Generalized Takagi-Sugeno fuzzy systems: rule reduction and robustcontrol

摘要

Presents model reduction and robust control using a generalizedform of Takagi-Sugeno fuzzy systems. We first define a generalized formof Takagi-Sugeno fuzzy systems. The generalized form has a decomposedstructure for each element of A_i and B_i matricesin consequent parts. The key feature of this structure is that it issuitable for reducing the number of rules. Conditions to reduce thenumber of rules are represented in terms of LMIs. The main idea is tofind a structure of if-then rules of the reduced model that agrees wellwith dynamics of the original model. Furthermore, we estimate the lowerbound of the norm of model uncertainty of the Takagi-Sugeno fuzzy systemthat can cover the reduction error. Finally, an example of modelreduction and robust control for a nonlinear system is illustrated. Inthis example, we achieve a robust controller design so as to compensatethe uncertainly of the Takagi Sugeno fuzzy system