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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.doi:10.1051/cocv:2002032 fatcat:thgnkfwxgzehfjbquo5a3fusr4