Adaptive control for spacecraft rendezvous subject to actuator faults and saturations

An adaptive saturated fault-tolerant controller is proposed for a spacecraft rendezvous maneuver with a cooperative target spacecraft. The six-degree-of-freedom (6-DOE) relative dynamics subject to unknown inertial parameters, external disturbances, actuator faults and saturations are formulated in the pursuer's body-fixed frame. To design controller satisfying asymmetric magnitude constraints, a modified smooth hyperbolic tangent function is applied to approximate the non-differentiable saturation function. Based on the augmented system technique, an adaptive fault-tolerant saturated controller is designed for the pursuer by using a Nussbaum function matrix compensating for the nonlinear term arising from the input saturations. In addition, a Levant differentiator is introduced to obtain the derivative of the virtual control in finite time that avoids the complicated calculation. It is proved via Lyapunov stability theory that all the signals in the closed-loop augmented system are bounded and the relative errors asymptotically converge to zero. Numerical simulations are performed to illustrate effectiveness of the proposed controller.