Control Policies for a Water-Treatment System Using the Markov Decision Process. Part 1: Mathematical Formulation

Abstract

A model is developed to assist decision-making for choosing control policies for a closed-loop space life-support system. The water-treatment system, which consists of hygiene and potable-water subsystems, is chosen as the focus of this model due to its direct impact to the crewmembers' water requirements. This paper is the fi rst part of the study where mathematical formulations of processes involved are presented. Input values and some constants are derived from the NASA Baseline and Assumptions Document (BVAD) [5] and previous research. In order to bridge the gap between descriptions in these documents and a realistic system, a simulation is built. Random processes are also introduced in the model to refl ect the stochastic nature of some physical processes. Relationships among these physical processes are described by the mathematical formulations. These formulations are set up in such a way that the conditions of the system can be assessed at the beginning of every hour. Output values are obtained from the simulation and are described in Part Two of the study (companion paper). Some benefi ts from this study include enhancing understanding of controlling physical systems as well as providing formulations that could serve as a base for further developments of other resource supply-and-demand models for closed-loop systems.