Deep Reinforcement Learning for Chaos Control of a Nonlinear Jumping Quarter-Car Model

Vibrations can reduce the controllability of vehicles and can be uncomfortable for passengers. In particular, nonlinear vibrations can lead to larger amplitudes and complex behaviors. Among these vibrations, chaotic vibrations are inherently unpredictable and may lead to instability, which is highly undesirable in practical applications. Although several control methods have been developed to eliminate chaotic vibrations in active suspension systems, they require a priori knowledge about vehicle systems. Thus, designing chaos controllers for practical scenarios can be very challenging. In this study, we propose a method based on machine learning to overcome this limitation. The deep deterministic policy gradient algorithm is used to learn optimal control input to suppress chaotic vibrations. As a typical model of nonlinear motion, we considered a quarter-car model with jumping nonlinearity and trained a reinforcement learning model to suppress chaotic vibrations. The numerical results show that learned policies were able to suppress chaotic vibration and reduce the overall level of vibration. The obtained policies were evaluated across a wide range of forcing frequencies and simulations with stochastic excitation noises. The results demonstrate that chaos control based on deep reinforcement learning was able to reduce vibrations and stabilize chaotic behavior effectively in this application.