Parametric method for spacecraft trajectory tracking control problem with stochastic thruster fault

This study deals with the spacecraft trajectory tracking control problem with stochastic thruster fault of the chaser spacecraft, whose aim is to make the output of the Markov jump linear system track the output of a given reference model. A new succinct general complete parametric expression for the tracking controller is established. Considering the actuator malfunction, a set of Clohessy-Wiltshire equations with Markov jump parameters are proposed to describe the relative motion while the target spacecraft into a circular orbit. A linear matrix inequality method is presented to make the Markov jump system stochastically stable and to guarantee the input constraints. Based on the theory of the generalised Sylvester equations, a parametric method is established for the model reference tracking problem. For certain systems, the proposed algorithm contains extra degrees of freedom in parametric design, which can be used to achieve some additional performance. The final numerical simulation results show the effectiveness of the proposed method.