On the stabilization of fixed-point iterations arising in hierarchical control design

Abstract

Fixed-point iterations are commonly used to break the algebraic loops involved in the distributed optimization among computational entities sharing only a partial knowledge. However, although this approach is appealingly simple and that it works astonishingly well in many practical situations, its use is rarely associated to an appropriate analysis of its convergence. In this paper, it is shown that this iteration can be rationally conducted using control theory in order to derive a provable stability under appropriate assumptions.