Modeling and optimal control of multiphysics problems using the finite element method
Interdisciplinary research like constrained optimization of partial differential equations (PDE) for trajectory planning or feedback algorithms is an important topic. Recent technologies in high performance computing and progressing research in modeling techniques have enabled the feasibility to investigate multiphysics systems in the context of optimization problems. In this thesis a conductive heat transfer example is developed and techniques from PDE constrained optimization are used to solve trajectory planning problems. In addition, a laboratory experiment is designed to test the algorithms on a real world application. Moreover, an extensive investigation on coupling techniques for equations arising in convective heat transfer is given to provide a basis for optimal control problems regarding heating ventilation and air conditioning systems. Furthermore a novel approach using a flatness-based method for optimal control is derived. This concept allows input and state constraints in trajectory planning problems for partial differential equations combined with an efficient computation. The stated method is also extended to a Model Predictive Control closed-loop formulation. For illustration purposes, all stated problems include numerical examples.
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