Proper Orthogonal Decomposition in Optimal Control of Fluids
نویسندگان
چکیده
In this article, we present a reduced order modeling approach suitable for active control of uid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady ows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial di erential equations. We here use it in active control of uid ows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very e cient for the computations of optimization and control problems in unsteady ows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of uid ow through channels.
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