A stabilized optimal nonlinear feedback control for satellite attitude tracking

An optimal nonlinear feedback control law with asymptotic stabilization is proposed for the satellite attitude tracking problem. With regard to the large angle or high angular rate task, the full nonlinear tracking error model is built in the form of modified Rodrigues parameters. Based on the optimality of the kinematics, the tracking error model is treated as a high-gain system and analyzed with the perturbation method, and eventually the tracking system is proved to be feedback equivalent to the Jurdjevic–Quinn type system. Then, a Lyapunov function satisfying the asymptotic stability and the Hamilton–Jacobi–Bellman equation simultaneously is used to design the feedback control profile which minimizes a performance index containing penalties on both the state and the control effort. The numerical results show the asymptotic stability and torque penalty features of the control law with the parameters of the control regulation carefully selected.