Adaptive Discretization and Solution Structure Detection of Multi-Stage Optimal Control Problems

摘要

This thesis deals with the formulation and optimization of multi-stage optimal control problems arising in process engineering with a known number of stages. Here, the stages of a multi-stage optimal control problem are defined as either physical stages, which are enforced by the underlying nonlinear process, or by algorithmic stages, which are due to the formulation of the optimal control problem. The case of state transition networks is not discussed in this work, however, the algorithms presented could be also generalized for this particular case. In the present thesis, wavelet-based adaptation concepts combined with the automatic detection of the switching structure introduced for single-stage problems are generalized for multi-stage and multiple-shooting problems. Further, a novel optimality-based adaptation criterion is introduced and combined with the adaptive switching structure approach.