Adaptive neural appointed-time prescribed performance control for the manipulator system via barrier Lyapunov function

• Published in: Journal of the Franklin Institute Vol. 362; no. 2; p. 107468
• Main Authors: Zhao, Kangwei, Xie, Yichen, Xu, Shijie, Zhang, Liang
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.2025
• Subjects: Appointed-time stability; Backstepping control; Barrier Lyapunov function; Modified prescribed performance function; Neural network compensation; Barrier Lyapunov function; Backstepping control; Modified prescribed performance function; Neural network compensation; Appointed-time stability
• ISSN: 0016-0032
• DOI: 10.1016/j.jfranklin.2024.107468

•An appointed time controller which ensures settling time achievement via barrier Lyapunov function.•A novel form of bounded time-vary gain designed for appointed time stability.•A new class of modified appointed time prescribed performance functions. In this paper, a novel adaptive neural prescribed performance backstepping controller is proposed to address the positioning problem of a perpetuated robotic manipulator subject to model uncertainties. Different from asymptotically stable and fixed-time stable controllers, the proposed appointed-time controller allows for the obtainment of the predefined convergence time regardless of initial conditions. Moreover, a modified prescribed performance function with appointed-time convergence characteristics is proposed based on K1 functions, alleviating the necessity for accurate initial errors. Building on this, the secant-type barrier Lyapunov function is employed to ensure appointed-time stability and error variables stabilize to a small set around zero with prescribed performance. Additionally, radial basis function neural networks are utilized to compensate perturbations, with approximation errors being compensated by adaptive laws. Finally, simulation results with different examples are demonstrated to validate the effectiveness of the proposed control algorithm.