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 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.
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.
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 , . When f is a constant, we then have a zero-order Sugeno fuzzy model,
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.
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).