English
Related papers

Related papers: Turnpike in optimal control and beyond: a survey

200 papers

In this paper we investigate the turnpike property for constrained LQ optimal control problem in connection with dissipativity of the control system. We determine sufficient conditions to ensure the turnpike property in the case of a…

Optimization and Control · Mathematics 2023-08-29 Zhuqing Li , Roberto Guglielmi

The concept of turnpike connects the solution of long but finite time horizon optimal control problems with steady state optimal controls. A key ingredient of the analysis of the turnpike is the linear quadratic regulator problem and the…

Optimization and Control · Mathematics 2021-05-24 Jan Heiland , Enrique Zuazua

We establish a polynomial turnpike estimate for an optimal control problem consisting of a system of infinitely many controlled oscillators, considered as an abstract differential equation in a Hilbert space, with a quadratic cost. Our…

Optimization and Control · Mathematics 2026-03-03 Alexander Zuyev , Emmanuel Trélat

In this work we derive an interval turnpike result for adjoints of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics…

Optimization and Control · Mathematics 2020-05-26 Timm Faulwasser , Lars Grüne , Jukka-Pekka Humaloja , Manuel Schaller

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

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

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 study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval $(0,\, T)$ that depends on…

Analysis of PDEs · Mathematics 2018-11-08 Martin Gugat , Falk Hante

Recent results in the literature have provided connections between the so-called turnpike property, near optimality of closed-loop solutions, and strict dissipativity. Motivated by applications in economics, optimal control problems with…

Optimization and Control · Mathematics 2022-02-18 Lars Grüne , Lisa Krügel

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

Optimal control problems with a very large time horizon can be tackled with the Receding Horizon Control (RHC) method, which consists in solving a sequence of optimal control problems with small prediction horizon. The main result of this…

Optimization and Control · Mathematics 2020-02-03 Tobias Breiten , Laurent Pfeiffer

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

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 manuscript, we study the turnpike property in stochastic discrete-time optimal control problems for interacting agents. Extending previous deterministic results, we show that the turnpike effect persists in the presence of noise…

Optimization and Control · Mathematics 2025-03-13 Fabio Cassini , Chiara Segala

Turnpike phenomena of nonlinear port-Hamiltonian descriptor systems under minimal energy supply are studied. Under assumptions on the smoothness of the system nonlinearities, it is shown that the optimal control problem is dissipative with…

Optimization and Control · Mathematics 2023-01-24 Attila Karsai

Classical turnpikes correspond to optimal steady states which are attractors of optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the…

Optimization and Control · Mathematics 2021-04-08 Timm Faulwasser , Kathrin Flaßkamp , Sina Ober-Blöbaum , Manuel Schaller , Karl Worthmann

In this paper, we introduce and study different dissipativity notions and different turnpike properties for discrete-time stochastic nonlinear optimal control problems. The proposed stochastic dissipativity notions extend the classic notion…

Optimization and Control · Mathematics 2025-04-02 Jonas Schießl , Michael H. Baumann , Timm Faulwasser , Lars Grüne

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 study the asymptotic behavior of solutions to linear-quadratic mean field stochastic optimal control problems. By formulating an ergodic control framework, we characterize the convergence between the finite time horizon control problem…

Optimization and Control · Mathematics 2025-10-24 Erhan Bayraktar , Jiamin Jian

This note discusses properties of parametric discrete-time Mixed-Integer Optimal Control Problems (MIOCPs) as they often arise in mixed-integer NMPC. We argue that in want for a handle on similarity properties of parametric MIOCPs the…

Systems and Control · Electrical Eng. & Systems 2020-02-07 Timm Faulwasser , Alexander Murray