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Volumn 34, Issue 1, 1996, Pages 1-30

Infinite-horizon linear-quadratic regulator problems for nonautonomous parabolic systems with boundary control

Author keywords

Boundary control; Infinite horizon; Optimal control; Parabolic systems; Riccati equation

Indexed keywords

CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; DISTRIBUTED PARAMETER CONTROL SYSTEMS; MATHEMATICAL OPERATORS; OPTIMAL CONTROL SYSTEMS; RICCATI EQUATIONS;

EID: 0029733715     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/0334001     Document Type: Article
Times cited : (22)

References (26)
  • 1
    • 0010762369 scopus 로고
    • Abstract linear non-autonomous parabolic equations: A survey
    • Differential Equations in Banach Spaces, Proceedings Bologna 1991, G. Dore, A. Favini, E. Obrecht, and A. Venni, eds., M. Dekker, New York
    • P. ACQUISTAPACE, Abstract linear non-autonomous parabolic equations: A survey, in Differential Equations in Banach Spaces, Proceedings Bologna 1991, G. Dore, A. Favini, E. Obrecht, and A. Venni, eds., Lecture Notes in Pure and Appl. Math. 148, M. Dekker, New York, 1993, pp. 1-19.
    • (1993) Lecture Notes in Pure and Appl. Math. , vol.148 , pp. 1-19
    • Acquistapace, P.1
  • 2
    • 0343772033 scopus 로고
    • Boundary control for parabolic problems in non-cylindrical domains
    • Boundary Control and Variation, Proceedings Sophia-Antipolis 1992, J. P. Zolésio, ed., M. Dekker, New York
    • _, Boundary control for parabolic problems in non-cylindrical domains, in Boundary Control and Variation, Proceedings Sophia-Antipolis 1992, J. P. Zolésio, ed., Lecture Notes in Pure and Appl. Math. 163, M. Dekker, New York, 1994, pp. 1-12.
    • (1994) Lecture Notes in Pure and Appl. Math. , vol.163 , pp. 1-12
  • 3
    • 0002417157 scopus 로고
    • A unified approach to abstract linear non-autonomous parabolic equations
    • P. ACQUISTAPACE AND B. TERRENI, A unified approach to abstract linear non-autonomous parabolic equations, Rend. Sem. Mat. Univ. Padova, 78 (1987), pp. 47-107.
    • (1987) Rend. Sem. Mat. Univ. Padova , vol.78 , pp. 47-107
    • Acquistapace, P.1    Terreni, B.2
  • 4
    • 0343772031 scopus 로고
    • On fundamental solutions for abstract parabolic equations
    • Differential Equations in Banach Spaces, Proceedings Bologna 1985, A. Favini and E. Obrecht, eds., Springer-Verlag, Berlin
    • _, On fundamental solutions for abstract parabolic equations, in Differential Equations in Banach Spaces, Proceedings Bologna 1985, A. Favini and E. Obrecht, eds., Lecture Notes in Math. 1223, Springer-Verlag, Berlin, 1986, pp. 1-11.
    • (1986) Lecture Notes in Math , vol.1223 , pp. 1-11
  • 5
    • 84972529597 scopus 로고
    • Regularity properties of the evolution operator for abstract linear parabolic equations
    • _, Regularity properties of the evolution operator for abstract linear parabolic equations, Differential Integral Equations, 5 (1992), pp. 1151-1184.
    • (1992) Differential Integral Equations , vol.5 , pp. 1151-1184
  • 6
    • 0026049936 scopus 로고
    • Initial boundary value problems and optimal control for non-autonomous parabolic systems
    • P. ACQUISTAPACE, F. FLANDOLI, AND B. TERRENI, Initial boundary value problems and optimal control for non-autonomous parabolic systems, SIAM J. Control Optim., 29 (1991), pp. 89-118.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 89-118
    • Acquistapace, P.1    Flandoli, F.2    Terreni, B.3
  • 8
    • 0026923515 scopus 로고
