Faculty of Science AMSI Summer School 2013

Structured Markov models and control theory. A unified approach via linear algebra

Yoni Nazarathy
The University of Queensland


Synopsis

Performance analysis and control of natural and engineered systems evolving over time is a central theme in applied mathematics, operations research and engineering. Many such systems can be modelled as stochastic by means of structured Markov chains, while others are well described by deterministic linear models with feedback control. In both cases the underlying linear algebra is very similar. This course aims to teach the students both types of methodologies, stochastic modelling and control theory via a unified linear algebraic approach.


Contact hours

28 teaching hours spread over the four weeks.

The course features three streamlined guest lectures by Dr Sophie Hautphenne, Dr Erjen Lefeber and Prof Peter Taylor.


Prerequisites

Basic knowledge of linear algebra, calculus and probability as well as working knowledge of at least one mathematical software package such as Mathematica, MATLAB or R.

This mathematical appendix contains most of the needed background.


Assessment


Resources

The lecture notes contain a detailed course schedule and will be updated throughout the course.

A recommended classic elementary book that analyses both deterministic and stochastic dynamical systems is: Luenberger DG, Introduction to Dynamic Systems: Theory, Models, and Applications, New York: Wiley; 1979.

A recommended book for structured Markov models of the type analysed in the course is: Latouche G., Ramaswami V, Introduction to Matrix Analytic Methods in Stochastic Modelling, PA:SIAM, 1999.

A recommended book on Deterministic Linear Systems and Control is: Antsaklis PJ, Michel AN, A Linear Systems Primer, Boston, Mass; Birkhauser Boston; 2007.


About Yoni Nazarathy

Dr. Yoni Nazarathy is a lecturer in the School of Mathematics and Physics at the University of Queensland. His research is in the field of applied probability, statistics, queueing networks and control. He obtained his PhD from the University of Haifa, Israel in 2009. He then spent two years as a post-doctoral researcher in the Netherlands, at the European Institute for Statistics, Probability, Stochastic Operations Research and their Applications (EURANDOM) and at CWI (Centrum Wiskunde & Informatica) Amsterdam. He then spent an additional year as a Lecturer at Swinburne University of Technology in Melbourne where he remains an adjunct member of the Centre for Advanced Internet Architectures. Prior to his PhD studies he was working as a developer of wireless networks protocols and software. You can read more on his webpage.

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