Tracking control via time-varying feedback for an uncertain robotic system with both output constraint and dead-zone input.

This paper is devoted to the tracking control for an uncertain robotic system with both output constraint and dead-zone input. Remarkably, the distinctive characters of the system are reflected by system uncertainties and output constraint. First, more serious uncertainties are involved since unknown nonlinear dynamic matrices, external disturbance and the dead-zone input (see unknown slopes and break points therein) are simultaneously considered, but those of the related literature are not. Second, weaker conditions on the output constraint are allowed since the constraint functions considered are only first but not more order continuously differentiable while any their time derivatives are not necessarily available for feedback. This leads to the incapability of the traditional control schemes on this topic. To solve the control problem, a novel control framework is proposed based on time-varying feedback which overcomes the serious system uncertainties while relaxes the conditions on output constraints. Specifically, a state transformation with a time-varying gain is first introduced to derive a new system. Then, by using the traditional backstepping method with the introduction of the time-varying gain in the estimations of some uncertain terms, a time-varying feedback controller is explicitly designed, which ensures that all the states of the resulting closed-loop system are bounded while system output asymptotically tracks the reference signal without any violation of the output constraint. Finally, simulation results for two practical examples are provided to validate the effectiveness of the proposed theoretical results, and moreover, a comparison with PID method is given to show the superiority of the proposed method on tracking accuracy and robustness.