H∞-control theory of fluid dynamics

Robust (or H-infinity-) control theory has been an expanding subject in recent years because of its wide applications and its close connection to operator theory on Hardy spaces. We develop an H-infinity-control theory for fluid dynamics. Our result establishes that if the H-infinity-control problem for the linearized Navier-Stokes equation has a gamma-suboptimal solution, then the corresponding H-infinity-control problem for the nonlinear system has a solution for small perturbations of the steady solution. The proof relies on the existence of positively invariant manifolds for certain Hamiltonian systems.