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Related papers: Uniform Turnpike Property and Singular Limits

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An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls…

Optimization and Control · Mathematics 2023-05-19 Karl Kunisch , Buddhika Priyasad

The goal of this paper is to analyze control properties of the parabolic equation with variable coefficients in the principal part and with a singular inverse-square potential:\,$\partial_tu(x,t)-{\rm div}(p(x)\nabla…

Analysis of PDEs · Mathematics 2018-11-15 Xue Qin , Shumin Li

In this paper we study the existence, the optimal regularity of solutions, and the regularity of the free boundary near the so-called \emph{regular points} in a thin obstacle problem that arises as the local extension of the obstacle…

Analysis of PDEs · Mathematics 2019-06-18 Agnid Banerjee , Donatella Danielli , Nicola Garofalo , Arshak Petrosyan

We prove an exact controllability result for a one-dimensional heat equation with delay in both lower and highest order terms and nonhomogeneous Dirichlet boundary conditions. Moreover, we give an explicit representation of the control…

Optimization and Control · Mathematics 2014-01-23 Denys Khusainov , Michael Pokojovy , Elvin Azizbayov

An abstract framework guaranteeing the continuous differentiability of local value functions on $H^1(\Omega)$ associated with optimal stabilization problems subject to abstract semilinear parabolic equations in the presence of norm…

Optimization and Control · Mathematics 2023-11-28 Karl Kunisch , Buddhika Priyasad

We will investigate the value and inactive region of optimal stopping and one-sided singular control problems by focusing on two fundamental ratios. We shall see that these ratios unambiguously characterize the solution, although usually…

Probability · Mathematics 2015-02-10 Pekka Matomäki

We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set $\Omega\subset\mathbb{R}^N$. Proofs…

Analysis of PDEs · Mathematics 2017-05-23 Umberto Biccari , Mahamadi Warma , Enrique Zuazua

We consider a heat conduction problem $S$ with mixed boundary conditions in a $n$-dimensional domain $\Omega$ with regular boundary and a family of problems $S_{\alpha}$ with also mixed boundary conditions in $\Omega$, where $\alpha>0$ is…

Optimization and Control · Mathematics 2021-03-30 C. M. Bollo , C. M. Gariboldi , D. A. Tarzia

An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of…

Optimization and Control · Mathematics 2010-08-20 Hongwei Lou

This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…

Numerical Analysis · Mathematics 2024-12-17 Aaron Pim , Tristan Pryer , Alex Trenam

This paper examines the impulse controllability of degenerate singular parabolic equations through a modern framework focused on finite-time stabilization. Furthermore, we provide an explicit estimate for the exponential decay of the…

Analysis of PDEs · Mathematics 2026-04-03 Walid Zouhair , Ghita El Guermai , Ilham Ouelddris

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 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 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

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

We present a general framework for thermodynamic limits and its applications to a variety of models. In particular we will identify criteria such that the limits are uniform in a parameter. All results are illustrated with the example of…

Probability · Mathematics 2019-01-28 Christoph Schumacher , Fabian Schwarzenberger , Ivan Veselic

In this article, we establish exponential turnpike theorems for a class of nonlinear deterministic meanfield optimal control problems. We carry out our analysis simultaneously in the so-called Lagrangian and Eulerian frameworks. In the…

Optimization and Control · Mathematics 2026-05-05 Benoît Bonnet-Weill , Giovanni Colombo , Denis Shishmintsev , Emmanuel Trélat

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 studies an infinite horizon optimal control problem for discrete-time linear systems and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. A classical approach…

Optimization and Control · Mathematics 2020-11-11 Kai Du , Qingxin Meng , Fu Zhang

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