H∞–control theory of fluid dynamics
Open Access
- 8 November 1998
- journal article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 454 (1979) , 3009-3033
- https://doi.org/10.1098/rspa.1998.0289
Abstract
Robust (or H∞–) 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∞–control theory for fluid dynamics. Our result establishes that if the H∞–control problem for the linearized Navier–Stokes equation has a γ–suboptimal solution, then the corresponding H∞–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.Keywords
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