A new worst-case iterative identification and control scheme is introduced which is based on the use of unfalsified model sets in parameter space. No a priori bounds are assumed on the norm of the 'unmodelled dynamics' or on the size of disturbances. In spite of the weak assumptions, the scheme converges close to an 'ideal' performance, which could be achieved only with perfect knowledge of the size of the unmodelled dynamics and the disturbances. An interesting feature of the scheme is that the model structure of the parametric part of the models does not have to be known a priori either. A finite set of alternative parametric models can be hypothesized. and structure selection is part of the iterative identification and control design scheme proposed. Finally, simulations are shown and numerical implementations are discussed.