针对存在参数不确定性以及外部有界干扰的直连式三体旋转绳系卫星系统姿态跟踪控制问题,提出了一种分布式鲁棒最优控制方法。该方法首先针对单体绳系卫星姿态模型,在不考虑参数不确定性和干扰的条件下,应用Hamilton-Jacobi-Bellman方程设计了最优控制器;接着,考虑到实际系统存在参数不确定性和干扰,采用自适应与鲁棒误差积分方法在线学习参数不确定性和有界干扰,与最优控制器结合设计了鲁棒最优控制器,使闭环系统满足了性能指标达到最小的要求,并应用Lyapunov稳定性定理证明了其闭环系统的渐近稳定性。进一步考虑到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直连式三体绳系卫星姿态系统,设计了分布式鲁棒最优控制器。最后在MATLAB/Simulink平台上进行了仿真,验证了方法的可行性与有效性,表明其具有潜在的应用前景。
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.
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