Generalized Fuzzy Sliding Mode Control for MIMO Nonlinear Uncertain and Perturbed Systems

In this paper, a stable adaptive fuzzy sliding mode based tracking control is developed for a class of non-square nonlinear systems that are represented by input output models involving system uncertainties and external disturbances. The main contribution of the proposed method is that non-square systems are be controlled in their original non-square form instead of squaring them by adding or eliminating variables. First, a fuzzy logic system is designed to estimate the unknown function. Secondly, in order to eliminate the chattering phenomenon brought by the conventional variable structure control, the signum function is replaced by an adaptive Proportional Derivative (PD) term in the proposed approach. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis, so that the convergence to zero of tracking errors and the boudedness of all signals in the closed-loop system can be guaranteed. The efficiency of the proposed approach is shown by computer simulations.