Lyapunov-aware Quantum-Inspired Reinforcement Learning Enables Stable Continuous-Time Vehicle Control

Controlling vehicles safely and efficiently represents a significant challenge for autonomous systems, and researchers are increasingly exploring reinforcement learning as a potential solution. Nutkritta Kraipatthanapong, Natthaphat Thathong, and Pannita Suksawas, all from Thammasat University, alongside their colleagues, now demonstrate a new approach that combines reinforcement learning with established principles of stability analysis. Their work introduces a Lyapunov-based reinforcement learning framework which integrates policy optimisation with Lyapunov stability constraints, ensuring the vehicle maintains safe and predictable behaviour even in dynamic environments. This research represents a crucial step towards developing provably safe control systems for autonomous vehicles and opens new avenues for combining classical control theory with the power of modern machine learning techniques.

Reproducibility, Stability, and Reinforcement Learning Integration

This research paper presents a comprehensive investigation into combining reinforcement learning with Lyapunov stability analysis, offering a strong foundation for future work. The study thoroughly explores the theoretical framework and provides a detailed practical implementation, demonstrating a commitment to rigorous research and reproducibility, providing all necessary code, configurations, and trained weights. The paper offers a detailed analysis of the results, discussing both strengths and limitations, and includes comprehensive appendices with supplementary information. To further strengthen the work, scientists could expand on the benefits of using a variational quantum circuit, explaining why it offers advantages over classical neural networks for this specific problem, and provide a more detailed comparison to a baseline DRL algorithm, including specific hyperparameters.

Lyapunov Quantum Reinforcement Learning for Safe Control

The research team developed a novel Lyapunov-Based Quantum Reinforcement Learning (LQRL) framework to achieve safe and stable control of autonomous vehicles, specifically addressing longitudinal cruise control scenarios. This work pioneers the integration of Lyapunov stability analysis directly into the quantum policy gradient learning process, ensuring asymptotic safety and convergence, a significant advancement over existing reinforcement learning methods. The system employs a continuous-time adaptive cruise control model, simulating vehicle states including spacing error, relative velocity, and ego velocity, all evolving within a dynamically changing environment. To accurately model vehicle dynamics, scientists formulated a continuous-time system described by differential equations governing changes in spacing, relative velocity, and ego velocity, implemented as an Euler-integrated environment with a time step of 0.

05 seconds. The core of the LQRL framework centers on a quadratic Lyapunov candidate function, defined as a combination of squared spacing error, relative velocity, and ego velocity, weighted by positive coefficients to assess system stability. Researchers then derived the time derivative of this Lyapunov function and established a stability condition requiring its rate of change to be less than or equal to a negative constant, ensuring convergence towards a stable equilibrium. To enforce this stability condition during training, the team introduced a Lyapunov penalty term, effectively penalizing trajectories that violate the stability constraint.

The reinforcement learning reward function was carefully designed to balance multiple objectives, including minimizing spacing error, acceleration magnitude, and jerk, promoting both safety and passenger comfort. The policy network, a two-layer variational quantum circuit surrogate, maps vehicle states to control actions using parameterized single-qubit rotation gates, enabling efficient exploration of the control space and facilitating the learning process. This innovative combination of Lyapunov stability analysis and quantum-inspired reinforcement learning represents a significant step towards provably safe control in autonomous systems and hybrid quantum-classical optimization domains.

Lyapunov Stability Guarantees Quantum Vehicle Control

Scientists have developed a novel Lyapunov-Based Quantum Reinforcement Learning (LQRL) framework that integrates policy optimization with Lyapunov stability analysis for continuous-time vehicle control, establishing a new benchmark for quantum-safe reinforcement learning. This work successfully embeds Lyapunov stability verification into quantum policy learning, enabling interpretable and stability-aware control performance in dynamic environments. This breakthrough links Lyapunov control theory with quantum reinforcement learning, providing rigorous stability guarantees for continuous-time learning systems. The LQRL framework constrains the quantum policy gradient to remain within a Lyapunov-decreasing region, ensuring asymptotic convergence toward equilibrium while maintaining safe operation under stochastic quantum perturbations.

Experiments conducted using a longitudinal vehicle cruise control scenario demonstrate the framework’s capabilities, validating its potential for real-world applications. By embedding Lyapunov functions within the quantum policy reward, the controller ensures safe vehicle following distances, bounded accelerations, and energy-efficient driving profiles. Results demonstrate that the LQRL framework achieves asymptotic convergence and safety, establishing a foundational step toward provably safe quantum control in autonomous systems. The theoretical formulation derived provides a rigorous foundation for stability guarantees in quantum learning environments, while the implementation in adaptive cruise control establishes a new benchmark for quantum-safe reinforcement learning in practical physical systems. This research delivers a significant advancement by linking Lyapunov stability theory to quantum policy gradient optimization, offering a pathway to mathematically provable safety guarantees in continuous control tasks.

Lyapunov Stability Guides Quantum Reinforcement Learning

This research presents a novel Lyapunov-Based Quantum Reinforcement Learning (LQRL) framework that successfully integrates quantum policy optimization with stability-constrained control theory. By embedding Lyapunov decrease conditions into the quantum policy gradient, the team enabled learning-based control guided by theoretical stability principles for continuous-time systems. Simulation experiments, conducted using an adaptive cruise control scenario, verified the feasibility of this approach, demonstrating smooth control performance and partial consistency with Lyapunov stability criteria. The LQRL agent maintained bounded control actions and exhibited general stability trends, despite some transient instability observed due to limitations in regularization strength.

Analysis confirmed moderate control effort and finite Lyapunov energy, highlighting the contribution of the hybrid quantum, Lyapunov design to energy-aware learning. While acknowledging this transient behaviour, the results demonstrate a reproducible foundation for integrating Lyapunov stability into quantum-enhanced policy networks. Future work will focus on adaptive regularization techniques, hardware implementation on near-term quantum devices, and extending the framework to multi-agent systems, paving the way for scalable quantum-safe control solutions.