Learning-Based Control for Deployment of Tethered Space Robot via Sliding Mode and Zero-Sum Game

The underactuated dynamics with input saturation due to limited tension is the greatest challenge of stabilizing the deployment of tethered space robot (TSR), and existing sliding mode methods rely on the assumptions of inherently bounded control command and vanishing state-dependent disturbance. This brief proposes a nearly optimal control law based on variable construct control and neural network technique, which can get rid of the assumptions. The new reduced-order system with synchronization states can be established by the nearly optimal reaching law based on the zero-sum game strategy, which is approximately solved by the actor-disturbance-critic neural network. Meanwhile, the terminal attractor is synthesized into the sliding surface to enhance fast convergence. A numerical simulation was conducted to verify the proposed analyses, and this study's results show that the method works effectively to ensure a fast response of the underactuated dynamics under limited input and disturbance.