A time-delayed control scheme using adaptive law with time-varying boundedness for robot manipulators

This paper presents an adaptive time-delayed control based on the sliding-mode (ATDC-SM). The proposed ATDC-SM provides a new adaptive law imposing time-varying boundedness that is developed to adjust the control gains appropriately while suppressing the negative impact generated by the robot manipulators. Moreover, the control gains are constructed as a continuous function with a fast adaptation rate and hence can remedy chattering and fluctuation inherent in the existing adaptive time-delayed control. These synergistic effects provide a fast convergence rate while producing stable control gains. Besides, the proposed ATDC-SM uses one-sample delayed estimation to cancel out complex nonlinear dynamics and unknown disturbances. Thus, it produces a simple structure but effective approach due to this estimation. From these benefits, the proposed ATDC-SM provides precise tracking performance without undesired side effects. It is shown that the tracking errors are uniformly ultimately bounded through a Lyapunov function. The effectiveness of the proposed ATDC-SM is illustrated through simulation with a one-link robot manipulator, which is compared to that of the existing control approaches. Keywords: time-delayed control; sliding-mode control; adaptive control; fast adaptation; time-varying.