Nonsingular predefined-time dynamic surface control of a flexible-joint space robot with actuator constraints

To achieve predefined-time trajectory tracking control of a flexible-joint space robot(FJSR) with actuator constraints, a nonsingular predefined-time dynamic surface control scheme is developed. The input saturation caused by actuator constraints is addressed via the designed predefined-time anti-saturation compensator. On this basis, two different control laws are designed for such high-order nonlinear systems by utilizing the backstepping technique, and a novel nonlinear filter is constructed to filter the virtual control signals, thus avoiding the “differential expansion” phenomenon. Moreover, a singularity-free auxiliary function is designed to solve the singularity issue generated by the derivative of fractional power terms in the predefined-time control algorithm framework. The closed-loop system is proven to be semi-globally predefined-timely uniformly ultimately bounded (SGPTUUB) via constructing the suitable Lyapunov function. The difference and effectiveness of the two designed control laws are illustrated by the conducted simulations. Both of them allow the FJSR system to track the desired trajectory in a reasonably predefined time.