GLOBAL STABILIZABILITY TO TRAJECTORIES FOR THE SCHLO spacing diaeresis GL EQUATION IN A SOBOLEV NORM

被引：0

作者：

Kunisch, Karl ^{[1
,2
]}

Rodrigues, Sergio S. ^{[1
]}

机构：

[1] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math, Altenbergerstr 69, A-4040 Linz, Austria

[2] Inst Math & Sci Comp, Heinrichstr 36, A-8010 Graz, Austria

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2023年 / 43卷 / 06期

基金：

奥地利科学基金会;

关键词：

Saturated feedback controls; control constraints; stabilizability to tra-semilinear finite-dimensional constrained control; NAVIER-STOKES EQUATIONS; NONLINEAR DISSIPATIVE SYSTEMS; FINITE DETERMINING PARAMETERS; UNSTABLE LINEAR-SYSTEMS; EXPONENTIAL STABILIZATION; LYAPUNOV EQUATIONS; BOUNDARY FEEDBACK; STABILITY; REGULARITY;

D O I：

10.3934/dcds.2023017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The stabilizability to trajectories of the Schlogl model is investigated in the norm of the natural state space for strong solutions, which is strictly contained in the standard pivot space of square integrable functions. As actuators a finite number of indicator functions are used and the control input is subject to a bound constraint. A stabilizing saturated explicit feedback control is proposed, where the set of actuators and the input bound are independent of the targeted trajectory. Further, the existence of open-loop optimal stabilizing constrained controls and related first-order optimality conditions are investigated. These conditions are then used to compute stabilizing receding horizon based controls. Results of numerical simulations are presented comparing their stabilizing performance with that of saturated explicit feedback controls.

引用

页码：2457 / 2493

页数：37

共 49 条

[1] On the convergence and mesh-independent property of the Barzilai-Borwein method for PDE-constrained optimization [J].

Azmi, Behzad ;

Kunisch, Karl .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2022, 42 (04) :2984-3021

[2] Analysis of the Barzilai-Borwein Step-Sizes for Problems in Hilbert Spaces [J].

Azmi, Behzad ;

Kunisch, Karl .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2020, 185 (03) :819-844

[3] A HYBRID FINITE-DIMENSIONAL RHC FOR STABILIZATION OF TIME-VARYING PARABOLIC EQUATIONS [J].

Azmi, Behzad ;

Kunisch, Karl .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2019, 57 (05) :3496-3526

[4] FEEDBACK CONTROL OF NONLINEAR DISSIPATIVE SYSTEMS BY FINITE DETERMINING PARAMETERS - A REACTION-DIFFUSION PARADIGM [J].

Azouani, Abderrahim ;

Titi, Edriss S. .

EVOLUTION EQUATIONS AND CONTROL THEORY, 2014, 3 (04) :579-594

[5] STABILIZATION OF PARABOLIC NONLINEAR SYSTEMS WITH FINITE DIMENSIONAL FEEDBACK OR DYNAMICAL CONTROLLERS: APPLICATION TO THE NAVIER-STOKES SYSTEM [J].

Badra, Mehdi ;

Takahashi, Takeo .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2011, 49 (02) :420-463

[6] Burgers' equation with nonlinear boundary feedback:: H1 stability, well-posedness and simulation [J].

Balogh, A ;

Krstic, M .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2000, 6 (2-3) :189-200

[7]

Barbu C, 1997, P AMER CONTR CONF, P848, DOI 10.1109/ACC.1997.611924

[8] Abstract settings for tangential boundary stabilization of Navier-Stokes equations by high- and low-gain feedback controllers [J].

Barbu, V ;

Lasiecka, I ;

Triggiani, R .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (12) :2704-2746

[9] Internal stabilization of Navier-Stokes equations with finite-dimensional controllers [J].

Barbu, V ;

Triggiani, R .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2004, 53 (05) :1443-1494

[10] Boundary Stabilization of Equilibrium Solutions to Parabolic Equations [J].

Barbu, Viorel .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2013, 58 (09) :2416-2420

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