On a degenerate Riccati equation

• Autorzy: Kesavan S. , Raymond J. P.
• 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.

Słowa kluczowe

EN

algebraic Riccati equation; optimal control; parabolic systems

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2009
• Tom: Vol. 38, no 4B
• Strony: 1393--1410
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Kesavan S.

autor

Raymond J. P.

• The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai - 600 113, India,

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.