Accessibility of a Class of Generalized Double-Bracket Flows

Abstract

We investigate a generalization of Brockett’s celebrated double bracket flow that is closely related to matrix Riccati differential equations. Using known results on the classification of transitive Lie group actions on homogeneous spaces, necessary and sufficient conditions for accessibility of the generalized double bracket flow on Grassmann manifolds are derived. This leads to sufficient Lie–algebraic conditions for controllability of the generalized double bracket flow. Accessibility on the Lagrangian Grassmann manifold is studied as well, with applications to matrix Riccati differential equations from optimal control.