6/25/2012 By Meghan Kelly
Written by By Meghan Kelly
Kun Deng co-authored the award-winning paper “A Simulation-Based Method for Aggregating Markov Chains” with his adviser Professor Prashant Mehta and ECE Professor Sean Meyn. Deng, Mehta, and Meyn are all associated with the Coordinated Science Laboratory (CSL).
Markov Chain – a sequence of dependent random variables – is named after the Russian mathematician Andrey Markov (1856-1922) who first described these models at the beginning of the twentieth century. Today, Markov chain models are indispensible to many applications including biology, computer science and engineering systems. Professor Sean Meyn, who has authored a book on the subject, asserted the significance of the application of the theory of Markov chains to the area of energy-efficient buildings. Markov chains are frequently used to describe occupancy evolution in buildings. Certain simplified models of thermal dynamics of a building can also be abstracted as large Markov chains.
A fundamental problem in using Markov chain models in many of these applications is the large dimension of the state space. For example, Markov chains that arise in building applications typically have millions of states. Deng said that the focus of his research thus is on the “reduction of abstract Markov chain models with very large state space.”
By combining ideas from dynamical systems, information theory and stochastic processes, Deng and colleagues have come up with a computationally efficient algorithm to simplify complex Markov chain models. A salient feature of the algorithm is that it can be implemented solely based on observations of the system of interest.
Although the research reported in the paper is mainly theoretical, Deng has since applied his algorithm to simplify thermal and occupancy models of large buildings. He uses the simplified models to describe macroscopic features of interest that can be used in monitoring and control applications in large buildings.
“Deng’s work can potentially be used to obtain energy-efficient control of heating, ventilation and air conditioning systems during normal building operation, and to synthesize efficient methods for evacuation of people from the building in the event of emergency,” said Deng’s adviser Mehta.
Deng, a third year graduate student, received his M.S. degree (2007) in the Department of Automotive and his B.S. degree (2005) in the Department of Automation from Tsinghua University in China. His research interests include robotics, building systems and energy-saving systems.