A reduced-order method for optimal control problems in infinite dimensions based on approximate inertial manifolds is developed. Convergence of the cost, optimal controls, and optimal states of the finite dimensional, reduced-order, optimal control problems to the original optimal control problem is analyzed. Special attention is given to the particular case when the dynamics are described by the Navier-Stokes equations in dimension two.
['Kazufumi Ito', 'Karl Kunisch']
Reduced-Order Optimal Control Based on Approximate Inertial Manifolds for Nonlinear Dynamical Systems