Robust Koopman Control Barrier Filters for Safe Actor-Critic Reinforcement Learning

Safe reinforcement learning (RL) for robotic systems requires policies that improve task performance while satisfying state and input constraints during both training and deployment. Control barrier functions (CBFs) provide a principled mechanism for enforcing forward invariance through minimally invasive safety filters, but their use in model-free RL is limited by the need for accurate dynamics and hand-designed barrier certificates. We propose Robust Koopman-CBF SAC, a safety-filtered actor--critic framework that learns a finite-dimensional Koopman predictor from data, constructs affine CBF constraints in the lifted space, and enforces them through a quadratic-program safety layer. To account for finite-dimensional Koopman approximation error, the CBF condition is tightened using a projected residual margin estimated from held-out rollout data. The critic is trained on the executed safe action, while the actor is regularized toward the Koopman-CBF feasible set, reducing dependence on the filter over training. Across safe-control benchmarks, the method achieves zero constraint violations on CartPole stabilization and tracking while matching or exceeding unconstrained SAC returns. On high-dimensional Safety Gymnasium locomotion tasks, the method reduces violations in some settings but also exposes important limitations of first-order velocity barriers and linear EDMD models, motivating high-order and multi-step Koopman-CBF extensions. These results suggest that robust Koopman-CBF filters are a promising bridge between model-free RL and certifiable safety, while clarifying the structural conditions under which such filters remain effective. All code is available at \href{https://github.com/DhruvKushwaha/Koopman-CBF-Soft-Actor-Critic}{Github Repository}.

Lyapunov Constrained Soft Actor-Critic (LC-SAC) using Koopman Operator Theory for Quadrotor Trajectory Tracking

Reinforcement Learning (RL) has achieved remarkable success in solving complex sequential decision-making problems. However, its application to safety-critical physical systems remains constrained by the lack of stability guarantees. Standard RL algorithms prioritize reward maximization, often yielding policies that may induce oscillations or unbounded state divergence. There has significant work in incorporating Lyapunov-based stability guarantees in RL algorithms with key challenges being selecting a candidate Lyapunov function, computational complexity by using excessive function approximators and conservative policies by incorporating stability criterion in the learning process. In this work we propose a novel Lyapunov-constrained Soft Actor-Critic (LC-SAC) algorithm using Koopman operator theory. We propose use of extended dynamic mode decomposition (EDMD) to produce a linear approximation of the system and use this approximation to derive a closed form solution for candidate Lyapunov function. This derived Lyapunov function is incorporated in the SAC algorithm to further provide guarantees for a policy that stabilizes the nonlinear system. The results are evaluated trajectory tracking of a 2D Quadrotor environment based on safe-control-gym. The proposed algorithm shows training convergence and decaying violations for Lyapunov stability criterion compared to baseline vanilla SAC algorithm. GitHub Repository: https://github.com/DhruvKushwaha/LC-SAC-Quadrotor-Trajectory-Tracking