Minimum sliding mode error feedback control for fault tolerant reconfigurable satellite formations with J2 perturbations

• A new control scheme – Minimum Sliding Mode Error Feedback Control (MSMEFC) – is proposed for spacecraft formation flying with high control precision.
• The concept of equivalent control error is proposed to define various kinds of system model errors.
• A cost function based on the principle of minimum sliding mode covariance constraint is established to estimate the optimal equivalent control error.

Minimum Sliding Mode Error Feedback Control (MSMEFC) is proposed to improve the control precision of spacecraft formations based on the conventional sliding mode control theory. This paper proposes a new approach to estimate and offset the system model errors, which include various kinds of uncertainties and disturbances, as well as smoothes out the effect of nonlinear switching control terms. To facilitate the analysis, the concept of equivalent control error is introduced, which is the key to the utilization of MSMEFC. A cost function is formulated on the basis of the principle of minimum sliding mode error; then the equivalent control error is estimated and fed back to the conventional sliding mode control. It is shown that the sliding mode after the MSMEFC will approximate to the ideal sliding mode, resulting in improved control performance and quality. The new methodology is applied to spacecraft formation flying. It guarantees global asymptotic convergence of the relative tracking error in the presence of J2 perturbations. In addition, some fault tolerant situations such as thruster failure for a period of time, thruster degradation and so on, are also considered to verify the effectiveness of MSMEFC. Numerical simulations are performed to demonstrate the efficacy of the proposed methodology to maintain and reconfigure the satellite formation with the existence of initial offsets and J2 perturbation effects, even in the fault-tolerant cases.