Dynamic augmentation and complexity reduction of set-based constrained control

Computing polytopic controlled invariant sets which are maximal inside a prescribed region often yields sets which have a really complex representation. Since the associated control has a complexity which drastically increases with that of the region, this turns out to be a major problem in the implementation of the theory of controlled invariant regions. In this paper, we consider the problem of reducing the complexity of these regions and/or the complexity of the associated compensator. We propose two heuristic techniques based on spectral properties of some relevant matrices and on vertex-elimination methods. The paper presents several preliminary results which are interesting on their own such as dynamic augmentation and the properties of complex (as opposed to real) polytopic invariant regions.