Consensus on nonlinear spaces

Consensus problems have attracted significant attention in the control community over the last decade. They act as a rich source of new mathematical problems pertaining to the growing field of cooperative and distributed control. This paper is an introduction to consensus problems whose underlying state-space is not a linear space, but instead a highly symmetric nonlinear space such as the circle and other relevant generalizations. A geometric approach is shown to highlight the connection between several fundamental models of consensus, synchronization, and coordination, to raise significant global convergence issues not present in linear models, and to be relevant for a number of engineering applications, including the design of planar or spatial coordinated motions.