Abstract: A decentralized robust optimal attitude control strategy is proposed for spinning tethered satellites with variable length. For a singletethered satellite, a HamiltonJacobiBellman optimization scheme is used along with an adaptive and robust error integral method to learn the dynamics uncertainties and bounded disturbances asymptotically. Specifically, a Lyapunov stability analysis is performed to show that the adaptive and robust integral of error terms asymptotically identifies the unknown dynamics, thus yielding semiglobal asymptotic tracking. In addition, the system converges to a state space system that has a quadratic performance index optimized by an additional control element. Based on exploiting geometric symmetries, the twobody tethered satellites system is reduced into simpler stable dynamics, and a decentralized attitude tracking controller is developed for the system. Numerical simulations have demonstrated the effectiveness of the approach proposed.

Key words: Tethered satellites, Uncertainty, Robust optimal control, Adaptive control