메뉴 건너뛰기




Volumn 42, Issue 3, 2003, Pages 1013-1032

Null controllability with vanishing energy

Author keywords

Algebraic Riccati equation; Minimal energy; Null controllability

Indexed keywords

ALGEBRAIC RICCATI EQUATIONS; MINIMAL ENERGY; NULL CONTROLLABILITY; VANISHING ENERGY;

EID: 2942592166     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902409970     Document Type: Article
Times cited : (41)

References (28)
  • 4
    • 0026909198 scopus 로고
    • Feedback exact null controllability for unbounded control problems in Hilbert space
    • S. CHEN AND I. LASIECKA, Feedback exact null controllability for unbounded control problems in Hilbert space, J. Optim. Theory Appl., 74 (1992), pp. 191-219.
    • (1992) J. Optim. Theory Appl. , vol.74 , pp. 191-219
    • Chen, S.1    Lasiecka, I.2
  • 5
    • 0001773481 scopus 로고
    • An introduction to infinite-dimensional linear systems theory
    • Springer-Verlag, New York
    • R. F. CURTAIN AND H. J. ZWART, An Introduction to Infinite-Dimensional Linear Systems Theory, Texts Appl. Math. 21, Springer-Verlag, New York, 1995.
    • (1995) Texts Appl. Math. , vol.21
    • Curtain, R.F.1    Zwart, H.J.2
  • 7
    • 0003250411 scopus 로고    scopus 로고
    • Ergodicity for infinite-dimensional systems
    • Cambridge University Press, Cambridge, UK
    • G. DA PRATO AND J. ZABCZYK, Ergodicity for Infinite-Dimensional Systems, London Math. Soc. Lecture Note Ser. 229, Cambridge University Press, Cambridge, UK, 1996.
    • (1996) London Math. Soc. Lecture Note Ser. , vol.229
    • Da Prato, G.1    Zabczyk, J.2
  • 8
    • 0001979591 scopus 로고
    • Spectral properties of finite-dimensional perturbed linear semigroups
    • W. DESCH AND W. SCHAPPACHER, Spectral properties of finite-dimensional perturbed linear semigroups, J. Differential Equations, 59 (1985), pp. 80-102.
    • (1985) J. Differential Equations , vol.59 , pp. 80-102
    • Desch, W.1    Schappacher, W.2
  • 9
    • 0027649565 scopus 로고
    • Feedback approximation of the minimum energy control for linear infinitedimensional systems with zero terminal state
    • Z. EMIRSAJLOW, Feedback approximation of the minimum energy control for linear infinitedimensional systems with zero terminal state, J. Optim. Theory Appl., 78 (1993), pp. 337- 363.
    • (1993) J. Optim. Theory Appl. , vol.78 , pp. 337-363
    • Emirsajlow, Z.1
  • 10
    • 0003215222 scopus 로고    scopus 로고
    • One-parameter semigroups for linear evolution equations
    • Springer-Verlag, New York
    • K. ENGEL AND R. NAGEL, One-parameter Semigroups for Linear Evolution Equations, Grad. Texts in Math. 194, Springer-Verlag, New York, 2000.
    • (2000) Grad. Texts in Math. , vol.194
    • Engel, K.1    Nagel, R.2
  • 12
    • 0032640903 scopus 로고    scopus 로고
    • Regularity of the minimum time function and minimum energy problems: The linear case
    • F. Gozzi AND P. LORETI, Regularity of the minimum time function and minimum energy problems: The linear case, SIAM J. Control Optim., 37 (1999), pp. 1195-1221.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 1195-1221
    • Gozzi, F.1    Loreti, P.2
  • 14
    • 0033276565 scopus 로고    scopus 로고
    • Control norms for large control times
    • S. IVANOV, Control norms for large control times, ESAIM Control Optim. Calc. Var., 4 (1999), pp. 405-418.
    • (1999) ESAIM Control Optim. Calc. Var. , vol.4 , pp. 405-418
    • Ivanov, S.1
  • 15
    • 0005561650 scopus 로고    scopus 로고
    • Stochastic PDE's and kolmogorov equations in infinite dimensions
    • G. Da Prato, ed., Springer-Verlag, Berlin
    • N. V. KRYLOV, M. RÖCKNER, AND J. ZABCZYK, Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions, Lecture Notes in Math. 1715, G. Da Prato, ed., Springer-Verlag, Berlin, 1999.
