Lyapunov function based design of heuristic fuzzy logic controllers

Abstract

A stability design of fuzzy logic controllers (FLCs) for non-linear systems is proposed in this paper. In heuristic design of FLCs, we often have a lot of rules. Although each rule governing the control of the plant refers to a stable closed-loop sub-system, the overall system stability cannot be guaranteed when all of these rules are put together into a rule base for the FLC. This limitation is tackled in this paper. It is shown that on adding arbitrary rules to the FLC without any restriction on the form of membership functions, the system stability can be ensured if each individual rule applying to the plant results in a stable sub-system in the sense of Lyapunov subject to a common Lyapunov function for all rules. Analytical proof of the result is given and its application on designing a heuristic of FLC is illustrated through an example.