Rule regulation of indirect adaptive fuzzy controller design

Rule regulation of an indirect adaptive fuzzy controller based on the Lyapunov theory is proposed. Two sets of fuzzy systems are used to represent the controlled system. The fuzzy controller based on the proposed adaptive law has the ability to modify the control rules during real-time operation. In particular, the representation of rules is formed as an analytic parameter equation, so that the scheme of adaptive control can be applied successfully. The derivation shows that the indirect adaptive fuzzy controller is stable in the sense of the Lyapunov theory. The design approach is synthesised through the following stages: first, the authors construct fuzzy system, and define the fuzzy sets as those whose membership functions of the IF-part are distributed equally in the individual universe of discourse; then, two adaptive laws are derived to adjust the constructed rules that are used to approximate an optimum control in which the mathematical model of the controlled system is unknown. Finally, a second-order nonlinear inverted pendulum system is applied to verify the effectiveness of the proposed approach