Optimal control of satellite attitude and its stability based on quaternion parameters

‎This paper proposes an optimal control method for the chaotic ‎attitude of the satellite when it is exposed to external disturbances. When there is no control over the satellite, its chaotic attitude ‎is investigated using Lyapunov exponents (LEs)‎, Poincare diagrams, and bifurcation diagrams. ‎In order to overcome the problem of singularity in the great maneuvers of satellite, ‎we consider the kinematic equations based on quaternion parameters instead of Euler angles, ‎and obtain control functions by using the Pontryagin maximum principle (PMP)‎. ‎These functions are able to reach the satellite attitude to its equilibrium point. ‎Also the asymptotic stability of these control functions is investigated by Lyapunov's stability theorem. ‎Some simulation results are given to visualize the effectiveness and feasibility of the proposed method.