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Volumn 49, Issue 12, 2004, Pages 2185-2202

Closed-form boundary state feedbacks for a class of 1-D partial integro-differential equations

Author keywords

Backstepping; Boundary control; Distributed parameter systems; Lyapunov function; Partial differential equations (PDEs); Stabilization

Indexed keywords

APPROXIMATION THEORY; BESSEL FUNCTIONS; BOUNDARY CONDITIONS; CLOSED LOOP CONTROL SYSTEMS; CONTROL SYSTEM SYNTHESIS; DISTRIBUTED PARAMETER CONTROL SYSTEMS; INTEGRAL EQUATIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; RICCATI EQUATIONS;

EID: 11044230320     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2004.838495     Document Type: Article
Times cited : (544)

References (33)
  • 2
    • 0008201333 scopus 로고
    • "Feedback stabilization of linear and semilinear parabolic systems"
    • H. Amann, "Feedback stabilization of linear and semilinear parabolic systems," Semigroup Theory and Applications, vol. 116, pp. 21-57, 1989.
    • (1989) Semigroup Theory and Applications , vol.116 , pp. 21-57
    • Amann, H.1
  • 3
    • 0000019511 scopus 로고    scopus 로고
    • "Infinite dimensional backstepping-style feedback transformations for a heat equation with an arbitrary level of instability"
    • A. Balogh and M. Krstic, "Infinite dimensional backstepping-style feedback transformations for a heat equation with an arbitrary level of instability," Eur. J. Control, vol. 8, pp. 165-175, 2002.
    • (2002) Eur. J. Control , vol.8 , pp. 165-175
    • Balogh, A.1    Krstic, M.2
  • 4
    • 0348155922 scopus 로고    scopus 로고
    • "Stability of partial differential equations governing control gains in infinite dimensional backstepping"
    • A. Balogh and M. Krstic, "Stability of partial differential equations governing control gains in infinite dimensional backstepping," Syst. Control Lett., vol. 51, no. 2, pp. 151-164, 2004.
    • (2004) Syst. Control Lett. , vol.51 , Issue.2 , pp. 151-164
    • Balogh, A.1    Krstic, M.2
  • 5
    • 0036647170 scopus 로고    scopus 로고
    • "Distributed control of spatially-invariant systems"
    • June
    • B. Bamieh, F. Paganini, and M. A. Dahleh, "Distributed control of spatially-invariant systems," IEEE Trans. Automat. Contr., vol. 47, pp. 1091-1107, June 2002.
    • (2002) IEEE Trans. Automat. Contr. , vol.47 , pp. 1091-1107
    • Bamieh, B.1    Paganini, F.2    Dahleh, M.A.3
  • 7
    • 0035546332 scopus 로고    scopus 로고
    • "Nonlinear stabilization of a thermal convection loop by state feedback"
    • D. M. Boskovic and M. Krstic, "Nonlinear stabilization of a thermal convection loop by state feedback," Automatica, vol. 37, pp. 2033-2040, 2001.
    • (2001) Automatica , vol.37 , pp. 2033-2040
    • Boskovic, D.M.1    Krstic, M.2
  • 8
    • 0037104858 scopus 로고    scopus 로고
    • "Backstepping control of chemical tubular reactors"
    • D. M. Boskovic and M. Krstic, "Backstepping control of chemical tubular reactors," Comput. Chem. Eng., vol. 26, pp. 1077-1085, 2002.
    • (2002) Comput. Chem. Eng. , vol.26 , pp. 1077-1085
    • Boskovic, D.M.1    Krstic, M.2
  • 9
    • 0345381799 scopus 로고    scopus 로고
    • "Stabilization of a solid propellant rocket instability by state feedback"
    • D. M. Boskovic and M. Krstic, "Stabilization of a solid propellant rocket instability by state feedback," Int. J. Robust Nonlinear Control, vol. 13, no. 5, pp. 483-95, 2003.
    • (2003) Int. J. Robust Nonlinear Control , vol.13 , Issue.5 , pp. 483-495
    • Boskovic, D.M.1    Krstic, M.2
  • 10
    • 0035704647 scopus 로고    scopus 로고
    • "Boundary control of an unstable heat equation via measurement of domain-averaged temperature"
    • Dec
    • D. M. Boskovic, M. Krstic, and W. J. Liu, "Boundary control of an unstable heat equation via measurement of domain-averaged temperature," IEEE Trans. Automat. Contr., vol. 46, pp. 2022-20288, Dec. 2001.
    • (2001) IEEE Trans. Automat. Contr. , vol.46 , pp. 2022-20288
    • Boskovic, D.M.1    Krstic, M.2    Liu, W.J.3
  • 11
    • 0035156096 scopus 로고    scopus 로고
    • "Numerical methods for approximating functional gains in LQR boundary control problems"
    • J. A. Burns and K. P. Hulsing, "Numerical methods for approximating functional gains in LQR boundary control problems," Math. Comput. Model., vol. 33, pp. 89-100, 2001.
    • (2001) Math. Comput. Model. , vol.33 , pp. 89-100
    • Burns, J.A.1    Hulsing, K.P.2
  • 12
    • 0031363581 scopus 로고    scopus 로고
