Turnpike in optimal control and beyond: a survey

Trélat E, Zuazua Iriondo E (2025)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2025

Open Access Link: https://hal.science/hal-05002039

Abstract

The turnpike principle is a fundamental concept in optimal control theory, stating that for a wide class of long-horizon optimal control problems, the optimal trajectory spends most of its time near a steady-state solution (the “turnpike”) rather than being influenced by the initial or final conditions.

In this article, we provide a survey on the turnpike property in optimal control, adding several recent and novel considerations. After some historical insights, we present an elemen- tary proof of the exponential turnpike property for linear-quadratic optimal control problems in finite dimension. Next, we show an extension to nonlinear optimal control problems, with a local exponential turnpike property. On simple but meaningful examples, we illustrate the local and global aspects of the turnpike theory, clarifying the global picture and raising new questions. We discuss key generalizations, in infinite dimension and other various settings, and review several applications of the turnpike theory across different fields. 

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Sorbonne Université FR France (FR)

How to cite

APA:

Trélat, E., & Zuazua Iriondo, E. (2025). Turnpike in optimal control and beyond: a survey. (Unpublished, Submitted).

MLA:

Trélat, Emmanuel, and Enrique Zuazua Iriondo. Turnpike in optimal control and beyond: a survey. Unpublished, Submitted. 2025.

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