This article investigates the attitude containment control problem for multiple spacecrafts based on optimized backstepping design strategy. First, the spacecrafts' attitude dynamics are modeled by modified Rodrigues parameters and are rewritten in the strict-feedback form. Then, we incorporate the idea of optimal control into each step of backstepping design procedure. At each step, the optimal virtual/actual control law is obtained via actor–critic reinforcement learning algorithm and approximated by fuzzy logic systems (FLSs). The updating laws of the parameter matrices are designed in a more concise form and the persistent excitation condition is relaxed. According to the Lyapunov stability analysis, the containment error and FLS parameter errors are semiglobally uniformly ultimately bounded. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

中文翻译：

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多航天器优化后退姿态遏制控制


本文研究了基于优化反步设计策略的多航天器姿态遏制控制问题。首先，航天器的姿态动力学通过修正的罗德里格斯参数进行建模，并以严格反馈形式重写。然后，我们将最优控制的思想融入到反步设计过程的每个步骤中。在每一步，最优的虚拟/实际控制律是通过行动者批评家强化学习算法获得的，并通过模糊逻辑系统（FLS）进行近似。参数矩阵的更新规律设计得更加简洁，并且放宽了持续激励条件。根据Lyapunov稳定性分析，包含误差和FLS参数误差是半全局一致最终有界的。最后给出仿真算例说明所提方法的有效性。