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

Niknam, Mohammad Reza; Kheiri, Hossein; Abdi Sobouhi, Nadereh

doi:10.22034/cmde.2021.43439.1854

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	Optimal control of satellite attitude and its stability based on quaternion parameters
Computational Methods for Differential Equations
مقاله 12، دوره 10، شماره 1، فروردین 2022، صفحه 168-178 اصل مقاله (784.56 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.43439.1854
نویسندگان
Mohammad Reza Niknam^* ¹؛ Hossein Kheiri²؛ Nadereh Abdi Sobouhi³
¹Department of Mathematics, Islamic Azad University, Khalkhal Branch, Khalkhal, Iran.
²Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
³Department of Mathematics, Farhangian University, Tabriz, Iran.
چکیده
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.
کلیدواژه‌ها
Optimal control؛ Stability؛ Quaternion؛ Chaotic systems

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