This study presents a reinforcement learning-based approach for the adaptive control of chaotic systems, where a Deep Q-Network (DQN) is employed to adjust the parameters of a nonlinear backstepping controller in order to maximize a predefined reward function. The proposed method is applied to a fractional-order chaotic system previously introduced as an integer order chaotic system in the literature. A comprehensive dynamical analysis of the system is conducted for different fractional orders, including phase portraits, bifurcation diagrams, and Lyapunov exponents. A nonlinear backstepping controller is then designed for the secondary system to achieve primary–secondary synchronization. The main novelty of this study lies in the integration of a DQN-assisted backstepping controller to perform synchronization across various fractional orders, specifically 0.999, 0.99, and 0.95. The results demonstrate that DQN-based backstepping controller successfully achieves synchronization despite the challenges posed by different fractional-order chaotic dynamics and produces better performance compared to the conventional backstepping controller. Furthermore, the chattering amplitude inherent to the conventional control law is significantly reduced. The evolution of the controller parameters, reward values, cumulative rewards, and loss values during training are presented and discussed in detail. Future studies will extend this approach to other reinforcement learning algorithms and nonlinear adaptive control systems.
Murat Erhan Çimen (Tue,) studied this question.