This chapter gives credence to the introduction of optimal control theory into oil spill modeling and develops an optimization process that will aid in the effective decision-making in marine oil spill management. The purpose of the optimal control theory is to determine the control policy that will optimize (maximize or minimize) a specific performance criterion, subject to the constraints imposed by the physical nature of the problem. A fundamental theorem of the calculus of variations is applied to problems with unconstrained states and controls, whereas a consideration of the effect of control constraints leads to the application of Markovian decision processes. The optimization objectives are expressed as value function or reward to be optimized, whereas the optimization models are formulated to adequately describe the marine oil spill control, starting from the transportation process. These models consist of conservation relations needed to specify the dynamic state of the process given by the chemical compositions and movements of crude oil in water.
Part of the book: Robust Control