메뉴 건너뛰기




Volumn 44, Issue 1, 2009, Pages 83-115

POD a-posteriori error estimates for linear-quadratic optimal control problems

Author keywords

A posteriori error estimates; Model reduction; Optimal control; Proper orthogonal decomposition

Indexed keywords

A-POSTERIORI ERROR ESTIMATES; ELLIPTIC PARTIAL DIFFERENTIAL EQUATION; ELLIPTIC PDES; LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEMS; MODEL REDUCTION; NUMERICAL EXAMPLE; OPTIMAL CONTROL; OPTIMAL CONTROL PROBLEM; PERTURBATION METHOD; POSTERIORI ANALYSIS; POSTERIORI ERROR ESTIMATES; PROPER ORTHOGONAL DECOMPOSITION; PROPER ORTHOGONAL DECOMPOSITIONS; QUADRATIC PROBLEM; SUBOPTIMAL CONTROL;

EID: 70449522381     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-008-9224-3     Document Type: Article
Times cited : (111)

References (32)
  • 1
    • 0036853826 scopus 로고    scopus 로고
    • Error estimates for the numerical approximation of a semilinear elliptic control problem
    • DOI 10.1023/A:1020576801966
    • N. Arada E. Casas F. Tröltzsch 2002 Error estimates for the numerical approximation of a semilinear elliptic control problem Comput. Optim. Appl. 23 201 229 1033.65044 10.1023/A:1020576801966 1937089 (Pubitemid 35377444)
    • (2002) Computational Optimization and Applications , vol.23 , Issue.2 , pp. 201-229
    • Arada, N.1    Casas, E.2    Troltzsch, F.3
  • 2
    • 1542773226 scopus 로고    scopus 로고
    • Reduced order controllers for Burgers' equation with a nonlinear observer
    • 1051.93045 1885507
    • J.A. Atwell J.T. Borggaard B.B. King 2001 Reduced order controllers for Burgers' equation with a nonlinear observer Int. J. Appl. Math. Comput. Sci. 11 1311 1330 1051.93045 1885507
    • (2001) Int. J. Appl. Math. Comput. Sci. , vol.11 , pp. 1311-1330
    • Atwell, J.A.1    Borggaard, J.T.2    King, B.B.3
  • 3
    • 0003709161 scopus 로고    scopus 로고
    • Trust-region proper orthogonal decomposition for flow control
    • ICASE
    • Arian, E., Fahl, M., Sachs, E.W.: Trust-region proper orthogonal decomposition for flow control. Technical Report 2000-25, ICASE (2000)
    • (2000) Technical Report 2000-25
    • Arian, E.1    Fahl, M.2    Sachs, E.W.3
  • 4
  • 6
    • 34547960540 scopus 로고    scopus 로고
    • Error estimates for the numerical approximation of dirichlet boundary control for semilinear elliptic equations
    • DOI 10.1137/050626600
    • E. Casas J.-P. Raymond 2006 Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations SIAM J. Control Optim. 45 1586 1611 1123.65061 10.1137/050626600 2272157 (Pubitemid 47457304)
    • (2006) SIAM Journal on Control and Optimization , vol.45 , Issue.5 , pp. 1586-1611
    • Casas, E.1    Raymond, J.-P.2
  • 7
    • 0036930759 scopus 로고    scopus 로고
    • Error estimates for the finite-element approximation of a semilinear elliptic control problem
    • E. Casas F. Tröltzsch 2002 Error estimates for the finite-element approximation of a semilinear elliptic control problem Control Cybern. 31 695 712 1126.49315 (Pubitemid 36291256)
    • (2002) Control and Cybernetics , vol.31 , Issue.3 , pp. 695-712
    • Casas, E.1    Troltzsch, F.2
  • 9
    • 85020468339 scopus 로고    scopus 로고
    • Nonlinear boundary control for the heat equation utilizing proper orthogonal decomposition
    • 1941054
    • F. Diwoky S. Volkwein 2001 Nonlinear boundary control for the heat equation utilizing proper orthogonal decomposition Int. Ser. Numer. Math. 138 73 87 1941054
    • (2001) Int. Ser. Numer. Math. , vol.138 , pp. 73-87
    • Diwoky, F.1    Volkwein, S.2
  • 10
    • 52449128832 scopus 로고    scopus 로고
    • Convergence estimates of POD Galerkin methods for parabolic problems
    • Institute of Mathematical Research of Rennes
    • Henri, T., Yvon, M.: Convergence estimates of POD Galerkin methods for parabolic problems. Technical Report No. 02-48, Institute of Mathematical Research of Rennes (2002)
    • (2002) Technical Report No. 02-48
    • Henri, T.1    Yvon, M.2
  • 13
    • 0041657515 scopus 로고    scopus 로고
    • The primal-dual active set strategy as a semismooth Newton method
    • DOI 10.1137/S1052623401383558, PII S1052623401383558
    • M. Hintermüller K. Ito K. Kunisch 2003 The primal-dual active set strategy as a semi-smooth Newton method SIAM J. Optim. 13 865 888 1080.90074 10.1137/S1052623401383558 (Pubitemid 36971115)
    • (2003) SIAM Journal on Optimization , vol.13 , Issue.3 , pp. 865-888
    • Hintermuller, M.1    Ito, K.2    Kunisch, K.3
  • 14
    • 49149100096 scopus 로고    scopus 로고
    • Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition
    • 05319287 10.1007/s10589-007-9058-4 2396870