    • (1999) Lecture Notes in Math. , vol.1715
    • Krylov, N.V.1    Röckner, M.2    Zabczyk, J.3
  • 16
    • 0040691346 scopus 로고    scopus 로고
    • Nonnegative solutions of algebraic Riccati equations
    • H. LANGER, A. C. M. RAN, AND D. TEMME, Nonnegative solutions of algebraic Riccati equations, Linear Algebra Appl., 261 (1997), pp. 317-352.
    • (1997) Linear Algebra Appl. , vol.261 , pp. 317-352
    • Langer, H.1    Ran, A.C.M.2    Temme, D.3
  • 17
    • 2942567144 scopus 로고    scopus 로고
    • Control theory for partial differential equations: Continuous and approximation theories. I. Abstract parabolic systems
    • Cambridge University Press, Cambridge, UK
    • I. LASIECKA AND R. TRIGGIANI, Control Theory for Partial Differential Equations: Continuous and Approximation Theories. I. Abstract Parabolic Systems, Encyclopedia Math. Appl. 74, Cambridge University Press, Cambridge, UK, 2000.
    • (2000) Encyclopedia Math. Appl. , vol.74
    • Lasiecka, I.1    Triggiani, R.2
  • 18
    • 2942595318 scopus 로고    scopus 로고
    • Control theory for partial differential equations: Continuous and approximation theories. II. Abstract hyperbolic-like systems over a finite time horizon
    • Cambridge University Press, Cambridge, UK
    • I. LASIECKA AND R. TRIGGIANI, Control Theory for Partial Differential Equations: Continuous and Approximation Theories. II. Abstract Hyperbolic-Like Systems over a Finite Time Horizon, Encyclopedia Math. Appl. 75, Cambridge University Press, Cambridge, UK, 2000.
    • (2000) Encyclopedia Math. Appl. , vol.75
    • Lasiecka, I.1    Triggiani, R.2
  • 19
    • 0023843114 scopus 로고
    • Null controllability of a class of functional differential systems
    • A. W. OLBROT AND L. PANDOLFI, Null controllability of a class of functional differential systems, Internat. J. Control, 47 (1988), pp. 193-208.
    • (1988) Internat. J. Control , vol.47 , pp. 193-208
    • Olbrot, A.W.1    Pandolfi, L.2
  • 20
    • 0003323341 scopus 로고
    • Positive harmonic functions and diffusion
    • Cambridge University Press, Cambridge, UK
    • R. G. PINSKY, Positive Harmonic Functions and Diffusion, Cambridge Stud. Adv. Math. 45, Cambridge University Press, Cambridge, UK, 1995.
    • (1995) Cambridge Stud. Adv. Math. , vol.45
    • Pinsky, R.G.1
  • 22
    • 84864114578 scopus 로고    scopus 로고
    • Preprint 10/2002, Department of Mathematics, University of Turin, Turin, Italy
    • E. PRIOLA AND J. ZABCZYK, Null Controllability with Vanishing Energy, Preprint 10/2002, Department of Mathematics, University of Turin, Turin, Italy, 2002; also available online from http://www2.dm.unito.it/paginepersonali/priola/ index.htm.
    • (2002) Null Controllability with Vanishing Energy
    • Priola, E.1    Zabczyk, J.2
  • 24
  • 25
    • 0035861358 scopus 로고    scopus 로고
    • Null controllability of an infinite dimensional SDE with state and control-dependent noise
    • M. SIRBU AND G. TESSITORE, Null controllability of an infinite dimensional SDE with state and control-dependent noise, Systems Control Lett., 44 (2001), pp. 385-394.
    • (2001) Systems Control Lett. , vol.44 , pp. 385-394
    • Sirbu, M.1    Tessitore, G.2
  • 26
    • 0024663157 scopus 로고
    • Admissibility of unbounded control operators
    • G. WEISS, Admissibility of unbounded control operators, SIAM J. Control Optim., 27 (1989), pp. 527-545.
    • (1989) SIAM J. Control Optim. , vol.27 , pp. 527-545
    • Weiss, G.1
  • 28
    • 2942556145 scopus 로고
    • Mathematical control theory: An introduction
    • Birkhäuser-Verlag, Basel
    • J. ZABCZYK, Mathematical Control Theory: An Introduction, Systems Control Found. Appl., Birkhäuser-Verlag, Basel, 1992.
    • (1992) Systems Control Found. Appl.
    • Zabczyk, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.