Barrier function-based adaptive synergetic control with state constraints for manipulator with uncertainty and input saturation

This study proposes a barrier function-based adaptive nonsingular terminal synergetic control to mitigate chattering and uncertainty in a nonlinear system with hard state constraints and actuator saturation. The controller addresses the uncertainty by utilizing a barrier function-based evolution constraint. Furthermore, the controller incorporates a barrier function-based macrovariable to modify the control behavior and constrain the system states within predefined ranges. The design is presented for an n-th-order nonlinear system, and the stability is proven using the Lyapunov stability theorem. Simulation with constant reference demonstrates the effectiveness of the proposed controller in constraining the system states, and experiments with impulse, sine, and bounded random uncertainty illustrate the controller's ability to handle uncertainty without explicitly defining the worst-case assumption. Moreover, implementation on a robotic manipulator demonstrates the advantage of the proposed method compared to four adaptive controllers in terms of continuous control law, chattering-free response, simplicity in tuning parameters, and tracking performance.