Analysis and formulation of a class of complex dynamic optimization problems

The Direct Transcription approach, also known as the direct simultaneous approach, is a widely used solution strategy for the solution of dynamic optimization problems involving differential-algebraic equations (DAEs). Direct transcription refers to the procedure of approximating the infinite dimensional problem by a finite dimensional one, which is then solved using a nonlinear programming (NLP) solver tailored to large-scale problems. Systems governed by partial differential equations (PDEs) can also be handled by spatially discretizing the PDEs to convert them to a system of DAEs.; The objective of this thesis is firstly to ensure that direct transcription using Radau collocation is provably correct, and secondly to widen the applicability of the direct simultaneous approach to a larger class of dynamic optimization and optimal control problems (OCPs). This thesis aims at addressing these issues using rigorous theoretical tools and/or characteristic examples, and at the same time use the results for solving large-scale industrial applications to realize the benefits.; The first part of this work deals with the analysis of convergence rates for direct transcription of unconstrained and final-time equality constrained optimal control problems. The problems are discretized using collocation at Radau points. Convergence is analyzed from an NLP/matrix-algebra perspective, which enables the prediction of the conditioning of the direct transcription NLP as the mesh size becomes finer. Several convergence results are presented along with tests on numerous example problems. These convergence results lead to an adjoint estimation procedure given the Lagrange multipliers for the large-scale NLP. The work also reveals the role of process control concepts such as controllability on the convergence analysis, and provides a very important link between control and optimization inside the framework of dynamic optimization.; As an effort to extend the applicability of the direct simultaneous approach to a wider class of problems, a PDE-constrained optimal control problem, the spatial discretization of which results in a DAE-constrained problem with an arbitrarily high-index inequality constraint, is studied. Optimal control problems with high-index path constraints are very hard to solve, numerically. Contrary to the intuitive belief that the direct transcription approach would not work for the high-index optimal control problem, an analysis is performed to show that NLP-based methods have flexibility with respect to constraint qualifications, and this can be put to use in the context of high-index inequality path-constrained problems to obtain meaningful solutions. (Abstract shortened by UMI.)...