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

Document Type : Research Paper


1 Department of Mathematics, Islamic Azad University, Khalkhal Branch, Khalkhal, Iran.

2 Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

3 Department of Mathematics, Farhangian University, Tabriz, Iran.


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.