Mathematical Modeling of Smart Space for Context-Aware System: Linear Algebraic Representation of State-Space Method Based Approach

Abstract

A smart space is embedded with several components such as sensors, actuators, and computing devices that enable the sensing and control of the environment, and the inhabitants interact with the devices in the smart space whenever they need to. To model a smart space, a dynamic relationship needs to be established among the elements of the space whereby the interactions with devices are considered a dynamic-process state. In this paper, a linear model of a smart space is presented using a state equation, where the two coefficient matricesLandHneed to be defined to model the smart space, and the coefficient matrixLis used to determine the states of the devices; similarly, the situation of the smart space is determined using coefficientH. An algorithm is presented to make a linear model from the logical functions that are used to describe the system. This model is flexible in terms of the control of the smart-space environment because the environmental factors are represented by a matrix element. This linear smart-space model is helpful for the control of a context-aware system, and we use an example to illustrate the effectiveness of the proposed model.