Receding horizon optimal control for infinite dimensional systems

Kazufumi Ito; Karl Kunisch

ESAIM: Control, Optimisation and Calculus of Variations (2002)

  • 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 (2002): 741-760. <http://eudml.org/doc/244631>.

@article{Ito2002,
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; closed loop dissipative system; Navier-Stokes equations},
language = {eng},
pages = {741-760},
publisher = {EDP-Sciences},
title = {Receding horizon optimal control for infinite dimensional systems},
url = {http://eudml.org/doc/244631},
volume = {8},
year = {2002},
}

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
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; closed loop dissipative system; Navier-Stokes equations
UR - http://eudml.org/doc/244631
ER -

References

top
  1. [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. [2] T.R. Bewley, Flow control: New challenges for a new Renaissance. Progr. Aerospace Sci. 37 (2001) 21-58. 
  3. [3] H. Chen and F. Allgöwer, A quasi–infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica 34 (1998) 1205-1217. Zbl0947.93013
  4. [4] H. Choi, M. Hinze and K. Kunisch, Instantaneous control of backward facing step flow. Appl. Numer. Math. 31 (1999) 133-158. Zbl0939.76027MR1708955
  5. [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. Zbl0810.76012MR1233904
  6. [6] R.A. Freeman and P.V. Kokotovic, Robust Nonlinear Control Design, State-Space an Lyapunov Techiques. Birkhäuser, Boston (1996). Zbl0857.93001MR1396307
  7. [7] W.H. Fleming and M. Soner, Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York (1993). Zbl0773.60070MR1199811
  8. [8] C.E. Garcia, D.M. Prett and M. Morari, Model predictive control: Theory and practice – a survey. Automatica 25 (1989) 335-348. Zbl0685.93029
  9. [9] M. Hinze and S. Volkwein, Analysis of instantaneous control for the Burgers equation. Nonlinear Analysis TMA (to appear). Zbl1022.49001MR1904464
  10. [10] K. Ito and K. Kunisch, On asymptotic properties of receding horizon optimal control. SIAM J. Control Optim (to appear). Zbl1031.49033
  11. [11] A. Jadababaie, J. Yu and J. Hauser, Unconstrained receding horizon control of nonlinear systems. Preprint. Zbl1009.93028
  12. [12] D.L. Kleinman, An easy way to stabilize a linear constant system. IEEE Trans. Automat. Control 15 (1970) 692-712. 
  13. [13] D.Q. Mayne and H. Michalska, Receding horizon control of nonlinear systems. IEEE Trans. Automat. Control 35 (1990) 814-824. Zbl0715.49036MR1058366
  14. [14] V. Nevistič and J. A. Primbs, Finite receding horizon control: A general framework for stability and performance analysis. Preprint. 
  15. [15] J.A. Primbs, V. Nevistič and J.C. Doyle, A receding horizon generalization of pointwise min–norm controllers. Preprint. Zbl0976.93024
  16. [16] P. Scokaert, D.Q. Mayne and J.B. Rawlings, Suboptimal predictive control (Feasibility implies stability). IEEE Trans. Automat. Control 44 (1999) 648-654. Zbl1056.93619MR1680132
  17. [17] F. Tanabe, Equations of Evolution. Pitman, London (1979). Zbl0417.35003
  18. [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.