Nonlinear Preconditioning in Problems of Optimal Control for Fluid Systems

This note discusses certain aspects of computational solution of optimal control problems for fluid systems. We focus on approaches in which the steepest descent direction of the cost functional is determined using the adjoint equations. In the first part we review the classical formulation by presenting it in the context of Nonlinear Programming. In the second part we show some new results concerning determination of descent directions in general Banach spaces without Hilbert structure. The proposed approach is illustrated with computational examples concerning a state estimation problem for the 1D Kuramoto-Sivashinsky equation.