Reply to "Further Comment on 'Optimal Fuzzy Controller Design: Local Concept Approach'"

Abstract

We proposed two approaches to solve a quadratic optimal problem of Takagi-Sugeno (T-S) fuzzy-model-based nonlinear systems. These two approaches are totally different in both concept and derivation even they deal with the same issue and the adopted notations look similar. Readers are suggested to clear local-concept approach away from their brains and reexamine the global-concept approach. Then, you will find out that in global-concept approach, via the proposed synthetical matrices, a quadratic optimal fuzzy problem is transformed into a general nonlinear quadratic optimal problem; a numerical approach (dynamic decomposition algorithm) is further introduced to speed up numerical solution and to keep the global optimality at the same time. The stability analysis, the derivation of controller, and the minimum energy are derived fully on the basis of nonlinear systems. Their formulation or representation are all in form of entire fuzzy system instead of fuzzy subsystems. Therefore, the mentioned issue is not the case for global approach. Those are only related to local-concept approach. In this article, we clarify the pointed issue and focus on reinforcing our theorem.