Feedback control for non-stationary 3D Navier–Stokes–Voigt equations

The goal of this article is to study the feedback control for non-stationary three-dimensional Navier–Stokes–Voigt equations. Based on the existence, uniqueness, and boundedness result of the weak solutions to the equations, we obtain the existence of solutions to the feedback control system. An existence result for an optimal control problem is also given. We illustrate our main result with an evolutionary hemivariational inequality.

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Optimal control of feedback control systems governed by systems of evolution hemivariational inequalities

Filomat ◽

10.2298/fil1815205c ◽

2018 ◽

Vol 32 (15) ◽

pp. 5205-5220 ◽

Cited By ~ 1

Author(s):

Lu-Chuan Ceng ◽

Zhenhai Liu ◽

Jen-Chih Yao ◽

Yonghong Yao

Keyword(s):

Optimal Control ◽

Control System ◽

Feedback Control ◽

Control Systems ◽

Existence Result ◽

Sufficient Conditions ◽

Hemivariational Inequalities ◽

Feedback Control System ◽

Feedback Control Systems ◽

Evolution Hemivariational Inequalities

In this paper, we introduce and consider a feedback control system governed by the system of evolution hemivariational inequalities. Several sufficient conditions are formulated by virtue of the properties of multimaps and partial Clarke?s subdifferentials such that the existence result of feasible pairs of the feedback control systems is guaranteed. Moreover, an existence result of optimal control pairs for an optimal control system is also established.

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Analysis of an optimal control problem for the three-dimensional coupled modified Navier–Stokes and Maxwell equations

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.10.053 ◽

2007 ◽

Vol 333 (1) ◽

pp. 295-310 ◽

Cited By ~ 23

Author(s):

Max Gunzburger ◽

Catalin Trenchea

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Maxwell Equations ◽

Three Dimensional ◽

Navier Stokes

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Analysis and control of differential inclusions with anti-periodic conditions

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s030821051200090x ◽

2014 ◽

Vol 144 (3) ◽

pp. 591-602 ◽

Cited By ~ 3

Author(s):

Z. H. Liu ◽

S. Migórski

Keyword(s):

Optimal Control ◽

Control System ◽

Optimal Control Problem ◽

Control Systems ◽

Differential Inclusions ◽

Existence Of Solutions ◽

Topological Properties ◽

Control Pair ◽

Control Variables ◽

And Control

We deal with the optimal control of systems driven by differential inclusions with anti-periodic conditions in Banach spaces. The operators in the differential inclusions, describing the control system, all depend on control variables. By a solution of the control system we mean a ‘trajectory-control’ pair. We first prove that, for fixed control variables, the set of solutions is non-empty for the corresponding differential inclusion with anti-periodic conditions. We then show the functional-topological properties of the set of solutions. Finally, we investigate the existence of solutions to the optimal control problem. These abstract results can be used to study optimal control systems of evolutionary hemi-variational inequalities.

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