Non-singular pre-defined time prescribed performance control of space manipulator achieving deterministic total convergence time

Pre-defined Time Control (PTC) or Fixed Time Control (FTC) is characterized by a pre-defined or fixed convergence time respectively. The convergence time is independent of initial condition but at the cost of introducing a singular term that causes infinite control input at equilibrium point (e.g., zero tracking error), which is well-known as the singularity issue of PTC and FTC. To handle this issue, Non-singular Fixed Time Control (NFTC) and Non-singular Pre-defined Time Control (NPTC) schemes have been extensively studied, which remove the singular term by equipping the derivative of system state with a fractional power between 1 and 2. However, the most works of NPTC (or NFTC) can only achieve a total convergence time consisting of a pre-defined (or fixed) time and an unknown finite time, thus a deterministic total convergence time of system state is lacked. Moreover, the stability analysis in the traditional literatures is valid only if the absolute value of a state-dependent term is greater than a positive scalar, which does not always hold true in the complete real number set. This paper proposes a model-free Non-singular Pre-defined Time Prescribed Performance Sliding Control (NPT-PPSMC) scheme for free-floating space robotic manipulators with external disturbance, which achieves prescribed performance (i.e., constrained tracking error) and Pre-defined Time Stability (PTS) at the same time. By using a novel varying power of derivative of system state, the proposed control scheme is not only singularity free but also strictly guaranteeing a deterministic total convergence time that does not include any unknown term. Moreover, the stability analysed by Lyapunov theory is valid in the complete real number set. The effectiveness is verified by numerical simulations.