Predefined performance control for fuzzy robotic systems with measurement noise: Adaptation, robustness, and fuzzy optimization

This study investigates a novel adaptive robust control for robotic systems to unify the research of prescribed performance control (PPC), uncertainty, and measurement noise. The focus is to achieve the PPC for robotic systems with the simultaneous existence of uncertainty and measurement noise. To deal with the uncertainty, fuzzy set theory is adopted to quantify the uncertainty. To ensure that the tracking errors of robotic systems subject to uncertainty and measurement noise can always confined to the predefined bound, an error conversion mechanism is introduced, by which a new transformed state is obtained. Based on the error conversion mechanism and fuzzy quantification of uncertainty, a saturation-type adaptive robust control is proposed, which can ensure the uniform boundedness (UB) and uniform ultimate boundedness (UUB) of the new transformed state. Furthermore, the problem of control parameter optimization is investigated. A fuzzy-based performance index that consists of the system performance and control effort is proposed. The control parameter optimization problem is then converted into finding a control parameter such that the performance index is minimized. By rigorous proofs, the solution to the optimization problem exists and is unique. Finally, a numerical simulation is conducted to illustrate the effectiveness of the suggested method. •To deal with the uncertainty, fuzzy set theory is adopted to quantify the uncertainty.•An adaptive robust prescribed performance control (ARPPC) is proposed to realize prescribed performance trajectory tracking for uncertain robotic systems with measurement noise, with adaptation to cope with uncertainty.•The control parameter optimization is discussed based on fuzzy uncertainty. By formulating the balance between system performance and control cost as a fuzzy performance index, an optimal control parameter is the one that minimizes the index.