Robust Stabilization of the Navier–Stokes Equation via the H∞-Control Theory
Since most of the fluid dynamic systems are subject to uncertainties and external disturbances, a major problem is the design of feedback controllers which achieve asymptotic stability not only for a nominal system (which is only partially known) but also for an entire set of systems covering a neighborhood of the given system. Such a control is called robust and the H ∞-control theory provides an efficient and popular approach to this question. We discuss in some details the H ∞-control problem for the stabilization problems studied in Chap. 3. We begin with a general presentation and some basic results on the H ∞-control problem for linear infinite-dimensional systems.
KeywordsControl Problem Hamiltonian System Invariant Manifold Feedback Controller Mild Solution