Stable and interpretable DDPG controllers: Integrating Control Lyapunov Functions and symbolic regression via...

This paper presents a stability-constrained deep reinforcement learning framework for nonlinear control systems by integrating Control Lyapunov Functions (CLFs) with the Deep Deterministic Policy Gradient (DDPG) algorithm. The proposed Stability-Constrained DDPG (SDDPG) ensures safety by filtering unstable actions in real time. When RL actions violate constraints, a backup controller enforces stability. Furthermore, we repurpose the backup controller's trajectories as expert demonstrations to boost training efficiency. We extract symbolic policies from trained networks via Kolmogorov-Arnold Networks (KANs), enabling formal verification through eigenvalue analysis and the Hartman-Grobman theorem. Validated on a cart-pole system, SDDPG demonstrates superior stability, convergence, and robustness to parameter variations compared to vanilla DDPG, CLF-QP, and LQR baselines. This framework advances safe, interpretable RL for safety-critical applications.