a well-known concept in optimal control, which has been the subject of several studies over the last decade. This notion, first introduced in economics, refers to the particular structure of certain solutions that remain close to a turnpike most of the time except at the beginning and at the end. Most of recent works on turnpikes in optimal control focuses on steady-state turnpikes i.e. on problems where the turnpike can be understood as the steady-state equilibrium of infinite-horizon optimal solutions. In this context, one of the most important results is the exponential turnpike property, which gives precision on the exponential convergence of the solution to the steady-state turnpike. However, it is not always possible to have a static turnpike, especially for systems with symmetries which we are interested in. In this presentation, we extend the well know exponential turnpike to the exponential trim turnpike for symmetric optimal control problems. The main step of this study are the following. First we use geometric reduction procedure to obtain from the initial problem are duced one without symmetries. Then we state, on this reduced problem, the exponential turnpike. Finally we use the group symmetry to recover the exponential trim turnpike for the full system. We draw some examples to illustrate our result.
