Optimal control of generalized storage models

Abstract

The purpose of this dissertation is to study to optimal control problem of the generalized storage processes over an infinite planning horizon. The generalization.of the controlled storage process allows for both positive and negative jumps by the stochastic input prqcess as well as controlled inputs and outputs. The extension of the theory for the optimal control of generalized storage processes mainly consists of studying various aspects of the uncontrolled storage model, deriving the sufficient condition of optimality, verifying the existence of a unique solution and studying its properties. The approach is to specify the stochastic structure of the processes involved in the model and monotonicity properties of the controls so as to guarantee the existence of a unique solution to the storage equation, to construct the Markov process model for the content level of the store and then to apply Markov decision theory in order to characterize the expected infinite time horizon discounted return. Consequently the sufficient condition of optimality is established as a functional differential equation in terms of the generator of the storage process and shown to possess a unique and continuously differentiable solution. In the process of verifying the existence and uniqueness of the optimal return and optimal controls, the deterministic version is considered first so as to shed light upon the nature of the solution methodology and then the results obtained are extended as to include the stochastic processes inherent in the generalized storage model.