Linear quadratic differential game approach for attitude takeover control of failed spacecraft

Spacecraft is mostly abandoned after its fuel exhausts or actuator fails. Using microsatellites to implement attitude takeover control for failed spacecraft is a cost efficient way to recycle on-board valuable payloads at a low cost. In order to achieve collaboration between independent microsatellites, a differential game based method is proposed to stabilize the combined spacecraft composed of multiple microsatellites and the failed spacecraft, in which each microsatellite can independently calculate its own control strategy. Firstly, based on the attitude model of combined spacecraft and the performance index function of each microsatellite, the linear quadratic differential game model is formulated. By optimizing individual performance index functions, the control strategies of multiple microsatellites can be obtained. Secondly, in order to find the Nash equilibrium strategies of microsatellites, the coupled Hamilton-Jacobi(HJ) equations are transferred to a set of coupled Riccati differential equations over finite time horizon. In order to avoid computational overhead, a set of coupled algebraic Riccati equations over infinite horizon is also derived, which can be solved easily with high precision by the Lyapunov iterations method. Finally, numerical simulations verify the effectiveness of the differential game method for the attitude takeover control of failed spacecraft.