Nonlinear control for spacecraft observation game using the state-dependent Riccati equation method

For spacecraft proximity observation missions, the competition between the pursuer and the evader over imaging conditions is formulated as a two-player zero-sum differential game. The relative motion is described in the line-of-sight frame, the factors affecting observation quality are modeled as a quadratic cost function of the state variables, and the state-dependent coefficient matrix is derived. When the evader keeps stationary, the game degenerates into an optimal tracking problem for desired observation state, and the state tracking control law is obtained based on the state-dependent Riccati equation method. For the observation game in which both players maneuver, a nonlinear differential game strategy is further derived, and a linear differential game strategy is provided for comparison. Comparative simulation results under multiple scenarios demonstrate that the proposed nonlinear game strategy outperforms the state tracking strategy and linear game strategy in terms of convergence rate, control cost and robustness against evader maneuvers.