The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed. Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions. For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional. Applications to the Navier-Stokes equations, semilinear wave equations and reaction diffusion systems are given.
Mots-clés : receding horizon control, control Lyapunov function, Lyapunov equations, closed loop dissipative, minimum value function, Navier-Stokes equations
@article{COCV_2002__8__741_0,
author = {Ito, Kazufumi and Kunisch, Karl},
title = {Receding horizon optimal control for infinite dimensional systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {741--760},
publisher = {EDP-Sciences},
volume = {8},
year = {2002},
doi = {10.1051/cocv:2002032},
mrnumber = {1932971},
zbl = {1066.49020},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2002032/}
}
TY - JOUR AU - Ito, Kazufumi AU - Kunisch, Karl TI - Receding horizon optimal control for infinite dimensional systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2002 SP - 741 EP - 760 VL - 8 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2002032/ DO - 10.1051/cocv:2002032 LA - en ID - COCV_2002__8__741_0 ER -
%0 Journal Article %A Ito, Kazufumi %A Kunisch, Karl %T Receding horizon optimal control for infinite dimensional systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 741-760 %V 8 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2002032/ %R 10.1051/cocv:2002032 %G en %F COCV_2002__8__741_0
Ito, Kazufumi; Kunisch, Karl. Receding horizon optimal control for infinite dimensional systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 741-760. doi : 10.1051/cocv:2002032. http://archive.numdam.org/articles/10.1051/cocv:2002032/
[1] ,,, and, Nonlinear predictive control and moving horizon estimation - an introductory overview, Advances in Control, edited by P. Frank. Springer (1999) 391-449.
[2] , Flow control: New challenges for a new Renaissance. Progr. Aerospace Sci. 37 (2001) 21-58.
[3] and, A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica 34 (1998) 1205-1217. | Zbl
[4] , and, Instantaneous control of backward facing step flow. Appl. Numer. Math. 31 (1999) 133-158. | MR | Zbl
[5] ,, and, Feedback control for unsteady flow and its application to the stochastic Burgers equation. J. Fluid Mech. 253 (1993) 509-543. | MR | Zbl
[6] and, Robust Nonlinear Control Design, State-Space an Lyapunov Techiques. Birkhäuser, Boston (1996). | MR | Zbl
[7] and, Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York (1993). | MR | Zbl
[8] , and, Model predictive control: Theory and practice - a survey. Automatica 25 (1989) 335-348. | Zbl
[9] and, Analysis of instantaneous control for the Burgers equation. Nonlinear Analysis TMA (to appear). | MR | Zbl
[10] and, On asymptotic properties of receding horizon optimal control. SIAM J. Control Optim (to appear). | Zbl
[11] , and, Unconstrained receding horizon control of nonlinear systems. Preprint. | Zbl
[12] , An easy way to stabilize a linear constant system. IEEE Trans. Automat. Control 15 (1970) 692-712.
[13] and, Receding horizon control of nonlinear systems. IEEE Trans. Automat. Control 35 (1990) 814-824. | MR | Zbl
[14] and, Finite receding horizon control: A general framework for stability and performance analysis. Preprint.
[15] , and, A receding horizon generalization of pointwise min-norm controllers. Preprint. | Zbl
[16] , and, Suboptimal predictive control (Feasibility implies stability). IEEE Trans. Automat. Control 44 (1999) 648-654. | MR | Zbl
[17] , Equations of Evolution. Pitman, London (1979). | Zbl
[18] , Navier-Stokes Equations, Theory and Numerical Analysis. North Holland, Amsterdam (1984). | Zbl
Cité par Sources :
