Rigid spacecraft nonlinear robust H_∞ attitude controller design under actuator misalignments

H_∞ control is well-known for its robustness performance, but the spacecraft attitude H_∞ controller design under actuator misalignments and disturbances remains unexplored. In addition, the heavy computational demands prevent the implementation of an H_∞ controller for nonlinear systems in higher dimensions. To address these challenges, a robust H_∞ controller is proposed for the rigid spacecraft attitude control problem in the presence of actuator misalignments and disturbances based on the solution of the Hamilton–Jacobi–Isaacs (HJI) partial differential equation (PDE). The L_2 -gain of the closed-loop system is proved to be bounded by a specified disturbance attenuation level. An efficient sparse successive Chebyshev–Galerkin method is also proposed to solve the nonlinear HJI PDE, thus the implementation of the proposed controller is facilitated. It is also proved that the computational cost grows only polynomially with the system dimension. The effectiveness of the proposed robust H_∞ controller is validated through numerical simulations.