Synchronization on Stiefel Manifolds
Synchronization on Stiefel Manifolds: a Theory on Almost Global Consensus is a three year research project financed by the The Swedish Research Council.
Synchronization is studied in engineering, physics, and biology in contexts such as multi-robot coordination, coupled oscillators, and neural signaling. Such systems contain large numbers of agents whose interactions are described by a graph and whose states evolve with time. The problem is to control, or determine conditions, such that states synchronize. This project addresses a key of such synchronization problem, the consensus problem, where all the states shall converge to the same point. The states are often confined to be in non-trivial sets that impose constraints on the convergence analysis. We study the consensus problem for sets that are Stiefel manifolds, which comprise matrices with orthonormal columns. This includes, rotation matrices and permutation matrices. A challenge is to show convergence.
The research project Synchronization on Stiefel Manifolds: a Theory on Almost Global Consensus aims to extend previous convergence results, and develop a more complete theory. The theory will leverage results from dynamical systems theory, control systems, and be used for applications within computer vision and physics.