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Related papers: The interval turnpike property for adjoints

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The paper establishes the exponential turnpike property for a class of mean-field stochastic linear-quadratic (LQ) optimal control problems with periodic coefficients. It first introduces the concepts of stability, stabilizability, and…

Optimization and Control · Mathematics 2024-07-26 Jingrui Sun , Lvning Yuan , Jiaqi Zhang

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 paper presents first results for near optimality in expectation of the closed-loop solutions for stochastic economic MPC. The approach relies on a recently developed turnpike property for stochastic optimal control problems at an…

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

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 the paper we consider the infinite horizon control problems on the interval with free right-hand endpoint. We obtain the necessary conditions of strict optimality. The method of the proof actually follows the classic paper by Halkin, and…

Optimization and Control · Mathematics 2013-01-01 Dmitry Khlopin

In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with…

Optimization and Control · Mathematics 2020-09-16 M. Soledad Aronna , J. Frédéric Bonnans , Axel Kröner

We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e.…

Optimization and Control · Mathematics 2021-04-13 Manuel Schaller , Friedrich Philipp , Timm Faulwasser , Karl Worthmann , Bernhard Maschke

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 work is concerned with two optimisation problems that we tackle from a qualitative perspective. The first one deals with quantitative inequalities for spectral optimisation problems for Schr\"{o}dinger operators in general domains, the…

Optimization and Control · Mathematics 2020-10-22 Idriss Mazari , Domenec Ruiz-Balet

Optimal processes in stochastic thermodynamics are a frontier for understanding the control and design of non-equilibrium systems, with broad practical applications in biology, chemistry, and nanoscale/mesoscale systems. Optimal mass…

Statistical Mechanics · Physics 2026-01-15 Atul Tanaji Mohite , Heiko Rieger

We consider an optimal control problem $\cQ$ governed by an elliptic quasivariational inequality with unilateral constraints. The existence of optimal pairs of the problem is a well known result, see \cite{SS}, for instance. We associate to…

Optimization and Control · Mathematics 2020-05-26 Mircea Sofonea , Domingo A. Tarzia

A counterexample to uniqueness of global minimizers of semilinear optimal control problems is given. The lack of uniqueness occurs for a special choice of the state-target in the cost functional. Our arguments show also that, for some…

Optimization and Control · Mathematics 2020-12-29 Dario Pighin

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

The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…

Condensed Matter · Physics 2009-10-31 Leticia F. Cugliandolo , Jorge Kurchan

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

In this article we fully describe the domain of the infinitesimal generator of the optimal state semigroup which arises in the theory of the linear-quadratic problem for a specific class of boundary control systems. This represents an…

Optimization and Control · Mathematics 2021-05-28 Paolo Acquistapace , Francesca Bucci

In this paper we study optimal control problems governed by a semilinear elliptic equation. The equation is nonmonotone due to the presence of a convection term, despite the monotonocity of the nonlinear term. The resulting operator is…

Optimization and Control · Mathematics 2020-06-11 Eduardo Casas , Mariano Mateos , Arnd Rösch

An infinite-horizon optimal control problem with a free right endpoint is considered. In this paper we proved that Lyapunov stability of the adjoint variable implying the vanishing of the adjoint variable at infinity along optimal solution.

Optimization and Control · Mathematics 2011-05-17 Dmitry Khlopin

Recent studies have explored finite-time dissipation-minimizing protocols for stochastic thermodynamic systems driven arbitrarily far from equilibrium, when granted full external control to drive the system. However, in both simulation and…

Statistical Mechanics · Physics 2022-10-27 Adrianne Zhong , Michael R. DeWeese

We would like to study the solution stability of a parametric control problem governed by semilinear elliptic equations with a mixed state-control constraint, where the cost function is nonconvex and the admissible set is unbounded. The…

Optimization and Control · Mathematics 2021-01-01 Nguyen Hai Son , Tuan Anh Dao