    • M. Hinze S. Volkwein 2008 Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition Comput. Optim. Appl. 39 319 345 05319287 10.1007/s10589-007-9058-4 2396870
    • (2008) Comput. Optim. Appl. , vol.39 , pp. 319-345
    • Hinze, M.1    Volkwein, S.2
  • 16
    • 38849134237 scopus 로고    scopus 로고
    • Proper orthogonal decomposition for optimality systems
    • 1141.65050 10.1051/m2an:2007054 2387420
    • K. Kunisch S. Volkwein 2008 Proper orthogonal decomposition for optimality systems ESAIM: Math. Model. Numer. Anal. 42 1 23 1141.65050 10.1051/m2an:2007054 2387420
    • (2008) ESAIM: Math. Model. Numer. Anal. , vol.42 , pp. 1-23
    • Kunisch, K.1    Volkwein, S.2
  • 17
    • 0038693394 scopus 로고    scopus 로고
    • Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics
    • 1075.65118 10.1137/S0036142900382612 1921667
    • K. Kunisch S. Volkwein 2002 Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics SIAM J. Numer. Anal. 40 492 515 1075.65118 10.1137/S0036142900382612 1921667
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 492-515
    • Kunisch, K.1    Volkwein, S.2
  • 18
    • 0036566376 scopus 로고    scopus 로고
    • A subspace approach to balanced truncation for model reduction of nonlinear control systems
    • DOI 10.1002/rnc.657
    • S. Lall J.E. Marsden S. Glavaski 2002 A subspace approach to balanced truncation for model reduction of nonlinear control systems Int. J. Robust Nonlinear Control 12 519 535 1006.93010 10.1002/rnc.657 1895968 (Pubitemid 34520056)
    • (2002) International Journal of Robust and Nonlinear Control , vol.12 , Issue.6 , pp. 519-535
    • Lall, S.1    Marsden, J.E.2    Glavaski, S.3
  • 19
    • 0021515790 scopus 로고
    • Convergence estimates for semidiscrete approximations of nonselfadjoint parabolic equations
    • 0558.65081 10.1137/0721058 760624
    • I. Lasiecka 1984 Convergence estimates for semidiscrete approximations of nonselfadjoint parabolic equations SIAM J. Numer. Anal. 21 894 909 0558.65081 10.1137/0721058 760624
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 894-909
    • Lasiecka, I.1
  • 20
    • 84966207079 scopus 로고
    • p -theory
    • 0608.65068 10.2307/2008082 842123
    • p -theory Math. Comput. 47 55 75 0608.65068 10.2307/2008082 842123
    • (1986) Math. Comput. , vol.47 , pp. 55-75
    • Lasiecka, I.1
  • 23
    • 0035176703 scopus 로고    scopus 로고
    • Modeling and control of physical processes using proper orthogonal decomposition
    • DOI 10.1016/S0895-7177(00)00240-5, PII S0895717700002405
    • H.V. Ly H.T. Tran 2001 Modeling and control of physical processes using proper orthogonal decomposition Math. Comput. Model. 33 223 236 0966.93018 10.1016/S0895-7177(00)00240-5 (Pubitemid 32062564)
    • (2001) Mathematical and Computer Modelling , vol.33 , Issue.1-3 , pp. 223-236
    • Ly, H.V.1    Tran, H.T.2
  • 24
    • 0000463120 scopus 로고    scopus 로고
    • Convergence of approximations to nonlinear control problems
    • A.V. Fiacco (eds). Marcel Dekker New York
    • Malanowski, K., Büskens, C., Maurer, H.: Convergence of approximations to nonlinear control problems. In: Fiacco, A.V. (ed.) Mathematical Programming with Data Perturbation, pp. 253-284. Marcel Dekker, New York (1997)
    • (1997) Mathematical Programming with Data Perturbation , pp. 253-284
    • Malanowski, K.1    Büskens, C.2    Maurer, H.3
  • 26
    • 0036447609 scopus 로고    scopus 로고
    • Adaptive reduced-order controllers for a thermal flow system using proper orthogonal decomposition
    • DOI 10.1137/S1064827500374716, PII S1064827500374716
    • S.S. Ravindran 2002 Adaptive reduced order controllers for a thermal flow system using proper orthogonal decomposition SIAM J. Sci. Comput. 28 1924 1942 10.1137/S1064827500374716 1923719 (Pubitemid 35427423)
    • (2002) SIAM Journal of Scientific Computing , vol.23 , Issue.6 , pp. 1924-1942
    • Ravindran, S.S.1
  • 29
    • 70449522218 scopus 로고    scopus 로고
    • Model reduction using proper orthogonal decomposition
    • Institute of Mathematics and Scientific Computing, University of Graz. see
    • Volkwein, S.: Model Reduction using Proper Orthogonal Decomposition. Lecture Notes, Institute of Mathematics and Scientific Computing, University of Graz. see http://www.uni-graz.at/imawww/volkwein/POD.pdf
    • Lecture Notes
    • Volkwein, S.1
  • 30
    • 62549102423 scopus 로고    scopus 로고
    • Impedance identification by POD model reduction techniques
    • 10.1524/auto.2008.0724
    • S. Volkwein A. Hepberger 2008 Impedance identification by POD model reduction techniques at-Autometisierungstechnik 8 437 446 10.1524/auto.2008.0724
    • (2008) At-Autometisierungstechnik , vol.8 , pp. 437-446
    • Volkwein, S.1    Hepberger, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.