Robust fuzzy tracking control for a class of perturbed non square nonlinear systems

A stable adaptive fuzzy control based tracking control is developed for a class of Multi Input Multi Output (MIMO) non square nonlinear systems with external disturbances using sliding mode algorithm. This control algorithm further justifies that non square systems can be controlled in their original non square form instead of squaring them by adding or eliminating variables. This method integrates adaptive fuzzy systems to approximate the unknown nonlinear functions. Then, in order to reduce the chattering phenomenon without deteriorating the tracking performances, the discontinuous term in the conventional sliding mode technique is replaced by an adaptive Proportional Integral (PI) term. All parameter adaptive laws are derived based on Lyapunov stability analysis. The overall adaptive fuzzy scheme guarantees the convergence to zero of tracking errors as well as the boundedness of all signals in the closed-loop system. The validity of the proposed approach is shown by computer simulations.