Chaotic attitude analysis of a satellite via Lyapunov exponents and its robust nonlinear control subject to disturbances and uncertainties

This article investigates chaotic attitude maneuvers in a satellite for a range of parameters via Lyapunov exponents (LEs) and designs an appropriate robust nonlinear controller to ensure chaos suppression and achieve desired performance. Since the dynamic equations of satellite are described as a nonlinear non-autonomous system, an improved technique for calculating the LEs of such systems as a measure of chaos phenomenon is presented. Using the proposed algorithm, the chaotic behavior of satellite is proved within a range of its parameters. Then, by converting dynamic equations to canonical form, a robust nonlinear control is proposed using back-stepping sliding mode method. The stability of closed-loop system and its robustness against disturbances and uncertainties are guaranteed by proving a theorem. Moreover, by converting the system description into a compatible form with the conditions of the Melnikov theorem, an analytical approach is presented to ensure chaos suppression in the controlled system. Finally, the simulation results for different operational conditions of a three-axis stabilized satellite are provided to show the effectiveness of the proposed analyses and syntheses.