English
Related papers

Related papers: On the uniqueness of the optimal control for 2-dim…

200 papers

We analyze optimal control problems for two-phase Navier-Stokes equations with surface tension. Based on $L_p$-maximal regularity of the underlying linear problem and recent well-posedness results of the problem for sufficiently small data…

Analysis of PDEs · Mathematics 2021-06-07 Elisabeth Diehl , Johannes Haubner , Michael Ulbrich , Stefan Ulbrich

We consider a velocity tracking problem for the Navier-Stokes equations in a 2D-bounded domain. The control acts on the boundary through a injection-suction device and the flow is allowed to slip against the surface wall. We study the…

Analysis of PDEs · Mathematics 2017-06-20 Nikolai V. Chemetov , Fernanda Cipriano

Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…

Optimization and Control · Mathematics 2010-10-11 Rouhollah Tavakoli

Necessary optimality conditions and numerical methods for solving an optimal control problem for a linear continuous-time dynanical system with controlled coefficients and quadratic goal functional are discussed.

Optimization and Control · Mathematics 2010-04-20 Olga V. Baturina , Alexander V. Bulatov , Vadim F. Krotov

In this paper, we consider a stochastic model of incompressible second grade fluids on a bounded domain of R^2 driven by linear multiplicative Brownian noise with anticipating initial conditions. The existence and uniqueness of the…

Probability · Mathematics 2017-06-21 Shijie Shang

We study the problem of state transition on a finite time interval with minimal energy supply for linear port-Hamiltonian systems. While the cost functional of minimal energy supply is intrinsic to the port-Hamiltonian structure, the…

Optimization and Control · Mathematics 2023-11-21 Timm Faulwasser , Jonas Kirchhoff , Volker Mehrmann , Friedrich Philipp , Manuel Schaller , Karl Worthmann

A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the…

Optimization and Control · Mathematics 2016-11-30 Sébastien Court , Karl Kunisch , Laurent Pfeiffer

We study a stochastic velocity tracking problem for the 2D-Navier-Stokes equations perturbed by a multiplicative Gaussian noise. From a physical point of view, the control acts through a boundary injection/suction device with uncertainty,…

Analysis of PDEs · Mathematics 2023-12-12 Nikolai Chemetov , Fernanda Cipriano

In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an…

Analysis of PDEs · Mathematics 2017-09-13 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

In this paper we study the optimal control of a parabolic initial-boundary value problem of viscous Cahn-Hilliard type with zero Neumann boundary conditions. Phase field systems of this type govern the evolution of diffusive phase…

Optimization and Control · Mathematics 2024-09-20 Pierluigi Colli , Jürgen Sprekels , Fredi Tröltzsch

A linear control system with quadratic cost functional over infinite time horizon is considered without assuming controllability/stabilizability condition and the global integrability condition for the nonhomogeneous term of the state…

Optimization and Control · Mathematics 2020-08-25 Jianping Huang , Jiongmin Yong , Hua-Cheng Zhou

We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence…

Analysis of PDEs · Mathematics 2013-09-20 Mahdi Boukrouche , Domingo A. Tarzia

An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical…

Optimization and Control · Mathematics 2018-11-01 Sébastien Court , Karl Kunisch , Laurent Pfeiffer

In this paper, we derive first-order Pontryagin optimality conditions for risk-averse stochastic optimal control problems subject to final time inequality constraints, and whose costs are general, possibly non-smooth finite coherent risk…

Optimization and Control · Mathematics 2023-05-30 Riccardo Bonalli , Benoît Bonnet

We survey results of recent activity towards studying controllability and accessibility issues for equations of dynamics of incompressible fluids controlled by low-dimensional or, degenerate, forcing. New results concerning controllability…

Optimization and Control · Mathematics 2007-05-23 Andrey A. Agrachev , Andrey V. Sarychev

In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations…

Analysis of PDEs · Mathematics 2010-04-20 De-Xing Kong , Qing-You Sun

In this work, we investigate the small-time global exact controllability of the Navier-Stokes equation, both towards the null equilibrium state and towards weak trajectories. We consider a viscous incompressible fluid evolving within a…

Analysis of PDEs · Mathematics 2017-03-07 Jean-Michel Coron , Frédéric Marbach , Franck Sueur

A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a…

Optimization and Control · Mathematics 2012-04-10 Jiongmin Yong

We consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\mathbb{R}^2$ driven by L\'evy noise. Applying the variational approach, global existence and uniqueness of strong probabilistic…

Probability · Mathematics 2017-01-03 Shijie Shang , Jianliang Zhai , Tusheng Zhang

In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these…

Optimization and Control · Mathematics 2026-05-20 Boris Vexler , Jakob Wagner