The orthogonal function approach is developed in this paper to solve the Takagi-Sugeno (TS) fuzzy-model-based dynamic equations. The new method simplifies the procedure of solving the TS-fuzzy-model-based dynamic equations into the successive solution of a system of recursive formulae only involving matrix algebra. Based on the presented recursive formulae, an algorithm only involving straightforward algebraic computation is also proposed in this paper. The computational complexity can therefore be reduced remarkably. An illustrated example shows that the proposed method based on the orthogonal functions can obtain satisfactory results.

In this paper, in order to control uncertain chaotic system, an adaptive fuzzy control (AFC) scheme is developed for the multi-input/multi-output plants represented by the Takagi-Sugeno (T-S) fuzzy models. The proposed AFC scheme provides robust tracking of a desired signal for the T-S fuzzy systems with uncertain parameters. The developed control law and adaptive law guarantee the boundedness of all signals in the closed-loop system. In addition, the chaotic state tracks the state of the stable reference model (SRM) asymptotically with time for any bounded reference input signal. The suggested AFC design technique is applied to control of a uncertain Lorenz system based on T-S fuzzy model such as stabilization, synchronization and chaotic model following control (CMFC).