Receding horizon optimal control for infinite dimensional systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 741-760.

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.

DOI : 10.1051/cocv:2002032
Classification : 49L15, 49N35, 93C20, 93Dx
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] F. Allgöwer, T. Badgwell, J. Qin, J. Rawlings and S. Wright, Nonlinear predictive control and moving horizon estimation - an introductory overview, Advances in Control, edited by P. Frank. Springer (1999) 391-449.

[2] T.R. Bewley, Flow control: New challenges for a new Renaissance. Progr. Aerospace Sci. 37 (2001) 21-58.

[3] H. Chen and F. Allgöwer, A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica 34 (1998) 1205-1217. | Zbl

[4] H. Choi, M. Hinze and K. Kunisch, Instantaneous control of backward facing step flow. Appl. Numer. Math. 31 (1999) 133-158. | MR | Zbl

[5] H. Choi, R. Temam, P. Moin and J. Kim, Feedback control for unsteady flow and its application to the stochastic Burgers equation. J. Fluid Mech. 253 (1993) 509-543. | MR | Zbl

[6] R.A. Freeman and P.V. Kokotovic, Robust Nonlinear Control Design, State-Space an Lyapunov Techiques. Birkhäuser, Boston (1996). | MR | Zbl

[7] W.H. Fleming and M. Soner, Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York (1993). | MR | Zbl

[8] C.E. Garcia, D.M. Prett and M. Morari, Model predictive control: Theory and practice - a survey. Automatica 25 (1989) 335-348. | Zbl

[9] M. Hinze and S. Volkwein, Analysis of instantaneous control for the Burgers equation. Nonlinear Analysis TMA (to appear). | MR | Zbl

[10] K. Ito and K. Kunisch, On asymptotic properties of receding horizon optimal control. SIAM J. Control Optim (to appear). | Zbl

[11] A. Jadababaie, J. Yu and J. Hauser, Unconstrained receding horizon control of nonlinear systems. Preprint. | Zbl

[12] D.L. Kleinman, An easy way to stabilize a linear constant system. IEEE Trans. Automat. Control 15 (1970) 692-712.

[13] D.Q. Mayne and H. Michalska, Receding horizon control of nonlinear systems. IEEE Trans. Automat. Control 35 (1990) 814-824. | MR | Zbl

[14] V. Nevistič and J. A. Primbs, Finite receding horizon control: A general framework for stability and performance analysis. Preprint.

[15] J.A. Primbs, V. Nevistič and J.C. Doyle, A receding horizon generalization of pointwise min-norm controllers. Preprint. | Zbl

[16] P. Scokaert, D.Q. Mayne and J.B. Rawlings, Suboptimal predictive control (Feasibility implies stability). IEEE Trans. Automat. Control 44 (1999) 648-654. | MR | Zbl

[17] F. Tanabe, Equations of Evolution. Pitman, London (1979). | Zbl

[18] R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis. North Holland, Amsterdam (1984). | Zbl

Cité par Sources :