含不确定性的绳系卫星姿态的鲁棒最优控制

针对绳长变化的旋转二体绳系卫星姿态跟踪控制问题，提出了一种分布式鲁棒最优控制方法。首先针对单体绳系卫星姿态模型，在假设模型精确和不存在干扰的条件下，设计基于HamiltonJacobiBellman方程的最优控制器；进一步考虑到实际系统存在参数不确定性和干扰，采用自适应方法和鲁棒误差积分方法隐式学习参数不确定性和有界干扰，与最优控制器结合设计鲁棒最优控制器，并应用Lyapunov稳定性定理证明其闭环系统的渐近稳定性。其次，根据绳系卫星系统的运动同步性，将单体绳系卫星姿态控制器设计扩展至二体绳系卫星系统，设计二体绳系卫星姿态系统的分布式鲁棒最优控制器。最后在Matlab/Simulink平台上进行仿真验证，结果表明了所设计控制器的可行性与有效性。

Nonlinear Robust Optimal Attitude Tracking of Tethered Satellite System with Uncertainties

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.