This thesis aims to develop and implement both nonlinear and linear distributed optimization methods that are applicable, but not restricted to the optimal control of distributed systems. Such systems are typically large scale, thus the well-established centralized solution strategies may be computationally overly expensive or impossible and the application of alternative control algorithms becomes necessary. Moreover, it is often desired that the information on the coupled subsystems inner dynamics is kept local, making the deployment of a centralized optimal control scheme impossible in practice. In such a case, optimization approaches based on some limited exchange of information remain the only possible option. In the first part of this thesis, we consider nonlinear optimal control problems with distributed structure, for which we design an efficient distributed shooting method resulting in up to 19 times faster integration time when compared to the conventional approaches. The first part reports the testing of the proposed method on two different dynamic optimization problems. The second part of this thesis investigates linear optimal control problems with quadratic cost functions, i.e. quadratic programs (QP). An overview of dual decomposition based approaches is given, followed by the development of a novel dual decomposition scheme. The proposed method employs second-order derivatives. Experimental results suggest that it requires up to 152 times less local optimization steps than classical first-order schemes. Furthermore, as a part of this thesis, an open-source QP solver (PyDQP) with 11 different dual decomposition based methods is implemented. A set of large scale distributed quadratic programs is set up and released for benchmarking purposes.
PhD thesis, Department of Electrical Engineering (ESAT), KU Leuven, Belgium, 2014