(560e) Equation-Free Multiparametric Model Predictive Control for Dissipative PDEs
In this work, an equation-free multiparametric MPC is proposed where there is no use of equations and only an available black-box simulator (such as COMSOL ) is employed, performing input-output tasks. An equation-free non-linear dynamic optimization has been developed based on its static counterpart  utilizing an equation-free model reduction. The mp-optimization takes advantage of the reduced gradients produced by the non-linear dynamic optimizer. The multiparametric approach aims to compute an off-line map that approximates the reduced non-linear problem efficiently. First, an initial solution is computed for the non-linear optimization problem employing the matrix-free Arnoldi iterations  for constructing a model reduction orthonormal basis without the use of full gradients. As a result a reduced order piecewise affine (PWA) model is produced as a good approximation of the model. Then, the mp-optimization is solved computing an initial set of critical regions (CR). Afterward, the CRs are refined using the non-linear dynamic optimization in order to approximate the non-linear problem within an arbitrary tolerance. The results show that only a small number of CR regions are necessary in order to sufficiently approximate the problem. The CRs are constructed in a form of a search tree, due to the refinement algorithm, which accelerates the on-line search. In order to demonstrate the effectiveness of this algorithm, the aforementioned methodology has been applied to a chemical engineering application modelled by COMSOL.
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