KAN-enhanced deep reinforcement learning for chaos control: Achieving rapid stabilization via minor perturbations

Based on the fact that chaotic systems own dense periodic orbits, chaos control methods represented by the OGY method successfully achieve stabilization with minor control inputs, offering advantages of low energy consumption and non-invasiveness. However, these methods heavily depend on the time required for trajectories to populate chaotic attractors and require prior knowledge of local dynamic information near the target state. These issues hinder their practical applications. In this paper, Kolmogorov–Arnold Networks (KANs) are demonstrated to exhibit significant potential for chaos control via deep reinforcement learning, which is a neural network architecture proposed recently. A new deep reinforcement learning algorithm called parametrized branching dueling Q-network (P-BDQ) is proposed. Then, a new controller is designed based on KANs and P-BDQ. This controller preserves the advantages of the OGY method while reducing the stabilization time through appropriate perturbations applied at each iteration step. Additionally, the data-driven property of deep reinforcement learning avoids the need for explicit modeling of the local system dynamics near a stable state. Numerical simulations demonstrate that this controller performs effectively across multiple chaotic systems.