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In this work, we study the steady-state (or periodic) exponential turnpike property of optimal control problems in Hilbert spaces. The turnpike property, which is essentially due to the hyperbolic feature of the Hamiltonian system resulting…

Optimization and Control · Mathematics 2016-12-02 Emmanuel Trelat , Can Zhang , Enrique Zuazua

This paper considers an optimal control problem for a linear mean-field stochastic differential equation having regime switching with quadratic functional in the large time horizons. Our main contribution lies in establishing the strong…

Optimization and Control · Mathematics 2025-11-04 Hongwei Mei , Svetlozar Rachev , Rui Wang

We first derive a general integral-turnpike property around a set for infinite-dimensional non-autonomous optimal control problems with any possible terminal state constraints, under some appropriate assumptions. Roughly speaking, the…

Optimization and Control · Mathematics 2017-05-09 Emmanuel Trelat , Can Zhang

This paper is concerned with an optimal control problem for a nonhomogeneous linear stochastic differential equation having regime switching with a quadratic functional in the large time horizon. This is a continuation of the paper…

Optimization and Control · Mathematics 2025-08-08 Hongwei Mei , Rui Wang , Jiongmin Yong

In this paper the turnpike property is established for a non-convex optimal control problem in discrete time. The functional is defined by the notion of the ideal convergence and can be considered as an analogue of the terminal functional…

Optimization and Control · Mathematics 2022-11-01 Musa Mammadov , Piotr Szuca

In this paper, we develop several necessary conditions of turnpike property for generalizaid linear-quadratic (LQ) optimal control problem in infinite dimensional setting. The term 'generalized' here means that both quadratic and linear…

Optimization and Control · Mathematics 2024-03-15 Roberto Guglielmi , Zhuqing Li

Our main contribution in this article is the achievement of the turnpike property in its integral and exponential forms for parameter-dependent systems with averaged observations in the cost functional. Namely, under suitable assumptions…

Optimization and Control · Mathematics 2024-04-29 Martín Hernández , Martin Lazar , Sebastián Zamorano

This paper presents a simulation study on turnpike phenomena in stochastic optimal control problems. We employ the framework of Polynomial Chaos Expansions (PCE) to investigate the presence of turnpikes in stochastic LQ problems. Our…

Systems and Control · Electrical Eng. & Systems 2020-10-26 Ruchuan Ou , Michael Heinrich Baumann , Lars Grüne , Timm Faulwasser

We consider averages convergence as the time-horizon goes to infinity of optimal solutions of time-dependent optimal control problems to optimal solutions of the corresponding stationary optimal control problems. Control problems play a key…

Analysis of PDEs · Mathematics 2020-08-11 Mahamadi Warma , Sebastian Zamorano

Optimal control problems with symmetries often admit a non stationary turnpike property called trim turnpike, which characterizes the convergence of optimal solutions to certain symmetry induced trajectories called trim primitives. In this…

Optimization and Control · Mathematics 2026-04-27 Sofya Maslovskaya , Sina Ober-Blöbaum , Boris Wembe

We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic…

Optimization and Control · Mathematics 2025-05-29 Jonas Schießl , Ruchuan Ou , Timm Faulwasser , Michael Heinrich Baumann , Lars Grüne

This paper is concerned with optimal control problems for a linear homogeneous stochastic differential equation having regime switching with purely quadratic functional in the large time horizons. We establish the so-called turnpike…

Optimization and Control · Mathematics 2025-06-12 Hongwei Mei , Rui Wang , Jiongmin Yong

We introduce and study the turnpike property for time-varying shapes, within the viewpoint of optimal control. We focus here on second-order linear parabolic equations where the shape acts as a source term and we seek the optimal…

Analysis of PDEs · Mathematics 2020-06-23 Gontran Lance , Emmanuel Trélat , Enrique Zuazua

We investigate the interior turnpike phenomenon for discrete-time multi-agent optimal control problems. While for continuous systems the turnpike property has been established, we focus here on first-order discretizations of such systems.…

Optimization and Control · Mathematics 2024-04-12 Martin Gugat , Michael Herty , Jiehong Liu , Chiara Segala

In this paper, we introduce turnpike arguments in the context of optimal state estimation. In particular, we show that the optimal solution of the state estimation problem involving all available past data serves as turnpike for the…

Optimization and Control · Mathematics 2025-10-22 Julian D. Schiller , Lars Grüne , Matthias A. Müller

We analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal control problem with general terminal cost and constrained…

Analysis of PDEs · Mathematics 2021-11-23 Carlos Esteve , Hicham Kouhkouh , Dario Pighin , Enrique Zuazua

This work is concerned with the exponential turnpike property for optimal control problems of particle systems and their mean-field limit. Under the assumption of the strict dissipativity of the cost function, exponential estimates for both…

Optimization and Control · Mathematics 2025-09-10 Michael Herty , Yizhou Zhou

Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing symmetries. Following recent works, which generalized the classical concept of static turnpike to manifold turnpike, we extend the exponential…

Optimization and Control · Mathematics 2024-06-25 Kathrin Flaßkamp , Sofya Maslovskaya , Sina Ober-Blöbaum , Boris Wembe

We investigate pathwise turnpike behavior of discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process…

Optimization and Control · Mathematics 2024-03-25 Jonas Schießl , Ruchuan Ou , Timm Faulwasser , Michael Heinrich Baumann , Lars Grüne

We consider a constrained eigenvalue optimization problem that arises in an important nonlinear dynamical model for mRNA translation in the cell. We prove that the ordered list of optimal parameters admits a turnpike property, namely, it…

Optimization and Control · Mathematics 2026-01-21 Adam Kaminer , Thomas Kriecherbauer , Lars Grüne , Michael Margaliot