Making use of instability and input saturation in a convergent unfalsification based iterative scheme

Abstract A new worst-case iterative identification and control scheme is introduced which is based on the use of unfalsified model sets in a parameter space extended with model uncertainty. Only very conservative a priori bounds are assumed to be known on the norm of the unmodelled dynamics and on the size of disturbances. In spite of the weak assumptions, the scheme converges close to an 'ideal' performance, which could only be achieved with perfect knowledge of the size of the unmodelled dynamics and the disturbances. Furthermore, based on recent results on the worst case robust l1 performance bounds, instability and input saturation will also be handled in the scheme. An interesting feature of the scheme is that the structure of the parametric part of the models does not have to be precisely known. A finite set of alternative parametric models can be hypothesized and structure selection is part of the iterative identification and control design scheme proposed.