Rule Reduction and Robust Control of Generalized Takagi-Sugeno Fuzzy Systems
Tadanari Taniguchi* and Kazuo Tanaka**
*Department of Mechanical Engineering and Intelligent Systems Department of Electrical and Computer Engineering
**Department of Mechanical Engineering and Intelligent Systems The University of Electro-Communications 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585 Japan’ Tel. & Fax. +81-424-43-5425
This paper presents model reduction and robust control using a generalized form of Takagi-Sugeno fuzzy systems. We first define a generalized form of TakagiSugeno fuzzy systems. The generalized form has a decomposed structure for each element of Ai and Bi matrices in consequent parts. The key feature of this structure is that it is suitable for reducing the number of rules. Conditions to reduce the number of rules are represented in terms of linear matrix inequality (LMIs). The main idea is to find a structure of if-then rules of the reduced model that agrees well with dynamics of the original model. Furthermore, we estimate the lower bound of the norm of model uncertainty of the Takagi-Sugeno fuzzy system that can cover the reduction error. Finally, we present an example of model reduction and robust control for a nonlinear system. In this example, we achieve a robust controller design to compensate for the uncertainly of the Takagi-Sugeno fuzzy system.