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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

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…

Optimization and Control · Mathematics 2021-02-10 Noboru Sakamoto , Enrique Zuazua

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 present a new proof of the turnpike property for nonlinear optimal control problems, when the running target is a steady control-state pair of the underlying system. Our strategy combines the construction of quasi-turnpike controls via…

Optimization and Control · Mathematics 2022-01-26 Carlos Esteve-Yagüe , Borjan Geshkovski , Dario Pighin , 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

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

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

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

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 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 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 revisit finite-dimensional linear-quadratic optimal control from the viewpoint of differential flatness. If the pair (A, B) is controllable, then the linear control system is flat, and every trajectory can be parametrized by a flat…

Optimization and Control · Mathematics 2026-04-08 Michel Fliess , Claude Lobry , Emmanuel Trélat

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

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

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

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

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

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 consider the singular optimal control problem of minimizing the energy supply of linear dissipative port-Hamiltonian descriptor systems subject to control and terminal state constraints. To this end, after reducing the problem to an ODE…

Optimization and Control · Mathematics 2022-02-16 Timm Faulwasser , Bernhard Maschke , Friedrich Philipp , Manuel Schaller , Karl Worthmann

In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…

Optimization and Control · Mathematics 2020-06-15 Martin Gugat , Michael Schuster , Enrique Zuazua