Adaptive non-backstepping fuzzy tracking control for a class of multiple-input–multiple-output pure-feedback systems with unknown dead-zones

In this study, the authors present a novel adaptive non-back-stepping alleviating computation tracking control algorithm for a class of MIMO pure-feedback systems with unknown dead-zone inputs. Based on the introduced new state variables and coordinate transforms, the pure-feedback form is converted into a normal form where back-stepping scheme is not necessary. Owing to the unavailability of the new states, the tracking control problem is changed from a state-feedback one to an output-feedback one. Therefore, observers need to be designed to estimate the indirect un-measurable states. In the controller and observer design procedure, the control method is based on non-back-stepping scheme and for each subsystem only three adaptive adjusted parameters are needed to be updated on-line. Thus, different from the back-stepping-based ones, this new algorithm can not only alleviate on-line computation burden but also can considerably simplify the control procedure. According to Lyapunov stable analysis methods, the bounded of all the signals in the closed-loop system can be guaranteed and the tracking error is proven to converge to a small neighbourhood of the origin. Simulation results are presented to illustrate the effectiveness of this proposed approach.