An LMI-based decoupling control for electromagnetic formation flight

Electromagnetic formation flight (EMFF) leverages electromagnetic force to control the relative position of satellites. EMFF offers a promising alternative to traditional propellant-based spacecraft flight formation. This novel strategy is very attractive since it does not consume fuel. Due to the highly coupled nonlinearity of electromagnetic force, it is difficult to individually design a controller for one satellite without considering others, which poses challenges to communications. This paper is devoted to decoupling control of EMFF, including regulations, constraints and controller design. A learning-based adaptive sliding mode decoupling controller is analyzed to illustrate the problem of existing results, and input rate saturation is introduced to guarantee the validity of frequency division technique. Through transformation, the imposed input rate saturation is converted to state and input constraints. A linear matrix inequalities (LMI)-based robust optimal control method can then be used and improved to solve the transformed problem. Simulation results are presented to demonstrate the effectiveness of the proposed decoupling control.