# Receding horizon optimal control for infinite dimensional systems

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

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

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topIto, 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- 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.
- T.R. Bewley, Flow control: New challenges for a new Renaissance. Progr. Aerospace Sci.37 (2001) 21-58.
- H. Chen and F. Allgöwer, A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica34 (1998) 1205-1217.
- H. Choi, M. Hinze and K. Kunisch, Instantaneous control of backward facing step flow. Appl. Numer. Math.31 (1999) 133-158.
- 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.
- 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).
- C.E. Garcia, D.M. Prett and M. Morari, Model predictive control: Theory and practice - a survey. Automatica25 (1989) 335-348.
- 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.
- D.L. Kleinman, An easy way to stabilize a linear constant system. IEEE Trans. Automat. Control15 (1970) 692-712.
- D.Q. Mayne and H. Michalska, Receding horizon control of nonlinear systems. IEEE Trans. Automat. Control35 (1990) 814-824.
- 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.
- P. Scokaert, D.Q. Mayne and J.B. Rawlings, Suboptimal predictive control (Feasibility implies stability). IEEE Trans. Automat. Control44 (1999) 648-654.
- F. Tanabe, Equations of Evolution. Pitman, London (1979).
- R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis. North Holland, Amsterdam (1984).

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