A hierarchical multivariable fuzzy controller for learning with genetic algorithms

Abstract

The most common approach to multivariate fuzzy control is to extend the single-variable case by combining more state-variable pairs. This approach, however, results in high-dimensional rule-bases that may not be implementable in practical systems. Typically, for each additional state variable, the number of rules increases exponentially. Clearly, the number of rules, even for systems of moderate complexity, becomes impractical in real-time, due to the required processing time. This paper proposes and implements a simplified structure for a multi-variable fuzzy controller, which also reduces the total number of rules. This approach is suitable for machine-learning applications since different rules can be derived to infer the correct control actions, dependent on the controller structure and the way in which the input variables have been paired. The number of rules using this approach is minimal and is a linear function of the number of the state inputs. Furthermore, no fuzzification/defuzzification scaling factors are required for the controllers in intermediate levels of composition. The methodology is demonstrated on an anaesthesia simulation case study.