What is it about?
The turnpike property consists in the situation where regardless of the initial state, optimal states for a dynamic optimal control problem approach a state that solves an optimal control problem where an initial state is not prescribed, for example a static optimal control problem. This static control is called the 'turnpike. Often for differentiable objective functionals, although the turnpike is approached exponentially fast it is not reached exactly. In this paper, we show that for non-smooth tracking terms the situation is different: The turnpike is reached exactly after finite time!
Featured Image
Photo by Jason Leung on Unsplash
Why is it important?
If the turnpike is reached exactly after finite time, the optimal dynamic state has a clear structure, where after a transient initial phase it remains equal to the turnpike.
Perspectives
The finite-time turnpike phenomenon for problems of optimal boundary control of the wave equation has been considered in Mathematical Reports 24 (2022).
Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Read the Original
This page is a summary of: The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking Terms, January 2021, Springer Science + Business Media,
DOI: 10.1007/978-3-030-61742-4_2.
You can read the full text:
Resources
Contributors
The following have contributed to this page
