Abstract In this paper, a robust control method is proposed for rigid spacecraft attitude stabilization under inertia matrix uncertainties and external disturbances. The attitude stabilization problem is firstly reformulated into an optimal control problem, then a state-dependent indirect Chebyshev pseudospectral (SDICP) method is designed to solve the resultant optimal control problem. It is proved that, by incorporating the uncertainties into the performance index and adaptively estimating the parameters, the stabilization problem can be converted into an infinite horizon optimal control problem. Based on successive state-dependent coefficient parameterization, time domain transformation and Chebyshev spectral discretization, the proposed SDICP method turns the resultant optimal control problem into a sequence of systems of linear equations, which can be efficiently solved by basic matrix operations. Simulation results also verify the effectiveness of the proposed robust adaptive attitude stabilization method.

中文翻译：

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刚性航天器鲁棒自适应姿态稳定使用状态相关的间接切比雪夫伪谱方法

摘要 本文提出了一种在惯性矩阵不确定性和外部扰动下用于刚性航天器姿态稳定的鲁棒控制方法。首先将姿态稳定问题重新表述为最优控制问题，然后设计一种状态相关的间接切比雪夫伪谱（SDICP）方法来解决由此产生的最优控制问题。证明通过将不确定性纳入性能指标并自适应估计参数，可以将镇定问题转化为无限期最优控制问题。基于连续状态相关系数参数化、时域变换和切比雪夫谱离散化，提出的 SDICP 方法将由此产生的最优控制问题转化为一系列线性方程组，这可以通过基本的矩阵运算有效地解决。仿真结果也验证了所提出的鲁棒自适应姿态稳定方法的有效性。