Nonlinear State Observer and Control Design for Triangular Tethered Satellite Formation

This article researches the control of triangular tethered satellite formation (TTSF) system and nonlinear state observer (NSO) design when velocity vector is unmeasured. First, the stability around the equilibrium of open-loop system is discussed, which is stable around certain equilibrium pairs. To improve the system performance, linear feedback control is designed using Jacobian matrix of original nonlinear system, which is locally stable around linearized point. Besides, nonlinear control is designed subsequently which owns global stability domain. Then in case of the unmeasured velocity states, NSO is designed which contains a nonlinear function of estimation error to regulate the observation bias. With the designed nonlinear control and NSO, the simulation of the deployment of TTSF is made thereafter. Compared with linear feedback control and general observer with linear regulation, the proposed nonlinear control together with NSO has global stability domain and less chattering, which is promising in practical application.