Nussbaum Function-Based Adaptive Boundary Control for Flexible Manipulator with Unknown Control Directions and Nonlinear Time-Varying Actuator Faults

This study proposes a novel boundary control strategy for a vibrating single-link flexible manipulator system modeled by partial differential equations. The system has uncertain control directions and actuator faults. Existing research studies model fault-tolerant control systems with fixed fault coefficients; in this study, the actuator faults are nonlinear and time-varying, and the control directions are unknown. To circumvent the obstacles introduced by the unknown control directions and nonlinear varying actuator failures, an adaptive boundary controller is designed by using Nussbaum functions with fast growth rates and the bound estimation method. In the developed control scheme, all closed-loop signals are shown to be uniformly bounded. Additionally, the angle tracking error and vibration asymptotically converge to zero. Finally, numerical simulations for five cases demonstrate the effectiveness of the modeled boundary controller.