This thesis focuses on the challenges that arise from the solution of decision-making problems in terms of convergence, efficiency and robustness. State-of-the-art solvers could fail to find the optimal solution or solve small instances of these problems. The original contribution of the current research consists of the development of a new methodology, based on optimal control theory, to solve different types of decision-making problems. The goal behind developing optimal control reformulations is to effectively solve these problems, while overcoming the drawbacks of the widely used commercial solvers, and three different types of problems are examined.

First, the proposed solution scheme is used for finding the best pairings between control and manipulated variables and utilising the optimal tuning parameters, simultaneously, while satisfying path and end-point constraints. The proposed methodology results in the same pairings and gives better control actions compared to well-established methods. Furthermore, a novel multistage feedback controller is presented, which is proven to be able to handle disturbances with and without uncertainty and switching between operating points.

Second, the Reverse Osmosis (RO) cleaning maintenance scheduling problem is examined. It is shown that the proposed framework can solve successfully this type of problem, even for large-scale configurations, long time horizons and arbitrary realistic model complexity of the underlying dynamic model of the RO process and produce an automated solution for the membrane cleaning scheduling, obviating the need for any form of combinatorial optimisation.

Two-Point Boundary Value Problems (TPBVPs) are examined and solved utilising a double shooting approach, where the initial TPBVP is reformulated into a set of Ordinary Differential Equations (ODEs) and is solved as a least-squares optimisation problem in order to obtain the solution trajectory. Furthermore, a TPBVP formulation is extended and applied to solve dynamic optimisation problems (OCP), based on Pontryagin's Minimum Principle. Three different algorithms are used to solve the OCPs: the forward, backward and double shooting methods. In the case of OCPs, the proposed solution scheme obviates the need for discretising the control actions through the time horizon. The proposed algorithm successfully solved the TPBVPs and found the optimal solution of the OCP, showing a robust performance.