    • "A distributed parameter control approach to sensor location for optimal feedback control of thermal processes"
    • San Diego, CA, Dec
    • J. A. Burns and D. Rubio, "A distributed parameter control approach to sensor location for optimal feedback control of thermal processes," in Proc. 36th Conf. Decision and Control, San Diego, CA, Dec. 1997, pp. 2243-2247.
    • (1997) Proc. 36th Conf. Decision and Control , pp. 2243-2247
    • Burns, J.A.1    Rubio, D.2
  • 14
    • 0040916125 scopus 로고
    • "The solution of initial-boundary value problems for parabolic equations by the method of integral operators"
    • D. Colton, "The solution of initial-boundary value problems for parabolic equations by the method of integral operators," J. Diff. Equat., vol. 26, pp. 181-190, 1977.
    • (1977) J. Diff. Equat. , vol.26 , pp. 181-190
    • Colton, D.1
  • 15
    • 0025447017 scopus 로고
    • "Robust stabilizability of normalized coprime factors: The infinite - Dimensional case"
    • R. F. Curtain, "Robust stabilizability of normalized coprime factors: The infinite - dimensional case," Int. J. Control, vol. 51, no. 6, pp. 1173-1190, 1990.
    • (1990) Int. J. Control , vol.51 , Issue.6 , pp. 1173-1190
    • Curtain, R.F.1
  • 18
    • 0000095183 scopus 로고
    • "Boundary control systems"
    • H. O. Fattorini, "Boundary control systems," SIAM J. Control, vol. 6, no. 3, pp. 349-385, 1968.
    • (1968) SIAM J. Control , vol.6 , Issue.3 , pp. 349-385
    • Fattorini, H.O.1
  • 21
    • 0020824027 scopus 로고
    • "Stabilization and structural assignment of Dirichlet boundary feedback parabolic equations"
    • I. Lasiecka and R. Triggiani, "Stabilization and structural assignment of Dirichlet boundary feedback parabolic equations," in SIAM J. Control Optim., vol. 21, 1983, pp. 766-803.
    • (1983) SIAM J. Control Optim. , vol.21 , pp. 766-803
    • Lasiecka, I.1    Triggiani, R.2
  • 23
    • 2942514669 scopus 로고    scopus 로고
    • "Boundary feedback stabilization of an unstable heat equation"
    • W. J. Liu, "Boundary feedback stabilization of an unstable heat equation," SIAM J. Control Optim., vol. 42, no. 3, pp. 1033-1043.
    • SIAM J. Control Optim. , vol.42 , Issue.3 , pp. 1033-1043
    • Liu, W.J.1
  • 25
    • 0042261026 scopus 로고
    • "On the stabilization of diffusion equations: Boundary observation and feedback"
    • T. Nambu, "On the stabilization of diffusion equations: Boundary observation and feedback," J. Diff. Equat., vol. 52, pp. 204-233, 1984.
    • (1984) J. Diff. Equat. , vol.52 , pp. 204-233
    • Nambu, T.1
  • 28
    • 0000820706 scopus 로고
    • "Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions"
    • D. L. Russell, "Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions," in SIAM Rev., vol. 20, 1978, pp. 639-739.
    • (1978) SIAM Rev. , vol.20 , pp. 639-739
    • Russell, D.L.1
  • 29
    • 84924157302 scopus 로고
    • "Differential-delay equations as canonical forms for controlled hyperbolic systems with applications to spectral assignment"
    • A. K. Aziz, J. W. Wingate, and M. J. Balas, Eds. New York: Academic
    • D. L. Russell, "Differential-delay equations as canonical forms for controlled hyperbolic systems with applications to spectral assignment," in Control Theory of Systems Governed by Partial Differential Equations, A. K. Aziz, J. W. Wingate, and M. J. Balas, Eds. New York: Academic, 1977.
    • (1977) Control Theory of Systems Governed By Partial Differential Equations
    • Russell, D.L.1
  • 30
    • 0039137861 scopus 로고
    • "Two results on exact boundary control of parabolic equations"
    • T. I. Seidman, "Two results on exact boundary control of parabolic equations," Appl. Math. Optim., vol. 11, pp. 145-152, 1984.
    • (1984) Appl. Math. Optim. , vol.11 , pp. 145-152
    • Seidman, T.I.1
  • 32
    • 0003766487 scopus 로고
    • "Well-posedness and regularity of boundary feedback parabolic systems"
    • R. Triggiani, "Well-posedness and regularity of boundary feedback parabolic systems," J. Diff. Equat., vol. 36, pp. 347-362, 1980.
    • (1980) J. Diff. Equat. , vol.36 , pp. 347-362
    • Triggiani, R.1
  • 33
    • 0019164651 scopus 로고
    • "Boundary feedback stabilization of parabolic equations"
    • R. Triggiani, "Boundary feedback stabilization of parabolic equations," Appl. Math. Optim., vol. 6, pp. 201-220, 1980.
    • (1980) Appl. Math. Optim. , vol.6 , pp. 201-220
    • Triggiani, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.