Title :

Piecewise Bilinear Modeling of A Nonlinear System and Its Application to the Design of A Looking-up Table Controller

Speaker :

Prof. Michio Sugeno

Emeritus Researcher

European Centre for Soft Computing, Spain

Venue :

Room 215, William M. W. Mong Engineering Building, CUHK

Date :

Sep 26, 2011, Monday
3:30 PM - 4:30 PM

Abstract :

The purpose of this research is to apply the idea of a piecewise bilinear (PB) model to a nonlinear system, where a nonlinear function is approximated by a piecewise bilinear function. A PB system is derived from fuzzy if-then rules with singleton consequents that are considered as a special case between the Mamdani rules and the Takagi-Sugeno rules. A PB model has a general approximation capability for any nonlinear system with a given precision. In this research, we build a PB model of a nonlinear system and take a model-based approach to design a stabilizing looking up table (LUT) controller. A LUT has been widely used for industrial control purpose and also as a nonlinear function approximator. A conventional LUT with bilinear interpolation is found to be exactly a PB system. Conversely, a PB system can be always expressed by a LUT. Using a Lyapunov function for a PB system, we can derive the necessary and sufficient stability conditions in the sense of Lyapunov, where a general Lyapunov function is also approximated by a piecewise quadratic function. A closed-loop system of a PB system with a feedback LUT controller becomes also a PB system: the structure is preserved. Therefore, we can apply the stability conditions to obtain a stabilizing LUT controller based on a PB model.

Biography :

After graduating from the Department of Physics, The University of Tokyo, Prof. Sugeno worked at Mitsubishi Atomic Power Industry. Then, he served the Tokyo Institute of Technology as Research Associate, Associate Professor and Professor from 1965 to 2000. After retiring from the Tokyo Institute of Technology, he worked as Laboratory Head at the Brain Science Institute, RIKEN from 2000 to 2005, and then, as Distinguished Visiting Professor at Doshisha University from 2005 to 2010. He is currently Emeritus Professor at the Tokyo Institute of Technology, Japan, and Emeritus Researcher at the European Centre for Soft Computing, Spain.

He was President of the Japan Society for Fuzzy Theory and Systems from 1991 to 1993, and also President of the International Fuzzy Systems Association from 1997 to 1999. He is the first recipient of the IEEE Pioneer Award in Fuzzy Systems with Zadeh in 2000. He also received the 2010 IEEE Frank Rosenblatt Award.

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Enquiries: Ms. Winnie Wong or Prof. Wen J. Li, Department of Mechanical and Automation Engineering, CUHK at 2609 8337. *MAE Series (2011-12) is contained in the World-Wide Web home page at http://www3.mae.cuhk.edu.hk/maeseminars.php#mae.