Adaptive fuzzy logic approximation of unknown nonlinear systems: state-variable feedback tuning

An online approximator using a linear fuzzy logic model with automatic tuning mechanism is presented. The proposed approximation method can be used to model a class of unknown nonlinear systems as long as they are Caratheodory ones. The structure of the fuzzy model is fixed but the parameters are tuned by the state errors. The fuzzy model is composed of several semi-closed, continuous, totally ordered, and well-defined fuzzy numbers defined in each state variable dimension, and a number of appropriately defined condition-action rules. Either the min-inference or product-inference technique is utilized to generate the weighted average of the linear coefficients, which make the whole unknown nonlinear system piecewise linearized. No offline preprocessing is needed. The initial values of the parameters of the fuzzy model can be arbitrarily assigned. Then they are tuned to their true values through adaptive update laws and, therefore, it is guaranteed that the unknown nonlinear system is linearized and approximated to any degree of accuracy by the linear fuzzy logic model.