Robust and stable indirect fuzzy adaptive control for SISO nonlinear systems

An adaptive fuzzy controller is constructed from a collection of fuzzy IF-THEN rules whose parameters are changed or adapted according to adaptive laws for the purpose of controlling a nonlinear plant to track a reference trajectory. The fuzzy adaptive control is composed in two classes: direct and indirect one. The indirect fuzzy adaptive controller will be designed through two steps. The first one consists in the construction of a controller based on linguistic description about the unknown plant from human expert. To guaranty stability, a supervisory controller is added. The second step adjusts, on line, the parameters of the fuzzy controller based on the gradient descend. To ensure the robustness, fuzzy controller parameters are adjusted, on line, by a robust gradient descent method. Simulation results show the effectiveness of proposed algorithms in tracking of the inverse pendulum output.