Prescribed Performance Bounded-H_∞ Control for Flexible-Joint Manipulators Without Initial Condition Restriction

Flexible-joint manipulators have a lightweight nature, compact structure, and high flexibility, making them widely applicable in industrial manufacturing, biomedical instruments, and aerospace fields. However, the inherent flexibility of single-link flexible-joint manipulators (SLFJMs) poses substantial control challenges. Compared to traditional control algorithms, prescribed performance control (PPC) algorithms provide superior transient response and steady-state performance by defining a prescribed performance function. However, existing PPC algorithms are limited to a specific range of system initial states, which reduces the joint manipulator's operational workspace and weakens the robustness of the control algorithm. To address this issue, this study proposes a prescribed performance bounded-H_∞ fault-tolerant controller for SLFJMs. By designing an improved tangent-type barrier Lyapunov function (BLF), a prescribed performance controller that is independent of the initial state of the SLFJM is developed. An input control function (ICF) is employed to mitigate the impulse response of the control input, ensuring a smooth transition from zero. Furthermore, the improved tangent-type BLF enables the tracking error to rapidly converge to a small neighborhood of zero. Finally, a stabilization control simulation experiment is conducted; the results validate the effectiveness of the proposed prescribed performance bounded-H_∞ controller.