Optimal control of neural differential equations: The turnpike property

Gugat M (2026)


Publication Type: Journal article

Publication year: 2026

Journal

Book Volume: 215

Article Number: 106491

DOI: 10.1016/j.sysconle.2026.106491

Abstract

Consider a system that is governed by a neural differential equation. Such systems model deep neural networks with continuous time. For systems of this type, we study an optimal control problem where the objective function consists of a tracking term that is given by the sum of a squared weighted H1-norm and a control cost that is given by a squared L2-norm. We prove that a simultaneous exact controllability property of the system implies a turnpike property for the optimal state that depends on the weight in this differentiable objective function. We also show the finite-time turnpike property for the non-differentiable objective function where the tracking term is not squared. Numerical results illustrate our findings.

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How to cite

APA:

Gugat, M. (2026). Optimal control of neural differential equations: The turnpike property. Systems & Control Letters, 215. https://doi.org/10.1016/j.sysconle.2026.106491

MLA:

Gugat, Martin. "Optimal control of neural differential equations: The turnpike property." Systems & Control Letters 215 (2026).

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