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Model Predictive Control for Nonlinear Parabolic Differential Equations Based on a Linear Quadratic Gaussian Design
Author(s) -
Benner Peter,
Hein Sabine
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910278
Subject(s) - linear quadratic gaussian control , model predictive control , nonlinear system , control theory (sociology) , mathematics , optimal control , gaussian , quadratic equation , optimal projection equations , gaussian process , linear quadratic regulator , mathematical optimization , control (management) , computer science , physics , geometry , quantum mechanics , artificial intelligence
We consider optimal control problems for semilinear parabolic partial differential equations where process and measurement noise can occur. If we apply a Model Predictive Control (MPC) scheme we obtain optimal control problems on small time intervals. The resulting “smaller problems” can be linearized around a reference and solved by using a Linear Quadratic Gaussian (LQG) design. We present some theoretical background of the strategy above as well as results of a numerical implementation for a 3D problem. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)