Construction of a linguistic adaptation law for a fuzzy sliding-mode controller

Fuzzy controllers are often used in the standard form of fuzzy sliding-mode controllers. The tuning of the numerous possible parameters of the fuzzy controller for optimal behaviour is difficult and time-consuming. Linguistically represented system knowledge as well as heuristic design principles of a control expert are expressed by fuzzy control principles, and are implemented in order to adapt the nonlinear input output characteristic of the fuzzy sliding-mode controller. Here, a detailed outline for the implementation of the linguistically defined adaptation law is given. Analysing the adaptation strategy, the adaptation algorithm itself proves to be of fuzzy sliding-mode controller type. Using Lyapunov theory, an analytic expression relating system uncertainties with parameter exactness is given. Simulation results for an inverted pendulum with time-varying pendulum length illustrate the effectiveness of the adaptation algorithm.