Robust adaptive synchronization of the chaotic fractional‐order satellite system subject to uncertainties and unknown inputs

Abstract

This article addresses the robust adaptive synchronization for a three‐dimensional unknown chaotic fractional‐order satellite system. It is considered that the satellite system is under unknown moments of inertia and exogenous disturbance torques. It is assumed that the upper bound of the exogenous disturbance is unknown, which makes the controller design more complex. The control is designed with the aim of synchronization of two satellites with perturbing torques considering unknown parameters. The proposed controller consists of three parts: (1) a linear term of the synchronization error, (2) the nonlinear part of the synchronization error, and (3) online estimations of the unknown parameters and disturbance, which are established by fractional‐order adaptation laws. The proposed robust adaptive control scheme uses Lyapunov theory and fractional concepts to guarantee the asymptotic stability of the closed‐loop system. The proposed controller is robust to unknown parameters and disturbance torques by taking advantage of the adaptive estimation. The computational simulations show the success of the theoretical attainments.