    • A Dirichlet boundary control problem for the strongly damped wave equation
    • F. BUCCI, A Dirichlet boundary control problem for the strongly damped wave equation, SIAM J. Control Optim., 30 (1992), pp. 1092-1100.
    • (1992) SIAM J. Control Optim. , vol.30 , pp. 1092-1100
    • Bucci, F.1
  • 10
    • 0001091909 scopus 로고
    • Uniform asymptotic stability of evolutionary process in Banach spaces
    • R. DATKO, Uniform asymptotic stability of evolutionary process in Banach spaces, SIAM J. Math. Anal., 3 (1972), pp. 428-445.
    • (1972) SIAM J. Math. Anal. , vol.3 , pp. 428-445
    • Datko, R.1
  • 12
    • 2442537391 scopus 로고
    • Quadratic control for linear periodic systems
    • _, Quadratic control for linear periodic systems, Appl. Math. Optim., 18 (1988), pp. 39-66.
    • (1988) Appl. Math. Optim. , vol.18 , pp. 39-66
  • 13
    • 0025400974 scopus 로고
    • Quadratic control for linear time-varying systems
    • _, Quadratic control for linear time-varying systems, SIAM J. Control Optim., 28 (1990), pp. 359-381.
    • (1990) SIAM J. Control Optim. , vol.28 , pp. 359-381
  • 14
    • 4243202503 scopus 로고
    • A boundary control problem for a parabolic equation in noncylindrical domain
    • A. V Balakrishnan and J. P. Zolésio, eds., Optimization Software Inc. Publications Division, New York
    • G. DA PRATO AND J. P. ZOLÉSIO, A boundary control problem for a parabolic equation in noncylindrical domain, in Stability of Flexible Structures, Proceedings Montpellier 1987, A. V Balakrishnan and J. P. Zolésio, eds., Optimization Software Inc. Publications Division, New York, 1988, pp. 52-61.
    • (1988) Stability of Flexible Structures, Proceedings Montpellier 1987 , pp. 52-61
    • Da Prato, G.1    Zolésio, J.P.2
  • 15
    • 0023345012 scopus 로고
    • Algebraic Riccati equation arising in boundary control problems
    • F. FLANDOLI, Algebraic Riccati equation arising in boundary control problems, SIAM J. Control Optim., 25 (1987), pp. 612-636.
    • (1987) SIAM J. Control Optim. , vol.25 , pp. 612-636
    • Flandoli, F.1
  • 16
    • 4243061447 scopus 로고
    • A new proof of an a priori estimate arising in boundary control theory
    • _, A new proof of an a priori estimate arising in boundary control theory, Appl. Math. Lett., 2 (1989), pp. 341-343.
    • (1989) Appl. Math. Lett. , vol.2 , pp. 341-343
  • 17
    • 0342901145 scopus 로고
    • On the direct solutions of Riccati equations arising in boundary control theory
    • _, On the direct solutions of Riccati equations arising in boundary control theory, Ann. Mat. Pura Appl. (4), 163(1993), pp. 93-131.
    • (1993) Ann. Mat. Pura Appl. (4) , vol.163 , pp. 93-131
  • 18
    • 84972510113 scopus 로고
    • Bounded solutions for abstract time-periodic parabolic equations with nonconstant domains
    • M. FUHRMAN, Bounded solutions for abstract time-periodic parabolic equations with nonconstant domains, Differential Integral Equations, 4 (1991), pp. 493-518.
    • (1991) Differential Integral Equations , vol.4 , pp. 493-518
    • Fuhrman, M.1
  • 19
    • 0018495942 scopus 로고
    • The Riccati integral equations for optimal control problems on Hubert spaces
    • J. S. GIBSON, The Riccati integral equations for optimal control problems on Hubert spaces, SIAM J. Control Optim., 17 (1979), pp. 537-565.
    • (1979) SIAM J. Control Optim. , vol.17 , pp. 537-565
    • Gibson, J.S.1
  • 20
    • 0020496680 scopus 로고
    • Dirichlet boundary control problem for parabolic equations with quadratic cost: Analyticiry and Riccati's feedback synthesis
