The reduced basis method for incompressible viscous flow calculations
SIAM Journal on Scientific and Statistical Computing
A reduced-order method for simulation and control of fluid flows
Journal of Computational Physics
Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach
Computational Optimization and Applications
POD-based feedback control of the burgers equation by solving the evolutionary HJB equation
Computers & Mathematics with Applications
Two-level discretizations of nonlinear closure models for proper orthogonal decomposition
Journal of Computational Physics
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We discuss the application of the reduced basis method for the simulation and control of unsteady viscous flows governed by the incompressible Navier-Stokes equations. We describe how to use this method in terms of the construction of a lower-order compensator design. Our approach includes a construction method of the optimal state feedback law for finite-dimensional nonlinear regulator problems. The method is applied to construct a feedback law for the reduced order control model of the Navier-Stokes equations, and then we apply our feedback law to the original control system. Our method is demonstrated on a control problem formulated in a channel flow using a boundary velocity control. We also show how these ideas can be extended to control problems governed by partial differential equations. Numerical results are reported for the open and closed loop controls, and a compensator design is proposed to complete the closed loop dynamics.