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A Penalized Neumann Control Approach for Solving an Optimal Dirichlet Control Problem for the Navier--Stokes Equations

Authors:

L. S. Hou,

S. S. RavindranAuthors Info & Claims

SIAM Journal on Control and Optimization, Volume 36, Issue 5

Pages 1795 - 1814

https://doi.org/10.1137/S0363012996304870

Published: 01 September 1998 Publication History

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Abstract

We introduce a penalized Neumann boundary control approach for solving an optimal Dirichlet boundary control problem associated with the two- or three-dimensional steady-state Navier--Stokes equations. We prove the convergence of the solutions of the penalized Neumann control problem, the suboptimality of the limit, and the optimality of the limit under further restrictions on the data. We describe the numerical algorithm for solving the penalized Neumann control problem and report some numerical results.

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Zhou KGong W(2022)Error Estimates for Finite Element Approximation of Dirichlet Boundary Control for Stokes Equations in Journal of Scientific Computing10.1007/s10915-022-01831-w91:2Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s10915-022-01831-w
Benner PHeiland JWerner S(2022)Robust output-feedback stabilization for incompressible flows using low-dimensional -controllersComputational Optimization and Applications10.1007/s10589-022-00359-x82:1(225-249)Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s10589-022-00359-x
Hu WShen JSingler JZhang YZheng X(2020)A superconvergent hybridizable discontinuous Galerkin method for Dirichlet boundary control of elliptic PDEsNumerische Mathematik10.1007/s00211-019-01090-2144:2(375-411)Online publication date: 1-Feb-2020
https://dl.acm.org/doi/10.1007/s00211-019-01090-2
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Index Terms

A Penalized Neumann Control Approach for Solving an Optimal Dirichlet Control Problem for the Navier--Stokes Equations
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
      2. Partial differential equations
    2. Mathematical optimization
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization

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cover image SIAM Journal on Control and Optimization

SIAM Journal on Control and Optimization Volume 36, Issue 5

Sept. 1998

367 pages

ISSN:0363-0129

Editor:
J. E. Lagnese
Georgetown Univ., Washington, DC

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 September 1998

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Zhou KGong W(2022)Error Estimates for Finite Element Approximation of Dirichlet Boundary Control for Stokes Equations in Journal of Scientific Computing10.1007/s10915-022-01831-w91:2Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s10915-022-01831-w
Benner PHeiland JWerner S(2022)Robust output-feedback stabilization for incompressible flows using low-dimensional -controllersComputational Optimization and Applications10.1007/s10589-022-00359-x82:1(225-249)Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s10589-022-00359-x
Hu WShen JSingler JZhang YZheng X(2020)A superconvergent hybridizable discontinuous Galerkin method for Dirichlet boundary control of elliptic PDEsNumerische Mathematik10.1007/s00211-019-01090-2144:2(375-411)Online publication date: 1-Feb-2020
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Burns JHe XHu W(2016)Feedback stabilization of a thermal fluid system with mixed boundary controlComputers & Mathematics with Applications10.1016/j.camwa.2016.01.01171:11(2170-2191)Online publication date: 1-Jun-2016
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Of GPhan TSteinbach O(2015)An energy space finite element approach for elliptic Dirichlet boundary control problemsNumerische Mathematik10.1007/s00211-014-0653-x129:4(723-748)Online publication date: 1-Apr-2015
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Ravindran S(2005)Real-Time Computational Algorithm for Optimal Control of an MHD Flow SystemSIAM Journal on Scientific Computing10.1137/S106482750240053426:4(1369-1388)Online publication date: 1-Jan-2005
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Prudencio EByrd RCai X(2004)Domain decomposition methods for PDE constrained optimization problemsProceedings of the 6th international conference on High Performance Computing for Computational Science10.1007/11403937_43(569-582)Online publication date: 28-Jun-2004
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Ravindran S(2000)Reduced-Order Adaptive Controllers for Fluid Flows Using PODJournal of Scientific Computing10.1023/A:101118471489815:4(457-478)Online publication date: 19-Dec-2000
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Hou LRavindran S(1999)Numerical Approximation of Optimal Flow Control Problems by a Penalty MethodSIAM Journal on Scientific Computing10.1137/S106482759732515320:5(1753-1777)Online publication date: 1-Jan-1999
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