POD-based Reduced Order Optimal Control of Parabolic PDE Systems via Diffusivity-Interior-Boundary Actuation
C. Xu, Y. Ou, E. Schuster
IEEE Conference on Decision and Control
New Orleans, Louisiana, December 12-14, 2007
Abstract
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We present a framework to solve an optimal
control problem for parabolic partial differential equations
(PDEs) with diffusivity-interior-boundary actuators. The proposed
approach is based on reduced order modeling (ROM)
and successive optimal control computation. First we simulate
the parabolic PDE system with given inputs to generate data
ensembles, from which we then extract the most energetic
modes to obtain a reduced order model based on the proper
orthogonal decomposition (POD) method and Galerkin projection.
The obtained reduced order model corresponds to a
bilinear system. By solving the optimal control problem of
the bilinear system successively, we update the given initial
optimal inputs iteratively until the convergence is obtained. The
simulation results demonstrate the effectiveness of the proposed
method.