# Vibration Control with Reinforcement Learning Based on Multi-Reward Lightweight Networks
## 1 Introduction  
When it comes to active vibration control, we face a high-dimensional, high-frequency, continuous, and complex dynamic problem. In order to cope with this challenge, a variety of traditional methods have been proposed. For example, PID controllers [1, 2, 3, 4] are used to control complex objects, especially those with large time delays, rapid parameter changes, significant uncertainties, and severe nonlinearity. However, the PID controller has poor control quality in these cases, and a large number of parameters need to be designed in advance. Another common method employs the LQR controller [5, 6, 7], which uses a quadratic performance index. However, in practical applications, not every scenario is suitable for such an indicator, and it can only be applied to systems that can be represented by state-space equations. Another method involves the FxLMS controller [8, 9, 10], which not only needs to construct the reference signal, but also needs to identify the auxiliary path. However, studies have shown that although these traditional methods can play a role in control, they all require a lot of design work and manual intervention. In recent years, the use of reinforcement learning (RL) technology to improve the efficiency of vibration controller designs has become a method of great concern. This method uses the reinforcement learning algorithm to automatically obtain the parameters of the controller, which brings new possibilities for vibration control. Compared with traditional methods, the reinforcement learning method is a data-driven approach, which does not require physical information on vibration control, such as the mass matrix, dampingmatrix, and stiffness matrix, thus reducing the required engineering and design investment. In fact, the use of reinforcement learning methods to construct agents to learn vibration control in complex environments has achieved remarkable results [11; 12; 13; 14; 15]. This method has been applied in many fields, such as for suspension vibration control [16; 17], manipulator vibration control [18; 19; 20], magnetorheological damper vibration control [21; 22], and other vibration control applications [23; 24; 25], and has made remarkable progress. In the field of suspension vibration control [16; 17], [PERSON] et al. [16] integrated model-free learning with model-based safety supervision. They used the underlying system dynamics and security-related constraints, used recursive feasibility techniques to construct security sets, and integrated them into the detection system constraints of reinforcement learning. This secure reinforcement learning framework was applied to the active suspension control system. Their experiments show that this secure reinforcement learning system can learn the control strategy safely and has better performance than the standard controller. [PERSON] et al. [17] discussed the set value tracking problem for the suspension system of a medium-speed maglev train, aiming at maintaining a fixed distance between the train and the track. They describe the set point tracking problem as a continuous-state and continuous-action Markov decision process under unknown transition probabilities, and obtain the state feedback controller from the sampled data of the suspension system through a Deterministic Policy Gradient and neural network approximation reinforcement learning algorithm. Their simulation results demonstrate the high performance of this model-free method, especially given that the response speed of their controller is 50 times faster than that of PID and no additional modeling work is required. In the field of robotic arm control [18; 19; 20], [PERSON] et al. [18] proposed an innovative human-computer interaction system and applied it to the cooperative operation control task of a robotic arm. Their human-computer interaction system includes an impedance model controller and a manipulator controller. The model-based reinforcement learning method is applied to the impedance mode for operator adaptation.