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The problem of controlling uncertain dynamic systems which are subject to external disturbances, uncertainty and sheer complexity is of considerable interest. Conventional modelling approaches employ mathematical models and examine the system’s evolution and its control. Such approaches are not completely successful when applied to large non-linear complex systems. These models work well provided the system meet the requirement and assumption of synthesis techniques. However due to uncertainty and sheer complexity of the actual dynamic system, it is very difficult to ensure that the mathematical model does not break down (Mohammadian & Stonier, 1995).
Progress in solving these problems has been with the aid of new advanced high-speed computers and the application of artificial intelligence paradigms, particularly neural networks, fuzzy logic systems and evolutionary algorithms. Fuzzy logic systems have been successfully applied in the place of the complex mathematical systems and they have numerous practical applications in modelling, control, prediction and automation. They have been found useful when the system is either difficult to predict and or difficult to model by conventional methods.
Fuzzy set theory (Zadeh, 1965) provides a mean for representing uncertainties. The underlying power of fuzzy logic is its ability to represent imprecise values in an understandable form. Fuzzy logic systems have a fuzzy knowledge base (FKB) consisting of a set of fuzzy rules of the form:If (
is 
and 
is 
and 
and 
is 
’)Then (
is 
else 
is 
else 
else 
is 
)where 
are normalised fuzzy sets for 
input variables 
, and where 
are normalised fuzzy sets for 
output variables 
. The inference engine of fuzzy logic system applies the fuzzy rules to output action/s from inputs. There are many types of inference engines in the literature, including the popular Mamdani inference engine.
Given a fuzzy knowledge base with 
rules and 
antecedent variables, a fuzzy logic system as given in Equation 1 uses a singleton fuzzifier, Mamdani product inference engine and centre average defuzzifier to determine output variables, has the general form for a single output variable, say 
:
(1) where
are centres of the output sets
and membership function
defines for each fuzzy set
the value of
in the fuzzy set, namely,
.