What are Neuro-Fuzzy Systems A neuro-fuzzy system is a fuzzy system that uses a learning algorithm derived from or inspired by neural network theory to determine its parameters (fuzzy sets and fuzzy rules) by processing data samples. A neuro-fuzzy system can be viewed as a 3-layer feedforward neural network. The first layer represents input variables, the middle (hidden) layer represents fuzzy rules and the third layer represents output variables.

Nuero fuzzy models Mamdani Fuzzy Model The Mamdani fuzzy model was proposed as the very first attempt to control a steam engine and boiler combination by a set of linguistic control rules obtained from experienced human operators. two fuzzy inference systems were used as two controllers to generate the heat input to the boiler and throttle opening of the engine cylinder, respectively, in order to regulate the steam pressure in the boiler and the speed of the engine. Since the plant takes only crisp values as inputs, we have to use a defuzzifier to convert a fuzzy set to a crisp value. Defuzzification refers to the way a crisp value is extracted from a fuzzy set as a representative value. The most frequently used defuzzification strategy is the centroid of area.

Sugeno Fuzzy Model The Sugeno fuzzy model (also known as the TSK fuzzy model) was proposed by Takagi,Sugeno, and Kang in an effort to develop a systematic approach to generating fuzzy rules from a given input-output data set. A typical fuzzy rule in a Sugeno fuzzy model has the form if z is A and y is B then z = f ( z,y ) where A and B are fuzzy sets in the antecedent, while z = f(z,y ) is a crisp function in the consequent. Usually f ( z, y) is a polynomial in the input variables z and y. When f(z,y ) is a first-order polynomial, the resulting fuzzy inference system is called a first-order Sugeno fuzzy model, which was originally proposed in [89], [96]. When f is a constant, we then have a zero-order Sugeno fuzzy model,

NEURO-FUZZY CONTROL Once a fuzzy controller is transformed into an adaptive network, the resulting ANFIS can take advantage of all the NN controller design techniques proposed in the literature. u(t) x(t) the block diagram of a typical feedback control system consists of a plant block and a controller block. The plant block is usually represented by a set of differential equations that describe the phy$ical system to be controlled. These equations govern the behavior of the plant state x ( t ) x(t) = f(x(t),u ( t ) ) (plant dynamics), u(t) = g(x(t)) (controller). ControllerPlant Dynamics