# The turnpike property in nonlinear optimal control -- A geometric approach

arXiv: https://arxiv.org/abs/1903.09069 · HTML: https://mlsanity.com/paper/1903.09069/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2019.

## Built on by (most cited first, 2 of 2)

- [On Dissipativity of Cross-Entropy Loss in Training ResNets](https://mlsanity.com/paper/2405.19013/) (2024)
- [Horizon-Uniform Sensitivity and Decay of Terminal Reward Perturbations in Discrete-Time Pontryagin Systems](https://mlsanity.com/paper/2606.17762/) (2026)

## Abstract (arXiv)

This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic equilibrium and then, apply it to optimal control problems to obtain sufficient conditions for the turnpike occurs. The approach taken is geometric and gives insights for the behaviors of controlled trajectories, allowing us to find simpler proofs for existing results on the turnpike properties. Attempts to remove smallness restrictions for initial and target states are also discussed based on the geometry of (un)stable manifold and exponential stabilizability of control systems.