###### Abstract  
High-dimensional high-frequency continuous-vibration control problems often have very complex dynamic behaviors. It is difficult for the conventional control methods to obtain appropriate control laws from such complex systems to suppress the vibration. This paper proposes a new vibration controller by using reinforcement learning (RL) and a finite-impulse-response (FIR) filter. First, a simulator with enough physical fidelity was built for the vibration system. Then, the deep deterministic policy gradient (DDPG) algorithm interacted with the simulator to find a near-optimal control policy to meet the specified goals. Finally, the control policy, represented as a neural network, was run directly on a controller in real-world experiments with high-dimensional and high-frequency dynamics. The simulation results show that the maximum peak values of the power-spectrum-density (PSD) curves at specific frequencies can be reduced by over 63%. The experimental results show that the peak values of the PSD curves at specific frequencies were reduced by more than 47% (maximum over 52%). The numerical and experimental results indicate that the proposed controller can significantly attenuate various vibrations within the range from 50 Hz to 60 Hz. active vibration control; reinforcement learning; deep deterministic policy gradient (DDPG); neural network; finite-impulse-response filter; experiment +
Footnote †: journal: Applied  
In suspension vibration-control problems [16; 17; 18; 19], the controllers are trained to suppress the vibration caused by road profiles, and they are only validated by numerical simulations. Bucak et al. [16] used a stochastic actor-critic reinforcement-learning control algorithm to provide control forces to a nonlinear quarter-car active-suspension model subjected to a sinusoidal road profile. The simulation results showed that the new algorithm stabilized the suspension very quickly. Kim et al. [17] applied the DDPG (deep deterministic policy gradient) algorithm to the vibration-control simulation of a quarter-vehicle active-suspension model. The quarter-vehicle model with a trained agent (controller) was tested at the low-frequency cosine road and step road, which confirmed the effectiveness of the DDPG algorithm. Liu et al. [18] presented an improved DDPG algorithm using empirical samples, and they applied it to a quarter-vehicle semiactive-suspension vibration-control simulation. The simulation results showed that, compared with the passive suspension, the semiactive suspension with the improved DDPG algorithm could better adapt to various road levels and vehicle speeds. Han et al. [19] presented a PPO-based vibration-control strategy for a vehicle semiactive-suspension system, in which the designed reward function realizes the dynamic adjustment according to the road-condition changes. The simulation results showed that the body acceleration was reduced by 46.93% under the continuously changing road. These suspension vibration-control studies mainly considered single-input control problems. In flexible-manipulator control problems [20; 21; 22], the controllers are trained to suppress the transient vibration, as well as to follow the given trajectories. Ouyang et al. [20] applied the actor-critic algorithm for a single-link flexible manipulator in an attempt to suppress the vibration due to its flexibility and lightweight structure. In the experiment, when the single link was given a desired position, the reinforcement-learning control could obtain a satisfactory tracking and vibration-suppression performance. He et al. [21] investigated the actor-critic reinforcement-learning control of a flexible two-link manipulator by a numerical and experimental study. In the simulation and experiment, when the links were given desired trajectories, the reinforcement-learning control had feasibility and stability in suppressing the vibration. Long et al.