Observer-based fractional-order adaptive type-2 fuzzy backstepping control of uncertain nonlinear MIMO systems with unknown dead-zone

A new problem of observer-based fractional adaptive type-2 fuzzy backstepping control for a class of fractional-order MIMO nonlinear dynamic systems with dead-zone input nonlinearity is considered in the presence of model uncertainties and external disturbances where the control scheme is constructed by combining the backstepping dynamic surface control (DSC) and fractional adaptive type-2 fuzzy technique. First, a linear state observer estimates immeasurable states. Second, the unknown nonlinear functions of the uncertain system are approximated with interval type-2 fuzzy logic systems. Third, to avoid the complication of backstepping design process, the DSC is used. Fourth, by using the fractional adaptive backstepping, fractional adaptive laws are constructed, the proposed method is applied to a class of uncertain fractional-order nonlinear MIMO system. In order to have a better control performance in reducing tracking error, the controller parameters are tuned by using the PSO algorithm. Stability of the system is proven by the Mittag-Leffler method. It is presented that the proposed design guarantees the boundedness property for the system and also the tracking error can converge to a small neighborhood of the zero. The simulation examples are given to show the efficiency of the proposed controller.