Robust Tracking Control of MIMO Underactuated Nonlinear Systems With Dead-Zone Band and Delayed Uncertainty Using an Adaptive Fuzzy Control

In this paper, trajectory tracking of multi-input multi-output underactuated nonlinear systems with dead-zone band and time delays is synthesized and analyzed using robust control technique based on adaptive fuzzy control. Fuzzy logic systems with online adaptations are utilized to evaluate each unknown nonlinear subsystem. It is assumed that the system includes a combined backlash and hysteresis resulting in a dead-zone band. Moreover, the gain from the delayed states and the upper bounds of the uncertainties caused by the fuzzy modeling errors are estimated online. H
_∞
control technique is developed to overcome the effects of the slopes of the dead-zone band and external disturbances. The stability analysis and tracking performance of the closed-loop system are verified based on the Lyapunov stability theory and Ricatti inequality, such that all the states of the system are uniformly ultimately bounded. Finally, a tower crane system is used as a case study in the simulations to validate the effectiveness and robustness of the proposed control scheme.