2011

Predicting Extreme Events in Finance, Internet Traffic, and Weather

2011
Webinar

Lecture Details

Date:

2011

Location Information:

CSS Webinar Series

Author:

Mathukumalli Vidyasagar

Author Bio:

Mathukumalli Vidyasagar was born in Guntur, India on September 29, 1947. He received the B.S., M.S. and Ph.D. degrees in electrical engineering from the University of Wisconsin in Madison, in 1965, 1967 and 1969 respectively. Between 1969 and 1989, he was a Professor of Electrical Engineering at various universities in the USA and Canada. His last overseas job was with the University of Waterloo, Waterloo, ON, Canada, where he served between 1980 and 1989. In 1989 he returned to India as the Director of the newly created Centre for Artificial Intelligence and Robotics (CAIR) in Bangalore, under the Ministry of Defence, Government of India. Between 1989 and 2000, he built up CAIR into a leading research laboratory with about 40 scientists and a total of about 85 persons, working in areas such as flight control, robotics, neural networks, and image processing. In 2000 he moved to the Indian private sector as an Executive Vice President of India's largest software company, Tata Consultancy Services. In the city of Hyderabad, he created the Advanced Technology Center, an industrial R&D laboratory of around 80 engineers, working in areas such as computational biology, quantitative finance, e-security, identity management, and open source software to support Indian languages. In 2009 he retired from TCS at the age of 62, and joined the Erik Jonsson School of Engineering & Computer Science at the University of Texas at Dallas, as a Cecil & Ida Green Professor of Systems Biology Science. In March 2010 he was named as the Founding Head of the newly created Bioengineering Department. His current research interests are in the application of stochastic processes and stochastic modeling to problems in computational biology, control systems and quantitative finance.

Abstract:

As far back as 1963, Beniot Mandelbrot (who sadly passed away just a few weeks ago) pointed out that asset price movements in the real world don't follow the Gaussian distribution. Instead they are "heavy-tailed" -- that is, they display a kind of self-similarity and scale-invariance. Since then, similar patterns have been observed in extreme weather such as rainfall, and more recently, in Internet traffic. Recent research in "pure" probability theory shows that heavy-tailed random variables have some very unusual properties. For instance, if we average many observations of such variables, the averages move in a few large bursts instead of moving smoothly. Such behavior has indeed been observed in the stock market.

The pervasiveness of heavy-tailed distributions in so many diverse arenas has implications for modeling, and risk mitigation. How do we design Internet traffic networks and storage servers if the volume of traffic is heavy-tailed? How do we hedge our equity positions if asset prices move in a heavy-tailed manner?

In this talk I will describe the issues involved through a combination of intuitive arguments, visualizations, and formal mathematics. My hope is to inspire practicing engineers to become familiar with this fascinating class of models, and theoretical researchers to study the many open problems that still remain.

Support Files

PDF Slides:

vidyasagar_css-webinar-2.pdf

Analysis and design of extremum seeking controllers

2011
Webinar

Lecture Details

Date:

2011

Location Information:

CSS Webinar Series

Author:

Dragan Nesic

Author Bio:

Dr. Dragan Nesic is a Professor in the Department of Electrical and Electronic Engineering (DEEE) at The University of Melbourne, Australia. He received his BE degree in Mechanical Engineering from The University of Belgrade, Yugoslavia in 1990, and his Ph.D. degree from Systems Engineering, RSISE, Australian National University, Canberra, Australia in 1997. Since February 1999 he has been with The University of Melbourne. His research interests include networked control systems, discrete-time, sampled-data and continuous-time nonlinear control systems, input-to-state stability, extremum seeking control, applications of symbolic computation in control theory, hybrid control systems, and so on. He was awarded a Humboldt Research Fellowship (2003) by the Alexander von Humboldt Foundation, an Australian Professorial Fellowship (2004-2009) and Future Fellowship (2010-2014) by the Australian Research Council.

He is a Fellow of IEEE and a Fellow of IEAust. He is currently a Distinguished Lecturer of CSS, IEEE (2008-2010). He served as an Associate Editor for the journals Automatica, IEEE Transactions on Automatic Control, Systems and Control Letters and European Journal of Control.

Abstract:

Design of engineered systems whose operation is "best" or "optimal" in some sense is increasingly important. In many cases, the optimal operation of the system in steady-state is more critical than during the transients as the system operates most of the time in a steady-state regime. Moreover, in many cases it is not possible to accurately model the steady-state behaviour of the system and online optimization approaches are called for.

Extremum seeking is an approach for steady-state online optimization that deals with situations when the plant model and/or the cost to optimize are not available to the designer but it is assumed that measurements of the plant input and output signals are available. Using these available signals, the goal is to design a controller that dynamically searches for the optimizing inputs. This method was successfully applied to biochemical reactors, ABS control in automotive brakes, variable cam timing engine operation, electromechanical valves, axial compressors, mobile robots, mobile sensor networks, optical fibre amplifiers and so on. Interestingly, it was observed in the literature that some bacteria (such as the flagella-actuated E. Coli) and swarms of fish collectively search for food using extremum seeking techniques.

This talk presents a summary of our results on a class of adaptive extremum seeking controllers that are very popular among the practitioners. We show that some popular control schemes can be interpreted in an appropriate sense as the gradient descent optimization methods. More importantly, we provide a unifying framework for design of more general extremum seeking schemes by combining an arbitrary optimization method, such as the continuous Newton, with an appropriate estimator of the derivatives of the input-output steady-state map for the system. We use the methods of averaging and singular perturbations to provide a precise characterization of the convergence properties of the closed loop system, as well as the tuning guidelines for the controller parameters.

Support Files

PDF Slides:

2010-UQ-ext-seeking-v1.ppt