Fuzzy Neural Networks for Real Time Control Applications

7.3.3 SMC Theory-Based Learning Algorithm for T2FNN with Elliptic MFs

In this section, the SMC theory-based parameter update rules for the T2FNN with elliptic MFs are discussed. As will be seen later from the parameter update rules, the introduced novel training algorithm is simple and computationally less expensive than the gradient-based methods and the adaptation laws have closed forms. Although the gradient-based methods may result in instability, the stability of the proposed method is proved using the Lyapunov approach.

The sliding surface for the nonlinear system is defined as:

$\begin{array}{l}\hfill S_p(e,ė)=ė+\chi e\end{array}$

  (7.137)

where χ is a positive variable that ...