Adaptive Robust Neural-Network-Based Backstepping Control of Tethered Satellites With Additive Stochastic Noise

This article introduces a new method for mitigating the fluctuations of a two-body tethered satellite system (TSS). Initially, a state-space representation of the TSS is derived from the extended Lagrange method; and, due to the uncertainties, unmodeled dynamics, and external disturbances exist in the TSS modeling, a novel robust adaptive backstepping controller is proposed. The presented approach utilizes the radial basis function (RBF) to estimate online the unmodeled dynamics and the uncertainties of the system and the concept of the bounded in probability to minimize the effect of the stochastic Weiner process on the system angles. Due to the special structure of the TSS, the angles dynamics of the TSS are stabilized separately, which simplifies the design procedure. Through the Lyapunov stability and the Ito concept, the tracking error is assured to be bounded in probability and the error dynamics of the RBF neural network estimated weights are bounded in the Lyapunov sense. The proposed controller is applied to the nonlinear TSS for two cases of nominal and uncertain perturbed systems. Simulation results verify the applicability and effectiveness of the proposed controller in eliminating the tether libration for the nondisturbed system and decreasing the tether libration for the disturbed system.