a In section 3. 3 we introduce conventional lo d least sql cares methods for identification, explain how they can be used to tune fuzzy systems, provide a simple example, and offer examples of how they can be used to train fuzzy systems-Next in Section 3, 4 we show how gradient methods can be used to train a standard and Takagi-Sugeno fuzzy system, These methods are quite similar to the ones used to train neural networks(e.g, the" back-propagation technique). We provide examples for standard and Takagi-Sugeno fuzzy systems. We highlight the fact that via either the recursive least squares method for fuzzy systems or the gradient method we can perform on-line parameter estimation. We will see in Chapter 6 that these methods can be combined with a controller construction procedure to provide a method for adaptive fuzzy control 1010 ◼ In Section 3,3 we introduce conventional least squares methods for identification, explain how they can be used to tune fuzzy systems, provide a simple example, and offer examples of how they can be used to train fuzzy systems- Next, in Section 3,4 we show how gradient methods can be used to train a standard and Takagi-Sugeno fuzzy system, These methods are quite similar to the ones used to train neural networks (e.g., the "back-propagation technique"). We provide examples for standard and Takagi-Sugeno fuzzy systems. We highlight the fact that via either the recursive least squares method for fuzzy systems or the gradient method we can perform on-line parameter estimation. We will see in Chapter 6 that these methods can be combined with a controller construction procedure to provide a method for adaptive fuzzy control