MPC/LQG-Based Optimal Control of Nonlinear Parabolic PDEs

• Main Author: Hein, Sabine
• Other Authors: Benner, Peter
• Format: Doctoral Thesis
• Language: English
• Published: 2010
• Subjects: info:eu-repo/classification/ddc/510; ddc:510; Kontrolltheorie; MPC; Partielle Differentialgleichung; Prädiktive Regelung; Reaktions-Diffusionsgleichung; Regelungstheorie; LQG; Riccatigleichung
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000134; https://monarch.qucosa.de/id/qucosa%3A19266; https://monarch.qucosa.de/api/qucosa%3A19266/attachment/ATT-0/; https://monarch.qucosa.de/api/qucosa%3A19266/attachment/ATT-1/

The topic of this thesis is the theoretical and numerical research of optimal control problems for uncertain nonlinear systems, described by semilinear parabolic differential equations with additive noise, where the state is not completely available. Based on a paper by Kazufumi Ito and Karl Kunisch, which was published in 2006 with the title "Receding Horizon Control with Incomplete Observations", we analyze a Model Predictive Control (MPC) approach where the resulting linear problems on small intervals are solved with a Linear Quadratic Gaussian (LQG) design. Further we define a performance index for the MPC/LQG approach, find estimates for it and present bounds for the solutions of the underlying Riccati equations. Another large part of the thesis is devoted to extensive numerical studies for an 1+1- and 3+1-dimensional problem to show the robustness of the MPC/LQG strategy. The last part is a generalization of the MPC/LQG approach to infinite-dimensional problems.