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 引用本文: 陈竑宇, 陈提. 挠性航天器姿态动力学数据驱动辨识与控制. 力学学报, 2024, 56(2): 433-445.
Chen Hongyu, Chen Ti. Data-driven identification and control of flexible spacecraft attitude dynamics. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(2): 433-445.
 Citation: Chen Hongyu, Chen Ti. Data-driven identification and control of flexible spacecraft attitude dynamics. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(2): 433-445.

## DATA-DRIVEN IDENTIFICATION AND CONTROL OF FLEXIBLE SPACECRAFT ATTITUDE DYNAMICS

• 摘要: 挠性航天器的姿态机动与其挠性部件的振动存在强耦合, 这导致系统表现出明显的非线性特征, 其动力学行为的描述与控制是非常具有挑战的问题. 为了处理挠性航天器建模与姿态控制中的非线性问题, 针对挠性航天器的姿态控制问题提出了一种基于Koopman算子理论的数据驱动建模方法, 并基于数据驱动辨识得到的模型设计了最优控制器, 实现对挠性航天器的姿态控制和振动抑制. 首先, 提出了一种基于Koopman算子理论和非线性系统稀疏性辨识算法(SINDY)的SO(3)上挠性航天器姿态动力学数据驱动辨识方法, 根据SO(3)上挠性航天器姿态的动力学特点, 设计了一组包含姿态动力学状态的观测函数, 用于提升空间上挠性航天器姿态动力学的广义线性模型稀疏性辨识. 然后, 在小角速度假设下进行全局线性化, 通过去除广义线性模型中的高阶项来得到挠性航天器姿态动力学的有限维Koopman稀疏模型, 并通过仿真验证了广义线性SINDY模型与Koopman线性化模型的预测能力. 最后, 以数据辨识得到的线性化模型为基础, 提出了基于Koopman算子的最优线性二次型调节器(LQR)用于挠性航天器的姿态控制与振动抑制. 通过仿真验证了所提出控制器的效果, 并将所提出的控制器与经典非线性最优控制方法进行对比, 证明了所提出算法的优势.

Abstract: The attitude motion of the flexible spacecraft is strongly coupling with the vibration of the flexible components, which will result in complicated nonlinear system characteristics. Because of the nonlinearity of the flexible spacecraft, the dynamics modeling and the control of its attitude motion are challenging problems. This paper aims to present a data-driven modeling method based on the Koopman operator theory for the flexible spacecraft, and design the LQR optimal controller based on the model obtained by data-driven identification for the attitude motion and flexible vibration suppression. Firstly, based on Koopman operator theory and sparse identification for nonlinear dynamics algorithm (SINDY), a data-driven identification method for the attitude dynamics of flexible spacecraft on SO(3) is proposed. According to the dynamics characteristics of the flexible spacecraft attitude dynamics on SO(3), a set of observables containing the original states of attitude dynamics is designed to identify the generalized linear model of the flexible spacecraft attitude dynamics on lifting space spanned by those observables. Secondly, the global linearization is carried out based on the Koopman operator theory. Under the assumption of small angular velocity, by removing the high-order terms in the generalized linear model, the finite-dimensional Koopman sparse model is obtained. The predict ability of such a linear model obtain by SINDY and Koopman linearized model is verified by simulation. Finally, on the basis of the Koopman linearization model identified from the data, an optimal linear quadratic regulator (LQR) controller based on Koopman operator is proposed for attitude motion control and vibration suppression of the flexible spacecraft. The effectiveness of the proposed controller is verified by simulation, and the proposed controller is compared with the classical nonlinear optimal control method to show its advantages.

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