Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T07:22:49.073Z Has data issue: false hasContentIssue false
  • English
  • Français

Receding horizon optimal controlfor infinite dimensional systems

Published online by Cambridge University Press:  15 August 2002

Kazufumi Ito  and
Karl Kunisch
Kazufumi Ito
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, North Carolina, USA. Research partially supported by National Science Foundation under grant UINT-8521208.
Karl Kunisch
Affiliation:
Institut für Mathematik, Karl-Franzens-Universität Graz, 8010 Graz, Austria; karl.kunisch@uni-graz.at. Research partially supported by the Fonds zur Förderung der wissenschaftlichen Forschung under SFB 03 “Optimierung und Kontrolle”.
Get access

Abstract

The receding horizon control strategy fordynamical systems posed in infinite dimensional spaces is analysed. Itsstabilising property is verified provided controlLyapunov functionals are used as terminal penalty functions.For closed loop dissipative systems the terminal penalty canbe chosen as quadratic functional. Applications to the Navier–Stokesequations, semilinear wave equations and reaction diffusion systems are given.

Keywords

Receding horizon controlcontrol Lyapunov functionLyapunov equationsclosed loop dissipativeminimum value functionNavier–Stokes equations.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 741 - 760
Copyright
© EDP Sciences, SMAI, 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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.
Bewley, T.R., Flow control: New challenges for a new Renaissance. Progr. Aerospace Sci. 37 (2001) 21-58. CrossRef
Chen, H. and Allgöwer, F., A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica 34 (1998) 1205-1217. CrossRef
Choi, H., Hinze, M. and Kunisch, K., Instantaneous control of backward facing step flow. Appl. Numer. Math. 31 (1999) 133-158. CrossRef
Choi, H., Temam, R., Moin, P. and Kim, J., Feedback control for unsteady flow and its application to the stochastic Burgers equation. J. Fluid Mech. 253 (1993) 509-543. CrossRef
R.A. Freeman and P.V. Kokotovic, Robust Nonlinear Control Design, State-Space an Lyapunov Techiques. Birkhäuser, Boston (1996).
W.H. Fleming and M. Soner, Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York (1993).
Garcia, C.E., Prett, D.M. and Morari, M., Model predictive control: Theory and practice - a survey. Automatica 25 (1989) 335-348. CrossRef
M. Hinze and S. Volkwein, Analysis of instantaneous control for the Burgers equation. Nonlinear Analysis TMA (to appear).
K. Ito and K. Kunisch, On asymptotic properties of receding horizon optimal control. SIAM J. Control Optim (to appear).
A. Jadababaie, J. Yu and J. Hauser, Unconstrained receding horizon control of nonlinear systems. Preprint.
Kleinman, D.L., An easy way to stabilize a linear constant system. IEEE Trans. Automat. Control 15 (1970) 692-712. CrossRef
Mayne, D.Q. and Michalska, H., Receding horizon control of nonlinear systems. IEEE Trans. Automat. Control 35 (1990) 814-824. CrossRef
V. Nevistic and J. A. Primbs, Finite receding horizon control: A general framework for stability and performance analysis. Preprint.
J.A. Primbs, V. Nevistic and J.C. Doyle, A receding horizon generalization of pointwise min-norm controllers. Preprint.
Scokaert, P., Mayne, D.Q. and Rawlings, J.B., Suboptimal predictive control (Feasibility implies stability). IEEE Trans. Automat. Control 44 (1999) 648-654. CrossRef
F. Tanabe, Equations of Evolution. Pitman, London (1979).
R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis. North Holland, Amsterdam (1984).