Adaptive Fuzzy Logic Control: Explicit Adaptive Control with Lyapunov Stability and Learning Capability

The objective of this paper is to introduce an adaptive fuzzy logic control system based on Lyapunov stability criteria. We consider the feedback control system in the crisp domain, and then, obtain the fuzzy control laws under the identification-control principle. The design is based on stability and hierarchy of identification and control. The fuzzy rulebase is stored in a fuzzy hypercube and the fuzzy control action is computed via a fuzzy inference mechanism. Initial conditions for the elements of a fuzzy hypercube are obtained by an off-line fuzzy clustering mechanism with large-grain uncertainty. Two fuzzy algorithms are developed: The first one is called a fuzzy identification-learning algorithm and the second is a fuzzy control-inferencing algorithm. The fuzzy identification learning algorithm updates the membership functions on the action side of the rules and the fuzzy control-inferencing algorithm calculate fuzzy control data. This approach guarantees stability, convergence and robustness of the closed-loop feedback system.