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On a degenerate Riccati equation

Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we study the existence of solutions to a degenerate algebraic Riccati equation associated to an optimal control problem with infinite time horizon. Under some assumptions on the control system, we can select a solution to this Riccati equation providing a feedback control law able to stabilize the system.
Rocznik
Strony
1393--1410
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai - 600 113, India, kesh@imsc.res.in
Bibliografia
  • AMIN, M.H. (1985) Optimal pole shifting for continuous multivariable linear systems. Int. J. Control 41, 701-707.
  • AMODEI, L., and BUCHOT, J.-M. (2008) An invariant subspace method for large-scale algebraic Riccati equations. Submitted to Numerical Mathematics.
  • BENNER, P. and BAUR, U. (2008) Efficient Solution of Algebraic Bernoulli Equations Using H-Matrix Arithmetic. In: K. Kunisch, G. Of, O. Stein-bach, eds., Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007. Springer- Verlag, Heidelberg, 127-134.
  • BENNER, P., Li, J.-R. and PENZL, T. (2008) Numerical Solution of Large Lyapunov Equations, Riccati Equations, and Linear-Quadratic Control Problems. Numerical Linear Algebra with Applications 15 (to appear).
  • BENSOUSSAN, A. (1987) Observateurs et stabilite. Collogue CNES, Paris.
  • BENSOUSSAN, A., DA PRATO, G., DELFOUR, M.C. and MITTER, S.K. (1993) Representation and Control of Infinite Dimensional Systems, Vol. 2. Birkhäuser.
  • BENSOUSSAN, A., DA PRATO, G., DELFOUR, M.C. and MITTER, S.K. (2007) Representation and Control of Infinite Dimensional Systems, Second Edition. Systems and Control: Foundations and Applications. Birkhäuser.
  • BURNS, J.A., SACHS, E.W. and ZIETSMAN, L. (2008) Mesh independence of Kleinman-Newton iterations for Riccati equations in Hilbert space. SIAM J. Control Optim. 47, 2663-2692.
  • FLANDOLI, F., LASIECKA, I. and TRIGGIANI, R. (1988) Algebraic Riccati equations with non-smoothing observation arising in hyperbolic and Euler-Bernoulli boundary control problems. Ann. Mat. Pura ed Appl. 153, 307-382.
  • FURSIKOV, A.V. and IMANUVILOV, O.Yu. (1996) Controllabiliy of Evolution Equations. Lecture Notes series 34, Seoul National University, Research Institute of Mathematics, Global Analysis Research Centre, Seoul.
  • IBBINI, M. and AMIN, M. (1993) A state feedback controller with minimum control effort. Control Theory and Advanced Technology 9, 1003-1013.
  • KATO, T. (1995) Perturbation theory for linear operators. Reprint of the 1980 Edition, Springer-Verlag.
  • KLEINMAN, D.L. (1968) On an iterative technique for Riccati equations. IEEE Trans. Automat. Control AC-13, 114-115.
  • LASIECKA, I. and TRIGGIANI, R. (2000a) Control Theory for Partial Differential Equations. Vol. 1, Cambridge University Press.
  • LASIECKA, I. and TRIGGIANI, R. (2000b) Control Theory for Partial Differential Equations. Vol. 2, Cambridge University Press.
  • PRIOLA, E. and ZABCZYK, J. (2003) Null controllability with vanishing energy. SIAM J. Control Optim. 42, 1013-1032.
  • RAYMOND, J.-P. (2006) Boundary feedback stabilization of the two dimensional Navier-Stokes equations. SIAM J. Control and Optim. 45, 790-828.
  • TRIGGIANI, R. (1975) On the stabilizability problem in Banach space. J. Math. Anal. Appl., 52, 383-403.
  • THEVENET, L., BUCHOT, J.-M. and RAYMOND, J.-P. (2009) Nonlinear Feedback Stabilization of a two-dimensional Burgers Equation. To appear in ESAIM COCV.
  • ZABCZYK, J. (2008) Mathematical Control Theory - An Introduction. Modern Birkhäuser Classics.
  • ZHOU, B., DUAN, G. and LIN, Z. (2008) A parametric Lyapunov equation approach to the design of low gain feedback. Trans. Aut. Control 53, 1548-1554.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0046-0022
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