Nonlinear optimal attitude tracking control of uncertain three-inline tethered satellite systems

An optimal robust decentralized attitude tracking control strategy is proposed for a three-inline spinning tethered satellite system with uncertainty in the dynamics. For a single-tethered satellite, a Hamilton-Jacobi-Bellman optimization scheme is used along with an adaptive method combined with a robust integral of error method that can learn the dynamic uncertainty and bounded disturbances asymptotically. Specifically, a Lyapunov stability analysis is performed to show that the adaptive and robust integral of error term asymptotically identifies the unknown dynamics, yielding semiglobal asymptotic tracking. In addition, the system converges to a state space system that has a quadratic performance index which is optimized by an additional control element. By exploiting the geometric symmetries, the three-inline tethered satellites system is reduced into a system of simpler stable dynamics, and a decentralized attitude tracking controller is developed for it. Numerical simulation results validate the stability of the three-inline tethered satellite system by implementing a tracking control law derived from the reduced dynamics.