Receding horizon optimal control for infinite dimensional systems
Department of Mathematics,
North Carolina State University, Raleigh, North
Carolina, USA. Research partially supported by
National Science Foundation under grant UINT-8521208.
2 Institut für Mathematik, Karl-Franzens-Universität Graz, 8010 Graz, Austria; email@example.com. Research partially supported by the Fonds zur Förderung der wissenschaftlichen Forschung under SFB 03 “Optimierung und Kontrolle”.
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.
Mathematics Subject Classification: 49L15 / 49N35 / 93C20 / 93Dx
Key words: Receding horizon control / control Lyapunov function / Lyapunov equations / closed loop dissipative / minimum value function / Navier–Stokes equations.
© EDP Sciences, SMAI, 2002