## 1 Introduction  
Due to the light weight, low stiffness, low fundamental frequency, and small damping of large-span structures in space, flexible solar panels are very vulnerable to suffering from vibrations due to external interference in microgravity environment. However, the vibration control of flexible structures is a difficult problem in the aerospace field. Such structures are large and complex and have constraints in aerospace applications concerning volume, mass, power consumption, and the installation of vibration control devices. Additionally, the special requirements of aerospace structures, particularly in the space environment, make vibration control challenging in theory and engineering [1, 2, 3, 4, 5, 6]. Therefore, exploring new vibration suppression methods for flexible space structures has significance and practical value. Currently, there exists passive, active, and semi-active control for solar panel vibrations. Passive suppression does not consume satellite energy and is easy to achieve. Herein, the vibration is isolated by energy consumption. By redesigning the material and structure, the stiffness and structural damping of flexible structures are regulated, and then the excitation effect on them is reduced [7, 8, 9, 10]. The damper on the Hubble Space Telescope can be regarded as a representative use of the passive vibration reduction of solar array [8]. A titanium alloy viscoelastic damper is installed between the solar array and its driving shaft. The shear deformation of the damping layer is adopted to dissipate the vibration energy and then to suppress the low-frequency vibration of solar panels. [PERSON] et al. [9] proposed a passive eddy current tuned mass damper (TMD), which uses non-contact magnetic eddy current buffer for energy dissipation to hinder the low- and ultra-low-frequency solar panel vibrations. Furthermore, [PERSON] et al. [10] proposed a passive control strategy using shunted piezoelectric transducers with the purpose of suppressing vibration. The passive method can achieve a vibration suppression effect to an extent [11; 12]. However, it is challenging to satisfy the vibration control demands of flexible space structures because of its poor adaptability to variable conditions and inflexible control. Especially, low-frequency vibrations (less than 1 Hz) with a large amplitude are difficult to suppress by passive methods [13; 14; 15; 16]. Unlike passive control, active control has the advantages of flexible control and robust adaptability for low-frequency vibration. In recent years, researchers have used smart piezoelectric structures to inhibit the vibration of solar arrays. [PERSON] et al. [17] proposed a neural network controller with a new Kalman filter to suppress the bending and torsional modes of a cantilever plate using piezoelectric actuators. [PERSON] et al. [18] proposed a radial basis function neural network (RBFNN) control algorithm in order to suppress the low-frequency vibration of hinged plates with the use of piezoelectric actuators. [PERSON] et al. [19] proposed a smart embedded piezoelectric stack for a scaled solar array model, aiming to investigate the decentralized vibration control of intelligent structures. [PERSON] et al. [20] proposed an online learning fuzzy control method based on intelligent piezoelectric structures for controlling the vibration of the cantilever. [PERSON] et al. [21] proposed a low-order online data-driven control method combined with piezoelectric macro-fiber composite (MFC) actuators to suppress the vibration of a flexible cantilever beam. [PERSON] et al. [22] proposed a coupling control strategy involving an adaptive sliding mode controller and a piezoelectric positive position feedback controller in order to realize the cooperative control of spacecraft attitude motion and structural elastic vibration, respectively. [PERSON] et al. [23] proposed a method to control the bending and free vibration response of intelligent epoxy composite beams using shape memory alloy (SMA) wire actuators.