M. R. Niknam - Department of Mathematics, Payame Noor University, P.O.Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran.‎
K. Kheiri - Faculty of Mathematical Sciences, University of Tabriz, Tabriz, ‎Iran‎.‎
A. Heydari - Department of Mathematics, Payame Noor University, P.O.Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran.

A long time ago, since the launch of the first artificial satellite in ۱۹۵۷, controling attitude of satellites has been considered by the designers and engineers of aerospace industry. Considering the importance of this issue various methods of control in response to this need have been presented and analyzed until now. In this paper, we propose and analyze a three-axis optimal control on the six-dimensional system which describes the kinetic and kinematic equations of a satellite subjected to deterministic external perturbations which induce chaotic motion. At first, the chaotic behavior of system using Lyapunov exponents (LE) and numerical simulations is investigated when no control is affected. Then, a three-axis optimal control is presented by the Pontryagin maximum principle (PMP). This optimal control stabilizes the satellite attitude around the equilibrium point of origin. Finally, we give some simulation results to visualize the effectiveness and feasibility of the proposed ‎method.‎

Lyapunov exponent, Satellite attitude, Pontryagin maximum principle, Optimal ‎control