    • I. LASIECKA AND R. TRIGGIANI, Dirichlet boundary control problem for parabolic equations with quadratic cost: Analyticiry and Riccati's feedback synthesis, SIAM J. Control Optim., 21 (1983), pp. 41-67.
    • (1983) SIAM J. Control Optim. , vol.21 , pp. 41-67
    • Lasiecka, I.1    Triggiani, R.2
  • 21
    • 0003343097 scopus 로고
    • Differential and Algebraic Riccati Equations with Application to Boundary/Point Control Problems: Continuous Theory and Approximation Theory
    • Springer-Verlag, Berlin Heidelberg
    • _, Differential and Algebraic Riccati Equations with Application to Boundary/Point Control Problems: Continuous Theory and Approximation Theory. Lecture Notes in Control and Inform. Sci. 164, Springer-Verlag, Berlin Heidelberg, 1991.
    • (1991) Lecture Notes in Control and Inform. Sci. , vol.164
  • 22
    • 21844520679 scopus 로고
    • Input dynamics and nonstandard Riccati equations with applications to boundary control of damped wave and plate equations
    • preprint, 1993
    • I. LASIECKA, D. LUKES, AND L. PANDOLFI, Input dynamics and nonstandard Riccati equations with applications to boundary control of damped wave and plate equations, preprint, 1993, J. Optim. Theory Appl., 84 (1995), pp. 549-574.
    • (1995) J. Optim. Theory Appl. , vol.84 , pp. 549-574
    • Lasiecka, I.1    Lukes, D.2    Pandolfi, L.3
  • 23
    • 84971777698 scopus 로고
    • Bounded solutions of linear periodic abstract parabolic equations
    • A. LUNARDI, Bounded solutions of linear periodic abstract parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A, 110 (1988), pp. 135-159.
    • (1988) Proc. Roy. Soc. Edinburgh Sect. A , vol.110 , pp. 135-159
    • Lunardi, A.1
  • 24
    • 0026190241 scopus 로고
    • Stabilizability of time periodic parabolic equations
    • _, Stabilizability of time periodic parabolic equations, SIAM J. Control Optim., 29 (1991), pp. 810-828.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 810-828
  • 25
    • 4243086692 scopus 로고
    • Neumann boundary stabilization of structurally damped time periodic wave and plate equations
    • Differential Equations with Applications in Biology, Physics and Engineering, Proceedings Leibnitz 1990, J. A. Goldstein, F. Rappel, and W. Schappacher, eds., M. Dekker, New York
    • _, Neumann boundary stabilization of structurally damped time periodic wave and plate equations, in Differential Equations with Applications in Biology, Physics and Engineering, Proceedings Leibnitz 1990, J. A. Goldstein, F. Rappel, and W. Schappacher, eds., Lecture Notes in Pure and Appl. Math. 133, M. Dekker, New York, 1991, pp. 241-257.
    • (1991) Lecture Notes in Pure and Appl. Math. , vol.133 , pp. 241-257
  • 26
    • 4243100360 scopus 로고
    • Optimal Quadratic Boundary Control Problem for Wave- and Plate-like Equations with High Internal Damping: An Abstract Approach
    • Control of Partial Differential Equations, Proceedings Trento 1993, G. Da Prato and L. Tubaro, eds., M. Dekker, New York
    • R. TRIGGIANI, Optimal Quadratic Boundary Control Problem for Wave- and Plate-like Equations with High Internal Damping: An Abstract Approach, in Control of Partial Differential Equations, Proceedings Trento 1993, G. Da Prato and L. Tubaro, eds., Lecture Notes in Pure and Appl. Math. 165, M. Dekker, New York, 1994, pp. 215-263.
    • (1994) Lecture Notes in Pure and Appl. Math. , vol.165 , pp. 215-263
    • Triggiani, R.1


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