English
Related papers

Related papers: The Turnpike Property for Two-Dimensional Navier-S…

200 papers

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

We consider the Navier-Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and…

Optimization and Control · Mathematics 2010-09-20 Viorel Barbu , Sergio S. Rodrigues , Armen Shirikyan

This work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by Navier-Stokes equations with state constraint in 3-D. Strong results in 2-D also are given.

Optimization and Control · Mathematics 2010-05-19 Hanbing Liu

We first derive a general integral-turnpike property around a set for infinite-dimensional non-autonomous optimal control problems with any possible terminal state constraints, under some appropriate assumptions. Roughly speaking, the…

Optimization and Control · Mathematics 2017-05-09 Emmanuel Trelat , Can Zhang

In this work, we study a boundary control problem for the evolutionary Navier-Stokes equations, under mixed boundary conditions, in two dimensions. The cost functional here considered is of quadratic type, depending on both state and…

Optimization and Control · Mathematics 2024-10-02 Telma Guerra , Irene Marín-Gayte , Jorge Tiago

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

In this paper we study a distributed optimal control problem for a three-dimensional Navier-Stokes-$\alpha$ model. We prove the solvability of the optimal control problem, and derive first-order optimality conditions by using a Lagrange…

Optimization and Control · Mathematics 2019-05-07 Exequiel Mallea-Zepeda , Elva Ortega-Torres , Élder J. Villamizar-Roa

The value function associated with an optimal control problem subject to the Navier-Stokes equations in dimension two is analyzed. Its smoothness is established around a steady state, moreover, its derivatives are shown to satisfy a Riccati…

Optimization and Control · Mathematics 2019-06-18 Tobias Breiten , Karl Kunisch , Laurent Pfeiffer

We consider averages convergence as the time-horizon goes to infinity of optimal solutions of time-dependent optimal control problems to optimal solutions of the corresponding stationary optimal control problems. Control problems play a key…

Analysis of PDEs · Mathematics 2020-08-11 Mahamadi Warma , Sebastian Zamorano

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

We provide explicit time-varying feedback laws that locally stabilize the two dimensional internal controlled incompressible Navier-Stokes equations in arbitrarily small time. We also obtain quantitative rapid stabilization via stationary…

Analysis of PDEs · Mathematics 2020-10-27 Shengquan Xiang

In this paper, we consider an optimal control problem for the two-dimensional evolutionary Navier-Stokes system. Looking for sparsity, we take controls as functions of time taking values in a space of Borel measures. The cost functional…

Optimization and Control · Mathematics 2020-07-09 Eduardo Casas , Karl Kunisch

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

We study the two-dimensional stationary Navier-Stokes equations with rotating effect in the whole space. The unique existence and the asymptotics of solutions are obtained without the smallness assumption on the rotation parameter.

Analysis of PDEs · Mathematics 2017-03-23 Mitsuo Higaki , Yasunori Maekawa , Yuu Nakahara

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 study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of…

Analysis of PDEs · Mathematics 2018-01-17 Mitsuo Higaki , Yasunori Maekawa , Yuu Nakahara

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 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

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

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