Receding horizon optimal control for infinite dimensional systems

Kazufumi Ito; Karl Kunisch

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 8, page 741-760
  • ISSN: 1292-8119

Abstract

top
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.

How to cite

top

Ito, Kazufumi, and Kunisch, Karl. "Receding horizon optimal control for infinite dimensional systems." ESAIM: Control, Optimisation and Calculus of Variations 8 (2010): 741-760. <http://eudml.org/doc/90669>.

@article{Ito2010,
abstract = { 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. },
author = {Ito, Kazufumi, Kunisch, Karl},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Receding horizon control; control Lyapunov function; Lyapunov equations; closed loop dissipative; minimum value function; Navier–Stokes equations.; receding horizon control; closed loop dissipative system; Navier-Stokes equations},
language = {eng},
month = {3},
pages = {741-760},
publisher = {EDP Sciences},
title = {Receding horizon optimal control for infinite dimensional systems},
url = {http://eudml.org/doc/90669},
volume = {8},
year = {2010},
}

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
DA - 2010/3//
PB - EDP Sciences
VL - 8
SP - 741
EP - 760
AB - 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.
LA - eng
KW - Receding horizon control; control Lyapunov function; Lyapunov equations; closed loop dissipative; minimum value function; Navier–Stokes equations.; receding horizon control; closed loop dissipative system; Navier-Stokes equations
UR - http://eudml.org/doc/90669
ER -

References

top
  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. Automatica34 (1998) 1205-1217.  Zbl0947.93013
  4. H. Choi, M. Hinze and K. Kunisch, Instantaneous control of backward facing step flow. Appl. Numer. Math.31 (1999) 133-158.  Zbl0939.76027
  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.  Zbl0810.76012
  6. R.A. Freeman and P.V. Kokotovic, Robust Nonlinear Control Design, State-Space an Lyapunov Techiques. Birkhäuser, Boston (1996).  Zbl0857.93001
  7. W.H. Fleming and M. Soner, Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York (1993).  Zbl0773.60070
  8. C.E. Garcia, D.M. Prett and M. Morari, Model predictive control: Theory and practice - a survey. Automatica25 (1989) 335-348.  Zbl0685.93029
  9. M. Hinze and S. Volkwein, Analysis of instantaneous control for the Burgers equation. Nonlinear Analysis TMA (to appear).  Zbl1022.49001
  10. K. Ito and K. Kunisch, On asymptotic properties of receding horizon optimal control. SIAM J. Control Optim (to appear).  Zbl1031.49033
  11. A. Jadababaie, J. Yu and J. Hauser, Unconstrained receding horizon control of nonlinear systems. Preprint.  
  12. D.L. Kleinman, An easy way to stabilize a linear constant system. IEEE Trans. Automat. Control15 (1970) 692-712.  
  13. D.Q. Mayne and H. Michalska, Receding horizon control of nonlinear systems. IEEE Trans. Automat. Control35 (1990) 814-824.  Zbl0715.49036
  14. V. Nevistic and J. A. Primbs, Finite receding horizon control: A general framework for stability and performance analysis. Preprint.  
  15. J.A. Primbs, V. Nevistic and J.C. Doyle, A receding horizon generalization of pointwise min-norm controllers. Preprint.  Zbl0976.93024
  16. P. Scokaert, D.Q. Mayne and J.B. Rawlings, Suboptimal predictive control (Feasibility implies stability). IEEE Trans. Automat. Control44 (1999) 648-654.  Zbl1056.93619
  17. F. Tanabe, Equations of Evolution. Pitman, London (1979).  Zbl0417.35003
  18. R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis. North Holland, Amsterdam (1984).  Zbl0568.35002

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.