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Related papers: The turnpike property in semilinear control

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This paper presents analyses for the maximum hands-off control using the geometric methods developed for the theory of turnpike in optimal control. First, a sufficient condition is proved for the existence of the maximum hands-off control…

Optimization and Control · Mathematics 2020-05-01 Noboru Sakamoto , Masaaki Nagahara

In this paper, we establish an exponential periodic turnpike property for linear quadratic optimal control problems governed by periodic systems in infinite dimension. We show that the optimal trajectory converges exponentially to a…

Optimization and Control · Mathematics 2024-02-06 Emmanuel Trélat , Xingwu Zeng , Can Zhang

The paper proposes first steps towards the formalization and characterization of time-varying turnpikes in optimal control of mechanical systems. We propose the concepts of velocity steady states, which can be considered as partial steady…

Optimization and Control · Mathematics 2019-07-04 Timm Faulwasser , Kathrin Flaßkamp , Sina Ober-Blöbaum , Karl Worthmann

This paper investigates the relations between three different properties, which are of importance in optimal control problems: dissipativity of the underlying dynamics with respect to a specific supply rate, optimal operation at steady…

Systems and Control · Computer Science 2017-07-18 Timm Faulwasser , Milan Korda , Colin N. Jones , Dominique Bonvin

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

This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time horizon $[0,T]$ as $T\rightarrow\infty$. The so-called turnpike properties are established for such problems, under…

Optimization and Control · Mathematics 2022-02-28 Jingrui Sun , Hanxiao Wang , Jiongmin Yong

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 establish the turnpike property for linear quadratic control problems for which the control operator is admissible and may be unbounded, under quite general and natural assumptions. The turnpike property has been well studied for bounded…

Optimization and Control · Mathematics 2025-06-03 Hoai-Minh Nguyen , Emmanuel Trélat

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

Turnpikes have recently gained significant research interest in optimal control, since they allow for pivotal insights into the structure of solutions to optimal control problems. So far, mainly steady state solutions which serve as optimal…

Systems and Control · Electrical Eng. & Systems 2020-02-12 Timm Faulwasser , Kathrin Flaßkamp , Sina Ober-Blöbaum , Karl Worthmann

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

We obtain turnpike results for optimal control problems with lack of stabilizability in the state equation and/or detectability in the state term in the cost functional. We show how, under weakened stabilizability/detectability conditions,…

Optimization and Control · Mathematics 2020-07-29 Dario Pighin , Noboru Sakamoto

This article aims at quantifying the long time behavior of solutions of mean field PDE systems arising in the theory of Mean Field Games and McKean-Vlasov control. Our main contribution is to show well-posedness of the ergodic problem and…

Probability · Mathematics 2024-09-17 Alekos Cecchin , Giovanni Conforti , Alain Durmus , Katharina Eichinger

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

This paper deals with the long time behavior of the optimal solution of stochastic backward linear-quadratic optimal control problem over the finite time horizon. Both weak and strong turnpike properties are established under appropriate…

Optimization and Control · Mathematics 2023-09-08 Yuyang Chen , Peng Luo

In this paper, we consider a linear quadratic (LQ) optimal control problem in both finite and infinite dimensions. We derive an asymptotic expansion of the value function as the fixed time horizon T tends to infinity. The leading term in…

Optimization and Control · Mathematics 2023-12-27 Veljko Askovic , Emmanuel Trélat , Hasnaa Zidani

Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity…

Optimization and Control · Mathematics 2023-08-30 Martin Hernandez , Enrique Zuazua

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 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

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