Observer-Based Adaptive Prescribed-Time Asymptotic Tracking Control for Flexible-Joint Manipulators

This study concentrates on adaptive prescribed-time tracking control for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i>-link flexible-joint (FJ) manipulators with unmeasurable state variables. First of all, auxiliary signals are constructed utilizing measurable variables. Based on auxiliary signals, the observer is directly designed to estimate the system states, which allows the observer dynamics to incorporate unknown terms. Owing to the uniqueness of the designed observer, the observation errors converge to zero. Furthermore, with the aim of enhancing control efficiency, the prescribed-time scale function is introduced into the controllers, and the unknown terms are processed based on the fuzzy logic system (FLS), so that the tracking error of FJ manipulators converges to the specified range within the prescribed time. Meanwhile, with the help of positive integrable time-varying functions, asymptotic tracking is further achieved. In the whole control design, the tuning functions are adopted to avoid overparameterization. In theory, it is ensured that all signals in the closed-loop system are bounded, and the tracking error converges to the small neighborhood of the zero within a specified time and gradually converges to zero. Finally, the simulation example confirms the feasibility of the control design.