Model Predictive Control for Partial Differential Equations

In this thesis we are concerned with model predictive control (MPC) of partial differential equations. The idea is to approximate an infinite time horizon optimal control problem by a sequence of finite horizon optimal control problems. The optimization horizon plays a crucial role in the stability analysis. In the first part we analyse the minimal stabilizing horizon for different classes of parabolic partial differential equations with distributed or boundary control. This horizon is for theoretical as well as for numerical reasons of particular interest. The proofs are essentially based on an exponential controllability condition. Our results can be exploited to deduce guidelines for the stage cost in the algorithm. Furthermore, we analyse the stability of the boundary controlled wave equation. The second part of this thesis deals with the algorithms in model predictive control. First, we summarize well known algorithms from optimal control of partial differential equations and analyse the applicability to MPC. Moreover, we show the possibility to combine predictive control with the model reduction technique proper orthogonal decomposition. Furthermore, we investigate the benefit of MPC algorithms with varying optimization horizon and present a new approach which uses multigrid methods. A short introduction into our numerical implementation can also be found in this thesis. In the last part we analyse the presented algorithms by means of numerical simulations of some test examples.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Bayreuth

Year

2014

Author dc:creator

• Altmüller, Nils

Contributors dc:contributor

• Grüne, Lars

Repository record source_url

https://epub.uni-bayreuth.de/id/eprint/1823/

OAI identifier oai:identifier

oai:epub.uni-bayreuth.de:1823