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Receding horizon optimal control for 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”.
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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.

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

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