Automatic Estimation of Parameters of Complex Fuzzy Control Systems
Since the first fuzzy controller was presented by Mamdani in 1974, different studies devoted to the theory of fuzzy control have shown that the area of development of fuzzy control algorithms has been the most active area of research in the field of fuzzy logic in the last years. From 80 s, fuzzy logic has performed a vital function in the advance of practical and simple solutions for a great diversity of applications in engineering and science. Due to its great importance in navigation systems, flight control, satellite control, speed control of missiles and so on, the area of fuzzy logic has become an important integral part of industrial and manufacturing processes. Some fuzzy control applications to industrial processes have produced results superior to its equivalent obtained by classical control systems. The domain of these applications has experienced serious limitations when expanding it to more complex systems, because a complete theory does not yet exist for determining the performance of the systems when there is a change in its parameters or variables. When some of these applications are designed for more complex systems, the number of fuzzy rules controlling the process is exponentially increased with the number of variables related to the system. For example, if there are n variables and m possible linguistic labels for each variable, mn fuzzy rules would be needed to construct a complete fuzzy controller. As the number of variables n increases, the rule base quickly overloads the memory of any computing device, causing difficulties in the implementation and application of the fuzzy controller. Sensory fusion and hierarchical methods are studied in an attempt to reduce the size of the inference engine for large scale systems. The combination of these methods reduces more considerably the number of rules than these methods separately. However, the adequate fusion hierarchical parameters should be estimated. In traditional techniques much reliance has to be put on the experience of the system designer in order to find a good set of parameters (Jamshidi, 1997) Genetic algorithms (GA) are an appropriate technique to find parameters in a large search space. They have shown efficient and reliable results in solving optimization problems. For